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  • Determine which of the following polynomials has x-2a factor (i) 3x^{2}+6x-24 (ii) 4x^{2}+x-2

Determine which of the following polynomials has x-2a  factor

            (i) 3x^{2}+6x-24

            (ii) 4x^{2}+x-2

Answers (1)

(i) 3x^{2}+6x-24  only

Solution

We know that if (x+a)  is factor of the polynomial f(x), then it always satisfies f(-a)=0

(i) Here polynomial is 3x^{2}+6x-24     

p(x)=3x^{2}+6x-24

According to remainder theorem if x-2  is a factor of p(x) then p(2)=0
\\p(2)=3(2)^{2}+6(2)-24\\ =3(4)+12-24\\ =12-12=0\\ p(2)=0

Hence x-2  is a factor of 3x^{2}+6x-24

(ii) Here p(x)=4x^{2}+x-2

According to remainder theorem if x-2  is a factor of p(x) then p(2)=0
\\p(2)=4(2)^{2}+2-2\\ =16\\ p(2)\neq 0

Hence x-2  is not a factor of 4x^{2}+x-2.

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