Functions and graphsAdditional / Further Maths

Using the factor theorem

Test a proposed linear factor by substituting its zero.

  • is a factor of exactly when .
  • For , substitute .
  • If the result is non-zero, the proposed expression is not a factor.

Example 1

Watch the sign

Use the factor theorem to test the stated factor.

is a factor.

Example 2

Use the factor theorem to test the stated factor. Is a factor?

Simplify the numerical terms and collect like terms.
is not a factor because .

Your turn

Question 1

Use the factor theorem to test whether is a factor.

Check answer
Yes: .
Question 2

Use the factor theorem to test whether is a factor.

Check answer
Yes: .
Question 3

Use the factor theorem to test whether is a factor.

Check answer
Yes: .
Question 4

Use the factor theorem to test whether is a factor.

Check answer
No: , which is not zero.
Question 5

Use the factor theorem to test whether is a factor.

Check answer
Yes: .
← All Functions and graphs cardsReport a mistake