Question

If the HCF of the polynomials f(x) = (x+3) (2x2

-3x+a)

and g(x) = (x-2) (3x2+10x-b) is (x+3) (x-2), then the values

of a and b are respectively​

Answer 1

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Answer 2

Concept

HCF is the largest positive integer that can divides each of the integers. Full form of HCF is highest common factor.

Given

Polynomials f(x)=(x+3)($2x^{2} -3x+a)$ and g(x)=(x-2)($3x^{2} +10x-b)$ and HCF of both the polynomials  is (x+3)(x-2)

To find

The values of a and b.

Explanation

We know that HCF divides both the numbers fully means the value of remainder must be 0.

HCF=(x+3)(x-2)

f(x)/HCF=$(2x^{2} -3x+a)/(x-2)$

Dividing  we get :

$2x^{2} -3x+a$=(x-2)*(2x+1)(a+2)

means a+2 is remainder so when we put a+2=0, we will get a=-2

g(x)/HCF=$(3x^{2} +10x-b)/(x+3)$

Dividing we get:

$3x^{2} +10x-b$=(x+3)*(3x+1)+(-b-3)

means (-b-3) is the remainder so when we put -b-3=0, we will get b=-3.

Hence the value of a=-2 and b=-3 if HCF of f(x)=(x+3)($(2x^{2} -3x+a)$ and g(x)=(x-2)($(3x^{2} +10x-b)$ is (x+3)(x-2).

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