Question

The remainder when the polynomial p(x)= x³ 3x² + 2x - 1 is divided by x-2 is​

Answer 1

Answer:

Step-by-step explanation:

assuming the polynomial is x^3+3x^2+2x-1

so p(2)= 2^3+3(2^2)+2(2)-1

=8+12+4-1

=23

Answer 2

To Find :- The remainder when the polynomial p(x) = x³ + 3x² + 2x - 1 is divided by x - 2 is ?

Concept used :- According to remainder theorem, If p(x) is divided by the linear polynomial (x - a), then the remainder is p(a) .

Solution :-

putting x - 2 equals to zero we get,

→ x - 2 = 0

→ x = 2 .

So,

→ p(x) = x³ + 3x² + 2x - 1

then,

→ p(2) = (2)³ + 3(2)² + 2×2 - 1

→ p(2) = 8 + 3 × 4 + 4 - 1

→ p(2) = 8 + 12 + 4 - 1

→ p(2) = 24 - 1

→ p(2) = 23 (Ans.)

Hence, The remainder when the polynomial p(x) = x³ + 3x² + 2x - 1 is divided by x - 2 is equal to 23 .

Extra :- If p(x) is equal to x³ - 3x² + 2x - 1 , then remainder will be :-

→ p(x) = x³ - 3x² + 2x - 1

→ p(2) = (2)³ - 3(2)² + 2×2 - 1

→ p(2) = 8 - 3 × 4 + 4 - 1

→ p(2) = 8 - 12 + 4 - 1

→ p(2) = 8 + 4 - 12 - 1

→ p(2) = 12 - 13

→ p(2) = (-1) (Ans.)

Learn more :-

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