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Byju's Answer

Standard VII

Mathematics

Zero Exponent

Let fx=x 13...

Question

Let $f (x) = x^{135} + x^{125} - x^{115} + x^{5} + 1$ . If $f (x)$ divided by $x^{3} - x$ , then the remainder is some function of $x$ say $g (x)$ . Then $g (x)$ is an:-

one-one function

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many one function

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into function

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onto function

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Solution

The correct option is A one-one function

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Similar questions

Q. Let

r (x)

be the remainder when the polynomial

x^{135} + x^{125} - x^{115} + x^{5} + 1

is divided by

x^{3} - x

. Then:

Q. Let

r (x)

be the remainder when the polynomial

x^{135} + x^{125} - x^{115} + x^{5} + 1

is divided by

x^{3} - x

. Then

Q. Let

f (x)

be a polynomial function. If

f (x)

is divided by

x - 1, x + 1

and

x + 2

, then remainders are

5, 3

and

2

respectively. When

f (x)

is divided by

x^{3} + 2 x^{2} - x - 2

, then 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)

is divided by

x + 1

, to get remainder

R_{1}

and

g (x)

is divided by

x + 2

, to obtain remainder

R_{2}

. Find

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

Q. Apply the division algorithm to find the quotient and remainder on dividing f(x) by g(x) as given below:
(i)

f (x) = x^{3} - 6 x^{2} + 11 x - 6, g (x) = x + 2

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Let f(x)=x135+x125−x115+x5+1. If f(x) divided by x3−x, then the remainder is some function of x say g(x). Then g(x) is an:-

The correct option is A one-one function

Let $f (x) = x^{135} + x^{125} - x^{115} + x^{5} + 1$ . If $f (x)$ divided by $x^{3} - x$ , then the remainder is some function of $x$ say $g (x)$ . Then $g (x)$ is an:-