Find the coefficient of x.

01 / Standard#Your turn

(\sqrt{x}-2)^5(2x-1)^4

Official paper · jm01-2024 · I.4 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Only powers x⁰ and x¹ from the first factor can contribute.

Hint 2

The second factor contains integer powers only.

Worked solution

Collect the required coefficients in both factors.
$[x^0](\sqrt x-2)^5=-32,\quad[x](\sqrt x-2)^5=\binom52(-2)^3=-80$
The second factor has constant 1 and x coefficient −8.
$[x]=(-32)(-8)+(-80)(1)=176$

C: 176.

Checks and common pitfalls: A √x term cannot combine with an integer power to produce x.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Collect the required coefficients in both factors.
$[x^0](\sqrt x-2)^5=-32,\quad[x](\sqrt x-2)^5=\binom52(-2)^3=-80$
The second factor has constant 1 and x coefficient −8.
$[x]=(-32)(-8)+(-80)(1)=176$

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

2024 JM01