Question

What are the zeros of P(x) = 2x3 − x2 + 2x − 1

Answer 1

• ±i
• 1/2

Explanation:

You want the zeros of P(x) = 2x³ -x² +2x -1.

Factored form

We can factor this expression by grouping:

P(x) = (2x³ -x²) +(2x -1)

P(x) = x²(2x -1) +1(2x -1) = (x² +1)(2x -1)

Zeros

The zeros are the values of x that make these factors zero:

x² +1 = 0 ⇒ x = ±√-1 = ±i

2x -1 = 0 ⇒ x = 1/2

The zeros of P(x) are ±i and 1/2.

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Answer 2

The remainder is 0

Explanation:

Using the remainder theorem,plug in the zeros of the factor into the polynomial.

The zeros of the factor—›x-1=0,x=1

Plugging 1 into the polynomial

P(1)=2(1)³+(1)²-2(1)-1=0

hope this helps :)