Use the factorization theorem to determine whether x−12 is a factor of f(x)=2x4−x3+2x−1.

Step 1 If x−12 is a factor then the remainder when f(x) divided by it will be zero. Put x−12=0 x=12 Step 2 Substitute x=12∈f(x). f(12)=2(12)4−(12)3+2(12)−1 =18−18+1−1 =0+0 =0 Thus the remainder is zero. x−12 is a factor of f(x).

Question: "Use the factorization theorem to determine whether x−12..."

Secondary
Algebra
Algebra II
Polynomial factorization

Falak Kinney

Answered question

2021-02-24

Use the factorization theorem to determine whether

x - \frac{1}{2}

is a factor
of

f (x) = 2 x^{4} - x^{3} + 2 x - 1

Answer & Explanation

pierretteA

Skilled2021-02-25Added 102 answers

Step 1
If

x - \frac{1}{2}

is a factor then 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).

Jeffrey Jordon

Expert2021-11-14Added 2575 answers

Answer is given below (on video)

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