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Remainder Theorem

Write the rem...

Question

Write the remainder when the polynomial f(x) = x³ + x² − 3x + 2 is divided by x + 1.

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Solution

When the polynomial f(x), divided by the remainder will be

Thus, the reminder = 5

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Similar questions

Q. The polynomial which when divided by −x² + x − 1 gives a quotient x − 2 and remainder 3, is

(a) x³ − 3x² + 3x − 5
(b) −x³ − 3x² − 3x − 5
(c) −x³ + 3x² − 3x + 5
(d) x³ − 3x² − 3x + 5

Consider an unknown polynomial which when divided by

(x - 3)

(x - 4)

leaves remainders

2

1

respectively. Let

R (x)

be the remainder when this polynomial is divided by

(x - 3) (x - 4)

.

f (x) = \frac{R (x)}{(x^{2} - 3 x + 2)}

Q. When the polynomial

x^{3} + 3 x^{2} + 3 x + 1

x + 1,

the remainder is

Q. Consider two polynomials

f (x) = x^{3} - 2 x^{2} + \frac{1}{2}

g (x) = x^{3} - 3 x + 1

f (x)

x + 1

, to get remainder

R_{1}

g (x)

x + 2

, to obtain remainder

R_{2}

(R_{1}^{2} + R_{2}^{2} - R_{1} R_{2})

.

Q. When the polynomial

x^{2} + 3 x + 1

x + 1

, the remainder is

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