Daily Math Problems — May 15, 2026: Polynomials, Calculus, Algebra

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Problems & worked solutions

RO M1

Problem 1 — Polynomials in ℂ

For $A = X^{2} + 3 X - 1$ and $B = 2 X^{2} - X + 4$ , the polynomial $A + B$ equals:

Show answer & worked solution

A. $X^{2} + 2 X + 3$
B. $3 X^{2} + 4 X + 5$
C. $3 X^{2} + 2 X + 3$ ✓ correct
D. $- X^{2} + 4 X - 5$

Add coefficients: $(1 + 2) X^{2} + (3 - 1) X + (- 1 + 4) = 3 X^{2} + 2 X + 3$ .

RO M1

Problem 2 — Rolle's Sign Method

The number of distinct real roots of $P (x) = x^{3} - 3 x + 1$ is:

Show answer & worked solution

A. $1$
B. $2$
C. $3$ ✓ correct
D. $0$

$P (- \infty) = - \infty$ , $P (- 1) = - 1 + 3 + 1 = 3 > 0$ , $P (1) = 1 - 3 + 1 = - 1 < 0$ , $P (\infty) = + \infty$ . The sign sequence $-, +, -, +$ shows three sign changes, hence three distinct real roots.

RO M1

Problem 3 — Modular Arithmetic (ℤₙ)

$(Z_{n}, +, \cdot)$ is a field iff:

Show answer & worked solution

A. $n is even$
B. $n \geq 5$
C. $n is prime$ ✓ correct
D. $n = n!$

$Z_{n}$ is a field iff every non-zero element is invertible, iff every element from $1$ to $n - 1$ is coprime to $n$ , iff $n$ is prime.

Problems & worked solutions

RO M1

Problem 1 — Polynomials in ℂ

For $A = X^{2} + 3 X - 1$ and $B = 2 X^{2} - X + 4$ , the polynomial $A + B$ equals:

Show answer & worked solution

A. $X^{2} + 2 X + 3$
B. $3 X^{2} + 4 X + 5$
C. $3 X^{2} + 2 X + 3$ ✓ correct
D. $- X^{2} + 4 X - 5$

Add coefficients: $(1 + 2) X^{2} + (3 - 1) X + (- 1 + 4) = 3 X^{2} + 2 X + 3$ .

RO M1

Problem 2 — Rolle's Sign Method

The number of distinct real roots of $P (x) = x^{3} - 3 x + 1$ is:

Show answer & worked solution

A. $1$
B. $2$
C. $3$ ✓ correct
D. $0$

RO M1

Problem 3 — Modular Arithmetic (ℤₙ)

$(Z_{n}, +, \cdot)$ is a field iff:

Show answer & worked solution

A. $n is even$
B. $n \geq 5$
C. $n is prime$ ✓ correct
D. $n = n!$

$Z_{n}$ is a field iff every non-zero element is invertible, iff every element from $1$ to $n - 1$ is coprime to $n$ , iff $n$ is prime.