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Byju's Answer

Standard X

Mathematics

Remainder Theorem

p x = x 3+8 x...

Question

p(x) = $x^{3}$ + 8 $x^{2}$ - 7x + 12 and g(x) = x - 1. If p(x) is divided by g(x), it gives q(x) and r(x) as quotient and remainder respectively. If 'a' is the degree of q(x) and b is the degree of r(x), what is the value of (a - b)?

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Solution

Remainder = r(x) = p(1) = $1^{3}$ + 8 $\times$ $1^{2}$ - 7 $\times$ 1 + 12 = 14

So, Degree of r(x) = b = 0

q(x) = $\frac{p (x)}{g (x)}$ = $x^{2}$ + 9x + 2

So, degree of q(x) = a = 2

a - b = 2 - 0 = 2

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Similar questions

$p (x) = x^{3} + 8 x^{2} - 7 x + 12$ and $g (x) = x - 1$ . If $p (x)$ is divided by $g (x)$ , it gives $q (x)$ and $r (x)$ as quotient and remainder respectively. If $a$ is the degree of $q (x)$ and $b$ is the degree of $r (x)$ , $(a - b) = ?$ .

Q. Find the quotient

q (x)

and remainder

r (x)

of the following when

f (x)

is divided by

g (x)

p (x) = x^{6} + x^{4} - x^{2} - 1

;

g (x) = x^{3} - x^{2} + x - 1

Q. Who is correct?
Aakanksha:

q (x) = \frac{p (x) - r (x)}{g (x)}

Arjun:

q (x) = \frac{p (x)}{g (x)} - r (x)

Aman:

q (x) = p (x) - \frac{r (x)}{g (x)}

Anasuya:

q (x) = p (x) + \frac{r (x)}{g (x)}

Given,

p (x)

is the dividend,

g (x)

is the divisor,

q (x)

is the quotient, and

r (x)

is the remainder

Q. Find the value of t, given that

p (x) = x^{3} - t x^{2} + 5 x - 3,

g (x) = x^{2} - 2,

q (x) = x - 3,

r (x) = 7 x - 9

Where,

p (x)

is the dividend,

g (x)

is the divisor,

q (x)

is the quotient, and

r (x)

is the remainder

Say true or false:

For polynomials

p (x)

and any non-zero polynomial

g (x)

, there are polynomials

q (x)

and

r (x)

such that

p (x) = g (x) q (x) + r (x)

, where

r (x) = 0

or degree

r (x) <

degree

g (x) .

This statement is correctly explains the remainder theorem.

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p(x) = x3 + 8x2 - 7x + 12 and g(x) = x - 1. If p(x) is divided by g(x), it gives q(x) and r(x) as quotient and remainder respectively. If 'a' is the degree of q(x) and b is the degree of r(x), what is the value of (a - b)? ___

Remainder = r(x) = p(1) = 13 + 8 × 12 - 7 × 1 + 12 = 14 So, Degree of r(x) = b = 0 q(x) = p(x)g(x) = x2 + 9x + 2 So, degree of q(x) = a = 2 a - b = 2 - 0 = 2

p(x) = $x^{3}$ + 8 $x^{2}$ - 7x + 12 and g(x) = x - 1. If p(x) is divided by g(x), it gives q(x) and r(x) as quotient and remainder respectively. If 'a' is the degree of q(x) and b is the degree of r(x), what is the value of (a - b)?

___

Remainder = r(x) = p(1) = $1^{3}$ + 8 $\times$ $1^{2}$ - 7 $\times$ 1 + 12 = 14

So, Degree of r(x) = b = 0

q(x) = $\frac{p (x)}{g (x)}$ = $x^{2}$ + 9x + 2

So, degree of q(x) = a = 2

a - b = 2 - 0 = 2