Find all real zeros, including multiplicity.

01 / Standard#Your turn

f(x)=x^3+3x^2-4

Official paper · jm02-2025 · 2(a)(i) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Test simple integer roots.

Hint 2

After removing x−1, factor the remaining quadratic.

Worked solution

Factor the cubic.
$f(x)=(x-1)(x^2+4x+4)=(x-1)(x+2)^2$
Set the factors equal to zero.
$x=1\quad\text{or}\quad x=-2\text{ (double root)}$

x=1 and x=−2; −2 is a double root.

Checks and common pitfalls: A repeated root is one distinct zero but has multiplicity two.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Factor the cubic.
$f(x)=(x-1)(x^2+4x+4)=(x-1)(x+2)^2$
Set the factors equal to zero.
$x=1\quad\text{or}\quad x=-2\text{ (double root)}$

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

2025 JM02