To factor 12x^2 - 8x, you should first look for the greatest common factor (GCF) of the two terms. In this case, the GCF is 4x since 4x divides both 12x^2 and -8x evenly.
So, pulling out the GCF, we get:
4x(3x - 2)
Factor 12x^2-8x with stemps please.
11 answers
Please Factor x^2+5x-36 with steps for me.
To factor the expression x^2 + 5x - 36, we can follow these steps:
Step 1: Find two numbers whose product is equal to the product of the coefficient of x^2 (which is 1) and the constant term (which is -36) and whose sum is equal to the coefficient of x (which is 5).
In this case, we need to find two numbers whose product is -36 and whose sum is 5.
After some calculation, we find that the two numbers are 9 and -4.
Step 2: Split the middle term in the expression using the two numbers found in Step 1.
Replace the middle term 5x with 9x - 4x.
x^2 + 9x - 4x - 36
Step 3: Group the terms and factor them separately.
(x^2 + 9x) - (4x + 36)
Step 4: Factor out the GCF from each group.
x(x + 9) - 4(x + 9)
Step 5: Notice that we now have a common binomial factor (x + 9).
(x - 4)(x + 9)
So, the fully factored form of x^2 + 5x - 36 is (x - 4)(x + 9).
Here is a summary of the steps:
Step 1: Find two numbers with the given conditions.
Step 2: Split the middle term using the two numbers found.
Step 3: Group the terms.
Step 4: Factor out the GCF from each group.
Step 5: Look for a common factor.
By following these steps, you can factor any quadratic expression.
Step 1: Find two numbers whose product is equal to the product of the coefficient of x^2 (which is 1) and the constant term (which is -36) and whose sum is equal to the coefficient of x (which is 5).
In this case, we need to find two numbers whose product is -36 and whose sum is 5.
After some calculation, we find that the two numbers are 9 and -4.
Step 2: Split the middle term in the expression using the two numbers found in Step 1.
Replace the middle term 5x with 9x - 4x.
x^2 + 9x - 4x - 36
Step 3: Group the terms and factor them separately.
(x^2 + 9x) - (4x + 36)
Step 4: Factor out the GCF from each group.
x(x + 9) - 4(x + 9)
Step 5: Notice that we now have a common binomial factor (x + 9).
(x - 4)(x + 9)
So, the fully factored form of x^2 + 5x - 36 is (x - 4)(x + 9).
Here is a summary of the steps:
Step 1: Find two numbers with the given conditions.
Step 2: Split the middle term using the two numbers found.
Step 3: Group the terms.
Step 4: Factor out the GCF from each group.
Step 5: Look for a common factor.
By following these steps, you can factor any quadratic expression.
Please Factor x^2+9 for me with steps included.
To factor the expression x^2 + 9, we first check if it can be factored using real numbers. However, x^2 + 9 cannot be factored using real numbers because it does not have any real roots.
Therefore, the final factored form of x^2 + 9 is simply x^2 + 9, since it cannot be further factored using real numbers.
Here is a summary of the steps:
Step 1: Check if the expression can be factored using real numbers.
Step 2: If it cannot be factored, the factored form is the same as the original expression.
In this case, since x^2 + 9 cannot be factored using real numbers, the expression remains as x^2 + 9.
Therefore, the final factored form of x^2 + 9 is simply x^2 + 9, since it cannot be further factored using real numbers.
Here is a summary of the steps:
Step 1: Check if the expression can be factored using real numbers.
Step 2: If it cannot be factored, the factored form is the same as the original expression.
In this case, since x^2 + 9 cannot be factored using real numbers, the expression remains as x^2 + 9.
Factor 3x^2+10x+8 with steps included, please.
To factor the expression 3x^2 + 10x + 8, we can follow these steps:
Step 1: Multiply the coefficient of x^2 (which is 3) by the constant term (which is 8).
3 * 8 = 24
Step 2: Find two numbers whose product is equal to the result from Step 1 (which is 24) and whose sum is equal to the coefficient of x (which is 10).
After some calculation, we find that the two numbers are 6 and 4, as 6 * 4 = 24 and 6 + 4 = 10.
Step 3: Split the middle term in the expression using the two numbers found in Step 2.
Replace the middle term 10x with 6x + 4x.
3x^2 + 6x + 4x + 8
Step 4: Group the terms and factor them separately.
(3x^2 + 6x) + (4x + 8)
Step 5: Factor out the GCF from each group.
3x(x + 2) + 4(x + 2)
Step 6: Notice that we now have a common binomial factor (x + 2).
(3x + 4)(x + 2)
So, the fully factored form of 3x^2 + 10x + 8 is (3x + 4)(x + 2).
Here is a summary of the steps:
Step 1: Multiply the coefficient of x^2 by the constant term.
Step 2: Find two numbers with the given conditions.
Step 3: Split the middle term using the two numbers found.
Step 4: Group the terms.
Step 5: Factor out the GCF from each group.
Step 6: Look for a common factor.
By following these steps, you can factor any quadratic expression.
Step 1: Multiply the coefficient of x^2 (which is 3) by the constant term (which is 8).
3 * 8 = 24
Step 2: Find two numbers whose product is equal to the result from Step 1 (which is 24) and whose sum is equal to the coefficient of x (which is 10).
After some calculation, we find that the two numbers are 6 and 4, as 6 * 4 = 24 and 6 + 4 = 10.
Step 3: Split the middle term in the expression using the two numbers found in Step 2.
Replace the middle term 10x with 6x + 4x.
3x^2 + 6x + 4x + 8
Step 4: Group the terms and factor them separately.
(3x^2 + 6x) + (4x + 8)
Step 5: Factor out the GCF from each group.
3x(x + 2) + 4(x + 2)
Step 6: Notice that we now have a common binomial factor (x + 2).
(3x + 4)(x + 2)
So, the fully factored form of 3x^2 + 10x + 8 is (3x + 4)(x + 2).
Here is a summary of the steps:
Step 1: Multiply the coefficient of x^2 by the constant term.
Step 2: Find two numbers with the given conditions.
Step 3: Split the middle term using the two numbers found.
Step 4: Group the terms.
Step 5: Factor out the GCF from each group.
Step 6: Look for a common factor.
By following these steps, you can factor any quadratic expression.
Please show me, with steps how you would use the quadratic formula to solve 2x2-10x+3.
To use the quadratic formula to solve the equation 2x^2 - 10x + 3, we can follow these steps:
Step 1: Identify the coefficients of the quadratic equation.
In this case, the coefficient of x^2 is 2, the coefficient of x is -10, and the constant term is 3.
Step 2: Write the quadratic formula.
The quadratic formula is given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
where a, b, and c are the coefficients of the quadratic equation.
For our equation, a = 2, b = -10, and c = 3. Plugging these values into the quadratic formula, we get:
x = (-(-10) ± sqrt((-10)^2 - 4 * 2 * 3)) / (2 * 2)
Simplifying this, we have:
x = (10 ± sqrt(100 - 24)) / 4
x = (10 ± sqrt(76)) / 4
Step 3: Simplify the expression inside the square root.
Since 76 is not a perfect square, we cannot simplify it further.
Step 4: Calculate the square root of 76.
Using a calculator or long division method, we find that the square root of 76 is approximately 8.7178.
Step 5: Substitute this value back into the quadratic formula.
We have:
x = (10 ± 8.7178) / 4
Step 6: Simplify further and solve for x.
Splitting the equation into two cases, with the positive and negative choice of the square root:
Case 1: x = (10 + 8.7178) / 4 ≈ 4.6795
Case 2: x = (10 - 8.7178) / 4 ≈ 0.8205
Therefore, the solutions to the quadratic equation 2x^2 - 10x + 3 are approximately x = 4.6795 and x = 0.8205.
Here is a summary of the steps:
Step 1: Identify the coefficients of the quadratic equation.
Step 2: Write the quadratic formula.
Step 3: Simplify the expression inside the square root, if possible.
Step 4: Calculate the square root.
Step 5: Substitute the calculated value back into the quadratic formula.
Step 6: Simplify further and solve for x.
By following these steps, you can use the quadratic formula to solve any quadratic equation.
Step 1: Identify the coefficients of the quadratic equation.
In this case, the coefficient of x^2 is 2, the coefficient of x is -10, and the constant term is 3.
Step 2: Write the quadratic formula.
The quadratic formula is given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
where a, b, and c are the coefficients of the quadratic equation.
For our equation, a = 2, b = -10, and c = 3. Plugging these values into the quadratic formula, we get:
x = (-(-10) ± sqrt((-10)^2 - 4 * 2 * 3)) / (2 * 2)
Simplifying this, we have:
x = (10 ± sqrt(100 - 24)) / 4
x = (10 ± sqrt(76)) / 4
Step 3: Simplify the expression inside the square root.
Since 76 is not a perfect square, we cannot simplify it further.
Step 4: Calculate the square root of 76.
Using a calculator or long division method, we find that the square root of 76 is approximately 8.7178.
Step 5: Substitute this value back into the quadratic formula.
We have:
x = (10 ± 8.7178) / 4
Step 6: Simplify further and solve for x.
Splitting the equation into two cases, with the positive and negative choice of the square root:
Case 1: x = (10 + 8.7178) / 4 ≈ 4.6795
Case 2: x = (10 - 8.7178) / 4 ≈ 0.8205
Therefore, the solutions to the quadratic equation 2x^2 - 10x + 3 are approximately x = 4.6795 and x = 0.8205.
Here is a summary of the steps:
Step 1: Identify the coefficients of the quadratic equation.
Step 2: Write the quadratic formula.
Step 3: Simplify the expression inside the square root, if possible.
Step 4: Calculate the square root.
Step 5: Substitute the calculated value back into the quadratic formula.
Step 6: Simplify further and solve for x.
By following these steps, you can use the quadratic formula to solve any quadratic equation.
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