Question

find the remainder when y^3+4y^2-3y+10 is divided by y+4

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Answer 1

Remainder is 22.

Given:

1. ${y}^{3} + 4 {y}^{2} - 3y +1 0$ and
2. $y + 4$

To find:

• Find the remainder.

Solution:

Theorem to be used:

Remainder Theorem: If polynomial p(x) is divided by (x-a) then remainder is given by p(a).

Step 1:

Find the value of y.

$y + 4 = 0$

or

$\bf y = - 4$

Step 2:

Put the value of y in polynomial.

Let

$p(y) = {y}^{3} + 4 {y}^{2} - 3y +1 0$

put y= -4

$p( - 4) = {( - 4)}^{3} + 4 {( - 4)}^{2} - 3( - 4) +10$

or

$p( - 4) = - 64 + 64 + 12 +10$

or

$p( - 4) = 12 + 10$

or

$\bf \red{p( - 4) = 22 }$

Thus,

Remainder is 22.

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