Real Zeros of Polynomials

Question

Given the function , and knowing one factor is , write  as a product of linear factors without fractions.

f(x) =

Answer 1

Because (x+9) is a factor of f(x), you can divide it into f(x)--use polynomial long division--to get the quotient =5x²+32x-21 without fractional remainder. Then factor this quotient to (5x-3)(x+7). Thus, the linear factors are (x+9), (5x-3), and (x+7). Check it by multiplying these three factors together!