Question

If the polynomial f(x) = ax³ + bx – c is divisible by the polynomial g(x) = x² + bx + c, then ab =
A. 1
B. 1/c
C. –1
D. -1/c

Answer 1

Given : polynomial f(x) = ax³ + bx – c is divisible by the polynomial g(x) = x² + bx + c

Concept : If f(x) is divisible by g(x), then remainder will be zero. So, to find the values, find the remainder and put it equal to zero to get the values .

Solution :

We have , f(x) = ax³ + bx + c and g(x) = x² + bx + c  

DIVISION PROCESS IS IN THE ATTACHMENT .

We get remainder r(x) = bx - acx + ab²x + abc - c

bx - acx + ab²x + abc - c

= x( b - ac + ab²) + c ( ab - 1)  

since f(x) is exactly divisible by g(x) , therefore remainder should be zero.

So put   x( b - ac + ab²) + c ( ab - 1) = 0

c ( ab - 1) = 0

ab - 1 = 0  , c ≠ 0

ab = 1

Hence, the value of ab is 1 .

The correct option is (a) : 1.

HOPE THIS ANSWER WILL HELP YOU……

 

Some more questions :  

If the polynomial $f(x)=ax^{3}+bx-c$ is divisible by the polynomial $g(x)=x^{2}+bx+c$,then c=

(a) b

(b) 2b

(c) $2b^{2}$

(d) -2b

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Apply division algorithm to find the quotient q(x) and remainder r(x) in dividing f(x) by g(x) in each of the following:

$f(x)= 15x^{3} -20x^{2} + 13x-12,g(x)=2-2x+x^{2}$

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Answer 2

Step-by-step explanation:

If the polynomial f(x) = ax³ + bx – c is divisible by the polynomial g(x) = x² + bx + c, then ab =

A. 1✓✓

B. 1/c

C. –1

D. -1/c