Directions: Factor completely. Show your work to receive full credit. (4.5 points each)

6x^2+42x

x^2-7x-30

x^2+9x+20

x^2-14x+48

2x^2+21x-11

5a^2-125

See below in bold.

Step-by-step explanation:

6x^2+42x    The greatest common factor is 6x so we have:

6x(x + 7).

x^2 - 7x - 30

Note that:  + 3 * -10 = -30 and + 3 - 10 = -7 so the factors are:

(x - 10)(x + 3).

x^2 + 9x + 20

Note that + 5 * +4 = +20 and +4 + 5 = + 9;

= (x + 5)(x + 4).

x^2 - 14x + 48

Note that -6 * -8 = 48  and -6 - 8 = -14 so:

= (x - 6)(x - 8).

2x^2 + 21x - 11

When the leading coefficient is greater than 1 we can use

the ac method:

2 * -11 = -22

Now  we need 2 numbers whose sum is + 21 and whose product is -22.

They are +22 and -1. So we write:

2x^2 + 21x - 11

= 2x^2 + 22x - 1x - 11     Factor this by grouping:

=  2x(x + 11) - 1(x + 11)

The x + 11 is common so the answer is:

(2x - 1)(x + 11).

5a^2 - 125       The GCF is 5 so we have:

5(a^2 - 25)    Now we have the difference of 2 squares in the parentheses so

this is  5(a - 5)(a + 5).

4

step-by-step explanation:

b. 2 and 4

step-by-step explanation: