Question

Express q(x)=12x^5+40x^4-32x^3 in the form described in the Linear Factorization Theorem. List each zero and its multiplicity.

Answer 1

Polynomial is an expression that consists of indeterminates(variable) and coefficients. The multiplicity of 0 is 3, 2/3 is 1 and -4 is 1.

What are polynomials?

Polynomial is an expression that consists of indeterminates(variable) and coefficients, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

Given polynomial equation q(x)=12x⁵+40x⁴-32x³, therefore, the factorised form of the equation will be,

$q(x)=12x^5+40x^4-32x^3\\\\q(x)=4x^3(3x^2+10x-8)\\\\q(x)=(4x^3-0)(3x^2+12x-2x-8)\\\\q(x)=(4x^3-0)[3x(x+4)-2(x+4)]\\\\q(x) = (4x^3-0)(3x-2)(x+4)$

Therefore, the multiplicity of 0 is 3, 2/3 is 1 and -4 is 1.

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