Question

Use the factorization theorem to determine whether x-\frac{1}{2} is a factor of f(x) = 2x^{4}-x^{3}=2x-1.

Polynomial factorization
ANSWERED
asked 2021-05-30
Use the factorization theorem to determine whether \(x-\frac{1}{2}\) is a factor of \(f(x) = 2x^{4}-x^{3}=2x-1\).

Answers (1)

2021-05-31

Step 1
If \(x-\frac{1}{2}\) is a factor the the remainder when f(x) divided by it will be zero.
Put \(x-\frac{1}{2}=0\)
\(x=\frac{1}{2}\)
Step 2
Substitute \(x=\frac{1}{2}\) in f(x).
\(f(\frac{1}{2})=2(\frac{1}{2})^{4}-(\frac{1}{2})^{3}+2(\frac{1}{2})-1\)
\(=\frac{1}{8}-\frac{1}{8}+1-1\)
\(=0+0\)
\(=0\)
Thus the remainder is zero.
\(x-\frac{1}{2}\) is a factor of f(x)

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