Question

Please help :)
Factor the trinomial.
x2 - 13x + 40

Answer 1

What two numbers multiply to 40?

Answer 2

20 times 2 or?

Answer 3

20*2 = 40 is correct

but notice how the factors 20 and 2 add to 20+2 = 22

Answer 4

we want the factors of 40 to add to -13

Answer 5

40 = 4*10

but

4+10 = 14

see how this works?

Answer 6

you're looking for two numbers that

multiply to 40

AND

add to -13

Answer 7

Yes :)I

Answer 8

which two numbers do that

Answer 9

1*40
2*20
4*10
5*8

1+40 = 41
1-40 = -39
2+20 = 22
2-20 = -18
4+10 = 14
4-10 = -6
5+8 = 13
5-8 = 3

Did we get a 13 in there? All you have to do is hunt for it. No need for guessing.

Answer 10

I don't get it

Answer 11

notice how 8*5 = 40

and 8+5 = 13

Answer 12

at the same time

-8 * (-5) = 40

and

-8 + (-5) = -13

Answer 13

the fact that -8 * (-5) = 40 and -8 + (-5) = -13

means x^2 - 13x + 40 factors to (x-8)(x-5)

Answer 14

notice how the -8 and -5 are in (x-8)(x-5)

Answer 15

That was every conceivable factorization of 40. That's all.