Question

Using complete sentences, explain how to completely factor 2x2 − 8x − 42.

Answer 1

your first task is to factor out the GCF

Answer 2

what's the GCF in this case?

Answer 3

2

Answer 4

factor that out to get what?

Answer 5

x-4- 21?

Answer 6

2(x^2 - 4x - 21) is what you should get

Answer 7

now we must factor x^2 - 4x - 21

how do we do this?

Answer 8

mulyiply?

Answer 9

you need to find two numbers that

a) multiply to -21 (the last term)

AND

b) add to -4 (the middle coefficient)

Answer 10

ok

Answer 11

what two numbers fit both descriptions?

Answer 12

7 and 3?

Answer 13

Look for factors of -21 with opposite signs that add up to -4. $$\huge (x+r)(x+s)$$

Answer 14

close, but notice how 7*3 = positive 21

Answer 15

one of the numbers has to be negative

Answer 16

so -7?

Answer 17

good, -7*3 = -21

Answer 18

2x2 − 8x − 42
2x^2 - 8x - 42
2(x^2-4x-21)
2(x^2-7x+3x-21)
2(x(x-7)+3(x-7))
2(x - 7)(x + 3)

Answer 19

and -7 + 3 = -4

Answer 20

so this means x^2 - 4x - 21 factors to (x-7)(x+3)

Answer 21

this trick only works if the leading x^2 coefficient is 1

Answer 22

so the full factorization is 2(x-7)(x+3)

Answer 23

ok thank you!

Answer 24

you're welcome

Answer 25

Check the result by multiplying the factors.

Answer 26

when the product of a & c is negative always subtract a number from a bigger number to get b.i.e.,
p-q=b