Question

Use the factor theorem to determine 2x^3+3x^2-5x-6 of the polynomials is divisible by(x+1)

Answer 1

The quotient of the polynomials $2x^{3} +3x^{2} -5x-6$ divided by (x+1) is $2x^{2} -x-6$.

Given two polynomials $2x^{3}+3x^{2} -5x-6$ and (x+1).

We have to determine whether $2x^{3}+3x^{2} -5x-6$ is divisible by (x+1).

Factors are the numbers which are multiplied to get the number whose factors are given. The factor theorem is a theorem which links factors and zeroes of a polynomial.

Polynomial is an expression of more than two algebraic terms may be in addition or subtraction.

We have to first find the factors of polynomial $2x^{3}+3x^{2} -5x-6$.

$2x^{3}+3x^{2} -5x-6$=$2x^{3}+3x^{2} -4x-x-6$

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

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

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

=[$x^{2}$-2x+x-2](2x+3)

=[x(x-2)+1(x-2)](2x+3)

=(x+1)(x-2)(2x+3)

Because (x+1) is a factor of $2x^{3}+3x^{2} -4x-x-6$,so it is divisible by (x+1).

Hence using factor theorem we can say that $2x^{3}+3x^{2} -4x-x-6$is divisible by (x+1).

Learn more about factorisation at  brainly.com/question/25829061

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