If $\mathrm{P}\left( x \right)=2{{x}^{3}}+5{{x}^{2}}-3x+1$ and \(\mathrm{Q}\left( x \right)=2

Question

If $\mathrm{P}\left( x \right)=2{{x}^{3}}+5{{x}^{2}}-3x+1$ and $\mathrm{Q}\left( x \right)=2x-4$, find $\mathrm{P}\left( x \right)\times \mathrm{Q}\left( x \right)$, $\mathrm{P}\left( 3 \right)\times \mathrm{Q}\left( 3 \right)$. Determine 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) $4x^4 + 2x^3 - 26x^2 + 14x - 4$ (ii) $182$; the degree of $\mathrm P(x) \times \mathrm Q(x)$ is the sum of 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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