Factor the following:

a. ( 2x^2 - 4x- 30.

First we notice that 2 is common factor for all terms.

Then we will factor 2.

==> 2 (x^2 - 2x - 15)

Now we will factor between brackets.

**==> 2( x- 5) ( x+ 3).**

b. (3x^3 - 6x^2 + 5x- 10)

We will factor the first two terms the last two terms.

==> ( 3x^3 - 6x^2) + (5x -10)

We will factor 3x^2 from the first two terms.

==> 3x^2(x - 2) + (5x-10).

Now we will factor 5 from the last two terms.

==> 3x^2(x-2) + 5( x-2).

Now we notice that (x-2) is a common factor.

Then, we will factor (x-2).

**==> (x-2) ( 3x^2 + 5) **

Factor the following:

a. ( 2x^2 - 4x- 30)

b. (3x^3 - 6x^2 + 5x- 10)

a)

2x^2-4x-30 = 2(x^2-2x-15).

We find the factors x^2-2x-15.

x^2-2x-15 = x^2-5x+3x-15 .

= x(x-5)+3(x-5).

= (x-5)(x+3).

Therefore 2x^2-4x-30 = 2(x-5)(x+3).

b)

(3x^3 - 6x^2 + 5x- 10).

= 3x^2 (x-2) +5(x-2).

= (x-2)(3x^2+5).

Therefore (3x^3 - 6x^2 + 5x- 10) = (x-2)(3x^2+5).