Question

factor x2-7x+10

Answer 1

This is a trinomial (as it has 3 terms). Notice that the coefficient of x^2 is just 1. When this is the case, the binomial factors look like (x+a)(x+b).

What are " a " and " b "? Look at the constant term in x^2-7x+10: it's 10. What are possible factors of 10?

1*10
2*5
(-1)(-10)
(-2)(-5)
The trick here is to find the 2 factors that sum up to -7x, the middle term.

Which set of factors of 10 satisfy that criteria?

Answer 2

-5 -2

Answer 3

but the first minus sign in the original equations says that the signs will be different

Answer 4

Actually, HiHo, that - sign tells us that both factors will have the same sign, and that that sign will be -. This is true ONLY if the 3rd (constant) term is +.

So: What do you think the 2 factors are?

Answer 5

x^2-7x+10 = (x - ?)(x - ?)