Answer:
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).
