Factoring Trinomials? Algebra 1 help?

Question

Factor each trinomial.
1. 4g^2-10g+6

2. 6p^2-18p-24

3. 12d^2+7d-12

Hint: You need to use the ax^2+bx+c method.

Thanks!

Answer 1

1). 4g² - 10g + 6.

Now solve the equation using factor method.

Look at the product of the first and last coefficients: (4)(6) = 24

We want two factors of 24 whose sum middle coefficient of  -10, and they are -4 and -6.

4g² - 4g -6g + 6.

Take out common terms.

4g(g - 1) - 6(g - 1).

Take out common factors.

(4g - 6)(g - 1).

Answer 2

2). 6p² - 18p - 24

Now solve the equation using factor method.

Look at the product of the first and last coefficients: (6)(-24) = -144

We want two factors of -144 whose sum middle coefficient of  -18, and they are -24 and 6.

6p² + 6p - 24p - 24.

Take out common terms.

6p(p + 1) - 24(p + 1)

Take out common factors.

(6p - 24)(p + 1).

6(p - 4)(p + 1).

Therefore Factoring Trinomials is 6(p - 4)(p + 1).

Answer 3

3). 12d² + 7d - 12

Now solve the equation using factor method.

Look at the product of the first and last coefficients: (12)(-12) = -144

We want two factors of -144 whose sum middle coefficient of  7, and they are 16 and -9.

12d² + 16d - 9d - 12

Take out common term.

4d(3d + 4) - 3(3d + 4)

(4d - 3)(3d + 4).

Therefore factoring trinomials is (4d - 3)(3d + 4).