Simplifying
Simplify the expression \(3x^2 - 2x + 1 - (2x^2 - x + 2)\)
Polynomial Division
Divide the polynomial \(3x^3 - 2x^2 + 5x - 7\) by the polynomial \(x - 2\).
Finding the Remainder Using Long Polynomial Division
Find the remainder when \(2x^3 - 3x^2 + 4x - 5\) is divided by \(x - 2\).
Reducing
Reduce the polynomial \(3x^4 - 2x^3 + 4x^2 - 5x + 2\) by factoring out the greatest common factor.
Cancelling the Common Factors
Simplify the expression \( \frac{4x^3y^2z^4}{2x^2y^2z^2} \)
Evaluate the Expression Using the Given Values
Evaluate the polynomial expression \(2x^3 - 5x^2 + 3x - 7\) for \(x = -2\).
Identifying Degree
What is the degree of the polynomial \(3x^4 - 2x^3 + x^2 - 5x + 7\)?
Multiplying Polynomials Using FOIL
Multiply the following polynomials using FOIL: \((x+3)\) and \((x-2)\)
Negative Exponents
Simplify the expression \(5x^{-2}y^{-3}\)
Operations on Polynomials
Given two polynomial expressions, \( P(x) = 3x^3 - 2x^2 + 4x - 1 \) and \( Q(x) = 2x^3 + 3x^2 - 5x + 2 \). Compute the sum of \( P(x) \) and \( Q(x) \).
Simplifying Expressions
Simplify the expression \(3x^2 - 2x + 5 + 7x^2 - 3x + 2\)
Factoring Using Any Method
Factorize the polynomial \( 4x^2 - 16x + 16 \)
Factoring a Difference of Squares
Factorize the given expression: \(a^4 - 16\)
Factoring a Sum of Cubes
Factor the polynomial expression \(x^3 + 8\).
Factoring Out Greatest Common Factor (GCF)
Factor out the Greatest Common Factor (GCF) from the polynomial \(12x^3y + 18x^2y^2 + 24x^4y^3\)
Trinomial Squares
Simplify the trinomial square \((x + 5)^2\).
Factoring by Grouping
Factorize the expression \(3x^3+3x^2-4x-4\) by grouping.
Factoring a Difference of Cubes
Factor the expression \(64x^{3}-125\)
Factoring Trinomials
Factorize the trinomial \(2x^2 - 5x - 3\)
Maximum Number of Real Roots/Zeros
What is the maximum number of real zeros for the polynomial \(f(x) = 7x^5 - 3x^4 + 9x^3 - 5x^2 + 2x - 8\)?
Finding All Possible Roots/Zeros (RRT)
Find all possible roots for the polynomial \(3x^3 - 2x^2 - 5x + 10\)
Finding All Roots with Rational Root Test (RRT)
Find all roots of the polynomial \(2x^3 - 3x^2 - 23x + 30\) using the Rational Root Test (RRT).