Question

By actual division , find the remainder when 2x4-6x3+x2-x+2 is divided by x+2.​

Answer 1

Given:-

• A quartic / biquadritic polynomial is given to us.
• The polynomial is 2x⁴-6x³+x²-x+2.

To Find:-

• The remainder when it is divided by ( x + 2 ).

Answer:-

Given polynomial is 2x⁴ - 6x³ + x² - x + 2 = p(x) [say]

So , when we divide this polynomial by ( x +2) , remainder will be equal to p(-2) .

Now , firstly equate x + 2 with 0 ,

⇒ x + 2 = 0.

⇒ x = 0 - 2 .

⇒ x = (-2) .

Now , substitute this value in the given polynomial ,

⇒ p(x) = 2x⁴ - 6x³ + x² - x + 2 .

⇒ p(-2) = 2 × (-2)⁴ - 6 × (-2)³ + (-2)² -(-2) + 2.

⇒ p(-2) = 2 × 16 - 6 × (-8) + 4 + 2 + 2.

⇒ p(-2) = 32 +48 + 8.

⇒ p(-2) = 88.

Hence the remainder will be 88.