Solving Polynomials by Factoring

Front

What is factoring in polynomials?

Back

Factoring is the process of breaking down a polynomial into simpler components (factors) that, when multiplied together, give the original polynomial.

Front

What is the purpose of factoring polynomials?

Back

The purpose of factoring polynomials is to simplify expressions, solve polynomial equations, and find the roots of the polynomial.

Front

What does it mean to factor by grouping?

Back

Factoring by grouping involves rearranging and grouping terms in a polynomial to factor out common factors from each group.

Front

How do you factor the polynomial 5n³ - 10n² + 3n - 6?

Back

(5n² + 3)(n - 2) is the factored form.

Front

What are the steps to solve a polynomial equation by factoring?

Back

1. Set the equation to zero. 2. Factor the polynomial. 3. Set each factor equal to zero. 4. Solve for the variable.

Tags

CCSS.HSA-REI.B.4B

Front

What is the factored form of 3x³ + 15x² + 30x = 0?

Back

0, -2, -3 are the solutions.

Tags

CCSS.HSA.APR.B.2

Front

What is the significance of the roots of a polynomial?

Back

The roots of a polynomial are the values of the variable that make the polynomial equal to zero; they represent the x-intercepts of the graph.

Front

How do you factor the polynomial 4p³ + 8p² + 3p + 6?

Back

(4p² + 3)(p + 2) is the factored form.

Front

What is a common factor in polynomials?

Back

A common factor is a number or variable that divides all terms of the polynomial without leaving a remainder.

Front

What is the relationship between the degree of a polynomial and its number of roots?

Back

The degree of a polynomial indicates the maximum number of roots it can have, according to the Fundamental Theorem of Algebra.

Tags

CCSS.HSN.CN.C.9