# Determine if x - c is A Factor...1

Discussion in 'Algebra' started by nycmathguy, Jul 18, 2022.

1. ### nycmathguy

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College Algebra
Chapter 1/Section 6

Use synthetic division to determine if x - c is a factor of the given polynomial. nycmathguy, Jul 18, 2022

2. ### MathLover1

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If we divide a polynomial f(x) by (x - c), and (x - c) is a factor of the polynomial f(x), then the remainder of that division is simply equal to 0. Thus, according to this theorem, if the remainder of a division like those described above equals zero, (x - c) must be a factor.

MathLover1, Jul 26, 2022
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3. ### nycmathguy

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The remainder here is not zero. This means my work is wrong.

nycmathguy, Jul 26, 2022
4. ### MathLover1

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-4 x^3 + 5 x^2 + 8 = (-4 x^2 + 17 x - 51)(x + 3) + 161

so, the remainder of that division is 161, which means (x + 3) is not a factor

MathLover1, Jul 26, 2022
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