Division of f(x) by x²−x−6 leaves remainder 3x−2. Find f(3).

01 / Standard#Your turn

Official paper · jm01-2023 · I.2 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Write the division identity.

Hint 2

The divisor vanishes at x=3.

Worked solution

D: 7.

Checks and common pitfalls: The remainder is evaluated at 3; it is not itself f(3).

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Introduce the polynomial quotient q.
$f(x)=(x^2-x-6)q(x)+3x-2$
Substitute the root of the divisor.
$f(3)=0q(3)+9-2=7$

Think first. Reveal a hint when the class is ready.

2023 JM01