8. Consider the polynomial y = x³ - 5x² - 8x + 12 a) What is the y-intercept of this polynomial? (i.e. when x = 0) b) What are the x-intercepts of this polynomial? (i.e. when y = 0) (You must use polynomial division to solve for the x intercepts to get full marks) c) Sketch the polynomial with x-intercepts & y-intercept labelled. d) Using the sketched curve, solve the inequality x³ - 5x² - 8x + 12 ? 0
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Plugging in \( x = 0 \) gives us \( y = 0^3 - 5 \cdot 0^2 - 8 \cdot 0 + 12 \), which simplifies to \( y = 12 \). Therefore, the \( y \)-intercept is \( (0, 12) \). Show more…
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