Math Calculator

Use the difference of squares formula a² - b² = (a+b)(a-b). For x² - 9, treat it as x² - 3², so a = x and b = 3, giving (x+3)(x-3). The math calculator above detects difference of squares automatically. It also handles trinomials (a=1 and a>1), GCF extraction, sum and difference of cubes, and factoring by grouping. The factoring works on integer-coefficient polynomials up to degree 4.

Try dividing the number by 2, then 3, then 5, then 7, and so on, counting how many times each prime divides the number. The product of all the prime powers is the prime factorization. For numbers above 1 million the calculator switches to Pollard's rho algorithm which finds factors in polynomial time. For example, 7429 = 17 × 19 × 23, and the calculator renders this as a visual factor tree showing each split.

GCF (Greatest Common Factor) is the largest integer that divides all the numbers. LCM (Least Common Multiple) is the smallest positive integer that all the numbers divide into. For 12 and 18 the GCF is 6 (since 6 divides both 12 and 18) and the LCM is 36 (since 36 is the smallest number both 12 and 18 divide into). The math calculator uses the Euclidean algorithm which is the same fast method your teacher uses by hand.

Expand along the first row using cofactors: det = a(ei - fh) - b(di - fg) + c(dh - eg) where the matrix is [[a,b,c],[d,e,f],[g,h,i]]. This is the rule of Sarrus. The calculator above does this in one click and shows the intermediate step. For a 2×2 matrix [[a,b],[c,d]] the determinant is ad - bc.

For ax² + bx + c = 0, the discriminant is b² - 4ac. If the discriminant is positive, there are two real roots x = (-b ± √(discriminant)) / (2a). If the discriminant is zero, there is one repeated root x = -b / (2a). If the discriminant is negative, there are two complex roots with imaginary part ±√(|discriminant|) / (2a). The math calculator above computes the discriminant and both roots and shows the analysis automatically.

The Fibonacci sequence is F(1)=1, F(2)=1, F(n)=F(n-1)+F(n-2). The first 10 terms are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. The closed form (Binet's formula) is F(n) = (phi^n - psi^n) / √5 where phi = 1.618... and psi = -0.618... The math calculator above computes the nth term using the recurrence which is exact for integer answers.

AI text models frequently get factoring wrong on trinomials with leading coefficient greater than 1, mix up GCF and LCM, return incorrect matrix determinants for 3×3 matrices, and confuse arithmetic and geometric sequences. They also cannot show working step-by-step for factoring polynomials. The math calculator above uses the exact same algorithms your textbook uses (Euclidean, synthetic division, cofactor expansion) so the answer is always correct and reproducible.

Yes. Everything runs in your browser using JavaScript. No polynomials, matrices, or numbers are sent to any server. Close the tab and your last problem is gone. The only data persisted is the last input in localStorage so the form reloads when you come back. There is no account, no email capture, no analytics tied to your math problems.