FREE Algebra and Calculus Maths

Apply the remainder theorem to compute the remainder when a polynomial is divided by ax+b by evaluating f(-b/a). Apply the factor theorem to confirm a linear factor by ensuring f(-b/a)=0.

use remainder and factor theorems on cubic polynomials via synthetic division, identify roots like x=1, and reduce to a quadratic solved by the quadratic formula.

Explain limits as a function’s value near a point, using factoring to resolve indeterminate forms and arrive at 10; then use the average gradient formula (y2−y1)/(x2−x1) to compute the slope.

Explore differentiation through first principles and rules, master the limit definition f'(x)=lim h→0 [f(x+h)-f(x)]/h, and work through a polynomial example.

Explore foil expansion and combining like terms to simplify a polynomial, while emphasizing patience and careful algebra to evaluate limits as h approaches zero.

Apply first principles and factor cancellation to evaluate a limit and obtain the derivative expression, then introduce core differentiation rules: constants’ derivative is zero and the power rule.

Apply derivative rules for constants, sums, and differences to compute f'(x). Break down F(x)=2x^3+2x-3x^2+2 into parts, derive each term, and combine results to obtain the derivative.

Learn to apply the product rule and power rule to differentiate expressions involving x, manage constants, and simplify the resulting derivative step by step.

Explore differentiation concepts in algebra and calculus, including f'(x) and dy/dx, as well as derivative forms with functions inside brackets. Compare four common notations to master the rules of differentiation.