To factor the given expressions, I will explain the steps for each one:

1. 2x^2 - 16x + 30:

- First, try to factor out the greatest common factor (GCF) if there is one. In this case, GCF = 2.

- Divide every term by 2: (2x^2)/2 - (16x)/2 + 30/2 = x^2 - 8x + 15.

- Now, factor the quadratic expression x^2 - 8x + 15. You need to find two numbers that multiply to give you 15 and add up to -8.

- The numbers that satisfy this condition are -3 and -5 (since -3 * -5 = 15 and -3 + -5 = -8).

- Thus, x^2 - 8x + 15 can be factored as (x - 3)(x - 5).

- Finally, multiply the GCF (2) with the factored expression to get the final factorization: 2(x - 3)(x - 5).

2. 4x^2 - 9:

- This expression is in the form of a difference of two squares, where 4x^2 can be treated as (2x)^2 and 9 as (3)^2.

- The difference of two squares can be factored as (a^2 - b^2) = (a - b)(a + b).

- Applying this here: 4x^2 - 9 = (2x - 3)(2x + 3).

3. x^2 - 5x:

- Here, you can factor out an x from each term: x(x - 5).

4. 5x^2 - 26x + 5:

- This expression cannot be factored directly by grouping or common factors.

- You can either use trial and error or apply the quadratic formula to find the roots (zeros) of the quadratic equation.

- In this case, factoring doesn't yield simple integer roots, so you might use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).

- Plugging in the values a = 5, b = -26, and c = 5 into the quadratic formula, you can solve for x: x ≈ 1/5 or x ≈ 1.

- Thus, the factorization for 5x^2 - 26x + 5 is (x - 1/5)(x - 1).

5. 25x^2 + 4:

- This expression is a perfect square trinomial with 25x^2 as a perfect square (5x)^2 and 4 as a perfect square (2)^2.

- The perfect square trinomial can be factored as (a + b)^2 = a^2 + 2ab + b^2.

- Applying this here: 25x^2 + 4 = (5x)^2 + 2(5x)(2) + (2)^2 = (5x + 2)^2.

Remember, factoring can sometimes involve trial and error or other methods like the quadratic formula. So, it's important to check your work and practice to become proficient in factoring expressions.

# How do I factor these:

2x2 - 16x + 30

4x^2-9

x^2-5x

5x^2-26x+5

25x^2+4

Example:

2x^2 - 16x + 30 =

2 (x^2 - 8 x + 15)

2(x - 5)(x - 3)

The first, factor out a 2 first. Then factor .

The second...difference of two squares

Third factor out an x

I will be happy to critique your work. You need to do some trial and error.

Explain Bot
answered

1 year ago

1 year ago