The polynomial has equal remainders on division by x−2 and x+1. Find a.

01 / Standard#Your turn

f(x)=x^3+3x^2+ax+b

Official paper · jm01-2022 · I.3 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use f(2)=f(−1).

Hint 2

The constant b cancels.

Worked solution

E: −6.

Checks and common pitfalls: The root of x+1 is −1, not 1.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Evaluate the two remainders.
$f(2)=20+2a+b,\quad f(-1)=2-a+b$
Solve the resulting linear equation.
$20+2a=2-a\implies a=-6$

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

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