Daily Math · 2026-06-01

Question 1

For $P(X) = X^3 - 2X + 5$, the value of $P(2)$ is:

Accepted Answer

$P(2) = 8 - 4 + 5 = 9$.

Answer

$5$

Answer

$7$

Answer

$9$

Answer

$13$

Question 2

The coefficient of $x^3$ in $(x + 2)^5$ is:

Accepted Answer

$5 - k = 3 \Rightarrow k = 2$. Coefficient: $\binom{5}{2} \cdot 2^2 = 10 \cdot 4 = 40$.

Answer

$20$

Answer

$32$

Answer

$40$

Answer

$80$

Question 3

The maximum value of $f(x) = \sin x + \cos x$ over $\mathbb{R}$ is:

Accepted Answer

$\sin x + \cos x = \sqrt{2}\!\left(\sin x \cdot \dfrac{\sqrt{2}}{2} + \cos x \cdot \dfrac{\sqrt{2}}{2}\right) = \sqrt{2}\sin\!\left(x + \dfrac{\pi}{4}\right)$.

Since $\sin$ has maximum $1$, the maximum of $f$ is $\sqrt{2}$, attained at $x = \dfrac{\pi}{4}$.

Answer

$1$

Answer

$\sqrt{2} - 1$

Answer

$\sqrt{2}$

Answer

$2$

Problems & worked solutions

Problem 1 — Polynomials in ℂ

Problem 2 — Binomial Theorem

Problem 3 — Trigonometric Identities