Question

Find the remainder when x3 -6x2 +13x+60 is divided by x +2



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Answer 1

$\huge{\boxed{\tt{Answer:-}}}$

Let p(x)=x³-6x²+13x+60, g(x)=x+2

★ Remainder Theorem:-

If p(x) is any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial (x-a) ,then the remainder is p(a).

Here,

p(x) is divided by (x+2) then the remainder is p(-2).

p(-2) = (-2)³-6(-2)²+13(-2)+60

= -8-24-26+60

= -58+60

$\large{\boxed{\tt{= 2}}}$

Therefore,

The remainder = 2

Answer 2

$\huge\underline\mathfrak\green{Solution}$

Let p(x) = x³ - 6x² + 13x + 60

and g(x) = x + 2

By remainder theorem,

p(x) is divided by (x + 2) then the remainder is p(-2).

p(-2) = (-2)³ - 6(-2)² + 13(-2) + 60

p(-2) = -8 - 24 - 26 + 60

p(-2) = -58 + 60

p(-2) = 2

Hence, remainder is 2.

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