Find m so that the polynomial is divisible by 2x+1.

01 / Standard#Your turn

f(x)=-16x^3-mx-m

Official paper · jm01-2021 · I.8 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

A factor 2x+1 gives a zero at x=−1/2.

Hint 2

Set f(−1/2)=0.

Worked solution

Apply the factor theorem at the root of the linear factor.
$0=f(-1/2)=2+m/2-m=2-m/2$
Solve the linear equation.
$m=4$

D: 4.

Checks and common pitfalls: The relevant input is −1/2, not −1.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Apply the factor theorem at the root of the linear factor.
$0=f(-1/2)=2+m/2-m=2-m/2$
Solve the linear equation.
$m=4$

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

2021 JM01