EasyMathematicsHigh School (9–10)GeneralAlgebra › Polynomials Algebra › Algebraic Identities and FactorisationNumerical

Use the factor theorem to decide each one.

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

Is $x + 2$ a factor of $x^3 + 2x^2 + x + 2$ ?

Is $x - 1$ a factor of $x^4 + x^3 - x + 2$ ?

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.

← All Problems

← When x³ + kx² - 3x + 2 is divided by x - 2, the remainder is 24. Find k.Find the value of k for which x - 2 is a factor of kx² - 5x + 2. →

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Use the factor theorem to decide each one.

The worked solution

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