The graph of $y={{x}^{3}}-4{{x}^{2}}+8x+c$ is shown. State the value of $c$. Explain if \({

Question

The graph of $y={{x}^{3}}-4{{x}^{2}}+8x+c$ is shown. State the value of $c$. Explain if ${{x}^{3}}-4{{x}^{2}}+8x+c$ can be expressed as a product of three linear factors. Find the linear factor of ${{x}^{3}}-4{{x}^{2}}+8x+c$ and hence find the value of $x$-intercept of the curve. Find the coordinates of the intersection points of the curve $y={{x}^{3}}-4{{x}^{2}}+8x+c$ and the line $y=7x-21$.

Accepted Answer

(a) $c=-15$ (b) No, it has only one real linear factor (c) Factor $x-3$, intercept $3$ (d) $(-1,-28)$, $(2,-7)$, $(3,0)$

Polynomials, Cubic Equations and Partial Fractions - Cubic Expressions and Equations

Polynomials, Cubic Equations and Partial Fractions - Cubic Expressions and Equations

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