# Chapter 3 - Polynomial and Rational Functions - Concept and Vocabulary Check - Page 386: 6

Fill the blanks with $-6$ and $(x+6)(2x^{2}-x-1)=0$

#### Work Step by Step

When dividing a polynomial with (x-c) using synthetic division, the last value of the last row is $f(c)$. We have a polynomial equation $f(x)=0$. from the synthetic division we see that $f(-6)=0$. So, $-6$ is a zero of f, which means it is a root of the equation. Since $-6$ is a zero of f, $(x-(-6))=(x+6)$ is a factor of $f(x)$ The first three values of the last row give coefficients of the quotient $f(x)\div(x+6)$ So we can write $f(x)=(x+6)(2x^{2}-x-1)$, and the equation as $(x+6)(2x^{2}-x-1)=0$

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