MediumMathematicsHigh School (9–10)GeneralAlgebra › PolynomialsNumericalBoard Exam

Find the remainder when x³ - 4x² + 2x + 5 is divided by x + 1, and then when it is divided by x - 3.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Find the remainder when $x^3 - 4x^2 + 2x + 5$ is divided by $x + 1$ , and then when it is divided by $x - 3$ .

Need a reminder? The key ideaShow

Remainder theorem: dividing $p(x)$ by $x - a$ leaves the remainder $p(a)$ . For $ax - b$ , use $p\left(\dfrac{b}{a}\right)$ . Factor theorem: $x - a$ is a factor exactly when $p(a) = 0$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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← The graph of a polynomial meets the x-axis at -3, 0 and 2, and nowhere else…Find the remainder when x⁴ - 2x³ + x - 5 is divided by x - 2. →

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Find the remainder when x³ - 4x² + 2x + 5 is divided by x + 1, and then when it is divided by x - 3.

The worked solution

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