Given $\mathrm{P}\left( x \right)=4{{x}^{2}}-6x+3$ and \(\mathrm{Q}\left( x \right)={{x}^{3}}

Question

Given $\mathrm{P}\left( x \right)=4{{x}^{2}}-6x+3$ and $\mathrm{Q}\left( x \right)={{x}^{3}}+2x$, find $\mathrm{P}\left( x \right)\times \mathrm{Q}\left( x \right)$, $\mathrm{P}\left( -1 \right)\times \mathrm{Q}\left( -1 \right)$. Establish the relationship between the degree of $\mathrm{P}\left( x \right)$, $\mathrm{Q}\left( x \right)$, and $\mathrm{P}\left( x \right)\times \mathrm{Q}\left( x \right)$.

Accepted Answer

(i) $4x^5 - 6x^4 + 11x^3 - 12x^2 + 6x$ (ii) $-39$; the degree of $\mathrm P(x) \times \mathrm Q(x)$ is the sum of the degrees of $\mathrm P(x)$ and $\mathrm Q(x)$.

Polynomials, Cubic Equations and Partial Fractions - Polynomial Notation, Degree and Evaluation

Polynomials, Cubic Equations and Partial Fractions - Polynomial Notation, Degree and Evaluation

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