Math Solutions

Find all primes up to 100 using the Sieve of Eratosthenes. Animate crossing out multiples of 2, 3, 5, 7.

Find the prime factorization of 360. Build the factor tree step by step.

Find LCM(12, 18, 20) using prime factorization. Show the Venn diagram of prime factors.

Find GCD(252, 198) using the Euclidean algorithm. Show the repeated division steps until the remainder is 0.

Expand (2x+3)⁵ using the binomial theorem with Pascal's triangle row 5.

Test f(x)=x³+x (odd) and g(x)=x⁴+x² (even). Show symmetry.

f(x) = {x² if x<0, 2x+1 if 0≤x<3, 7 if x≥3}. Evaluate at x=−2, 1, 5.

If f(x)=x²+1 and g(x)=3x−2, find f(g(x)) and g(f(x)).

Find the inverse of f(x) = (2x+3)/(x−1). Swap x and y, solve for y.

Find the domain and range of f(x) = √(4−x²). The domain requires 4−x² ≥ 0, so −2 ≤ x ≤ 2.

Solve (x−3)/(x+1) ≥ 0. Use sign chart with critical points x=3, x=−1.

Solve (x−1)(x+2)(x−4) > 0 using a sign chart with test points.

Solve |x−4| ≤ 3. This means −3 ≤ x−4 ≤ 3, so 1 ≤ x ≤ 7.

Solve |2x−3| = 7. Two cases: 2x−3 = 7 or 2x−3 = −7.

Solve x²−5x+6 < 0. Factor: (x−2)(x−3) < 0. Solution: 2 < x < 3.

Solve −3 < 2x+1 ≤ 9. Show the solution interval on a number line.

Solve 2x−5 > 7. Show the solution on a number line.

Evaluate Σ(k=1 to n) [1/k − 1/(k+1)]. Most terms cancel, leaving 1 − 1/(n+1).

Find 1+1/3+1/9+1/27+... = 1/(1−1/3) = 3/2.

Find 1+2+4+8+...+512 = 2^10 − 1 = 1023.