Question

Factor the trinomial and enter the factorization below. Write each factor as a polynomial in descending order.

x2 + 16x + 63

Answer 1

x2 + 16x + 63
x2 + 9x + 7x +63
x(x+9) + 7(x+9)
(x+7)(x+9)

Answer 2

\[(x+a)(x+b) = x^2+ax+bx+ab\]\[ = x^2 + (a+b)x + ab\]Compare that with your original equation\[x^2+16x+63\]You can see that to make each term match, we need to find a pair of numbers \(a,b\) such that \[a+b = 16\](for the middle term) and\[a*b = 63\](for the constant term)

9 and 7 is such a pair, so the factorization is \((x+9)(x+7) = x^2+16x+63\)