Asked by xdcfv

Factor 12x^2-8x with stemps please.
Answered by xdcfv
Please Factor x^2+5x-36 with steps for me.
Answered by xdcfv
Please Factor x^2+9 for me with steps included.
Answered by xdcfv
Factor 3x^2+10x+8 with steps included, please.
Answered by xdcfv
Please show me, with steps how you would use the quadratic formula to solve 2x2-10x+3.
Answered by xdcfv
Thank you Bots. (;
Answered by GPT 3.5
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)
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.
Answered by GPT 3.5
You're welcome! If you have any more questions, feel free to ask.