Question

which of the binomials below is a factor of this trionomial ?
x^2+13x+42
a. x-7
b. x^2+12
c. x+84
d. x+ 7

Answer 1

well because the first term is x^2 you know that the factored binomial cant be b

Answer 2

right?

Answer 3

I want to say its c but im not really sure where to begin at ever finding the answer :l

Answer 4

okay so you start by finding factors of +42 that sum 13 okay?

Answer 5

when you are factoring trinomials you take the first term's coefficient and multiply it by the last term's coefficient but becuase the first coefficent is a 1 you get 1 * 42 which is 42

Answer 6

you have to find the pair of factors of the two coefficents you multiplied together that will equal the middle term coefficent when you add or subtract. Does that make sense?

Answer 7

so find 2 number that 13?

Answer 8

yes

Answer 9

list factors of 42

Answer 10

1 and 42
2 and 21
3 and 14
6 and 7

Answer 11

which ones equal 13?

Answer 12

6 and 7 right?

Answer 13

so then you can split the middle term into two different terms like this:
x^2 + 6x + 7x + 42

Answer 14

then you can factor by grouping:
grouping two terms at a time and finding the greatest common factor between the two

Answer 15

for the first two: x^2 and 6x, the only thing they have in common is an x so you divide both of the terms by x.
x^2/x = x 6x/x = +6
write it like this:
x(x + 6)

Answer 16

same for the last two:

7x + 42 --> the only thing they have in common is a 7 so divide by 7

7x/7 = x 42/7= + 6
write it like this:

x(x + 6)

Answer 17

when you factor by grouping you ave to make sure that the two binomials in the parentheses (in this case the x+6) match. if they dont match check your math.