Question

determine the remainder when the polynomial p(x)=x^4-3x^2+2x+1 is divided by (x-1)

Answer 1

Answer:

Step-by-step explanation:

p(x)=x⁴-3x²+2x+1

g(x)=x-1

p(1)=(1)⁴-3*(1)²+2*1+1

    =1-3+2+1

    =-2+3

    =1

HOPE IT HELPS

MARK AS BRAINLIEST

Answer 2

The remainder obtained on dividing p(x) =  $x^{4}$-3x²+2x+1 by (x-1) is 1.

Given:

p(x)=$x^{4}$-3x²+2x+1

To Find:

The remainder obtained on dividing the polynomial p(x) by (x-1).

Solution:

We can solve this problem using the long division method.

Step 1: Since the polynomial is of degree 4, we will re-write it to include all powers of x ≤ 4.

⇒ p(x) = $x^{4}$ +0x³-3x²+2x+1

Step 2: p(x) = (x - 1)(x³) + (x³- 3x² + 2x + 1)

Step 3: p(x) = (x - 1)(x³+x²) + (-2x²+2x+1)

Step 3: p(x) = (x - 1)(x³+x²-2x) +1

We know that

Dividend = Divisor x Quotient + Remainder

Here

Dividend = p(x) = $x^{4}$-3x²+2x+1

Divisor = (x - 1)

Quotient = (x³+x²-2x)

Remainder = 1

∴ The remainder when p(x) =  $x^{4}$-3x²+2x+1 is divided by (x-1) is 1.

#SPJ3