Question

Use remainder theorem to find the remainder when P(x)=x3+5x-7 is divided by
1. x-2 2. x+3 3. 3x+1

Answer 1

Answer:

49

Step-by-step explanation:

P(x)=(7)3+5(7)-7

= 21+35-7

=14+35

=49

Answer 2

Given:

A polynomial P(x)=x3+5x-7.

To find:

Remainder using the remainder theorem when P(x)=x3+5x-7 is divided by x - 1, x + 3 and 3x + 1.

Solution:

The remainder theorem states that when a given polynomial P(x) is divided by x - b, then the remainder can be obtained by finding P(b).

So, we will solve the above parts one by one.

1. x - 2

Using the remainder theorem, we have

x - 2 = 0

x = 2

On putting the value of x = 2 in P(x), we have

${x}^{3} + 5x - 7$

$= {2}^{3} + 5(2) - 7$

$= 8 + 10 - 7$

$= 18 - 7$

$= 11$

Hence by remainder theorem, 11 is the remainder when the given polynomial P(x) is divided by x - 2.

2. x + 3

Using the remainder theorem, we have

x + 3 = 0

x = -3

On putting the value of x = -3 in P(x), we have

${x}^{3} + 5x - 7$

$= {-3}^{3} + 5(-3) - 7$

$= -27 - 15 - 7$

$= -42-7$

$= -49$

Hence by remainder theorem, -49 is the remainder when the given polynomial P(x) is divided by x +3.

3. 3x + 1

Using the remainder theorem, we have

3x + 1 = 0

x = -1/3

On putting the value of x = -1/3 in P(x), we have

${x}^{3} + 5x - 7$

$= {(-1/3)}^{3} + 5(-1/3) - 7$

$= -1/27 -5/3 - 7$

$= -46/27 - 7$

$= -46/27-189/27$

$= -235/27$

Hence by remainder theorem, -235/27 is the remainder when the given polynomial P(x) is divided by 3x + 1.