[SPLIT] How to solve x^2 + 7x + 10 = 0 by factoring

[texasgirl251980]

Okay you guy's I need help to remember how to do this it's been 10 years since I have done this.
x^2 + 7x + 10 = 0 I cant figure out how to get the ten in the equation (x + ?)(x + 7)? ? ?

 

[jwpaine]

Re: Factoring Expressions: x^2 + 4x - 21

Okay you guy's I need help to remember how to do this it's been 10 years since I have done this.
x^2 + 7x + 10 = 0 I cant figure out how to get the ten in the equation (x + ?)(x + 7)? ? ?

\(\displaystyle x^2 + 7x + 10\)

(a)(c) = 10

divisible factors of 10: 1,2,5,10

what two factors of 10 add up to 7?

how about 2 and 5?

re-write the trinomial with b as the sum of 2 and 5

\(\displaystyle x^2 + 5x +2x + 10\)
Group

\(\displaystyle (x^2 + 5x) + (2x + 10)\)

Factor each group

\(\displaystyle x(x + 5) + 2(x + 5)\)

Factor

\(\displaystyle (x + 5)(x + 2)\)

Check by FOILing your two binomial factors (expansion)