5.2 Solving Polynomial Equations

Front

What is a polynomial equation?

Back

A polynomial equation is an equation that involves a polynomial expression, which is a mathematical expression consisting of variables raised to whole number powers and coefficients.

Front

What does GCF stand for in polynomial equations?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides two or more numbers.

Front

How do you factor out a GCF from a polynomial?

Back

To factor out a GCF, identify the largest factor common to all terms in the polynomial and divide each term by this factor, then express the polynomial as the product of the GCF and the remaining polynomial.

Front

Solve for x: x^2 + 14x = 0

Back

x = -14, 0

Front

What is the first step in solving polynomial equations by factoring?

Back

The first step is to set the equation to zero and look for common factors or patterns that can be factored.

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two or more factors equals zero, then at least one of the factors must be zero.

Front

Solve for x: x^4 + 4x^3 + 3x^2 = 0

Back

x = 0, -3, -1

Front

What is the purpose of factoring in solving polynomial equations?

Back

Factoring simplifies the polynomial equation, making it easier to find the roots or solutions.

Front

Factor the polynomial: x^4 - x^2 - 20

Back

(x^2 - 5)(x^2 + 4)

Front

Solve for x: x^2 + 5x + 6 = 0

Back

x = -3, -2