Factoring Polynomials by Grouping

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by rearranging and grouping terms to find common factors.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What does it mean for (x - a) to be a factor of a polynomial?

Back

If (x - a) is a factor of a polynomial, then substituting x = a into the polynomial results in a value of zero.

Front

How do you determine if (x - 3) is a factor of 3x³ + 10x² - x - 12?

Back

Substitute x = 3 into the polynomial. If the result is zero, then (x - 3) is a factor.

Front

What is the first step in factoring by grouping?

Back

The first step is to look for common factors in pairs of terms.

Front

Factor the polynomial 2x² + 4x - 3x - 6 by grouping.

Back

(2x - 3)(x + 2) is the factored form.

Front

What is the significance of finding common factors in polynomials?

Back

Finding common factors simplifies the polynomial and makes it easier to factor completely.

Front

Factor the polynomial x³ - 2x - 4x² + 8 by grouping.

Back

(x - 4)(x² - 2) is the factored form.

Front

What is the role of rearranging terms in factoring by grouping?

Back

Rearranging terms can help in identifying pairs that have common factors, making the factoring process easier.

Front

Factor the polynomial 4y³ + y + 12y² + 3 by grouping.

Back

(4y² + 1)(y + 3) is the factored form.