factoring by grouping

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by grouping terms with common factors together, allowing for easier factorization.

Front

What is the first step in factoring by grouping?

Back

The first step is to rearrange the polynomial into two groups that can be factored separately.

Front

How do you factor the polynomial 12x^3 + 4x^2 + 3x + 1?

Back

(4x^2 + 1)(3x + 1)

Front

What is the result of factoring 5x^3 - 10x^2 + 3x - 6?

Back

(5x^2 + 3)(x - 2)

Front

What is the factored form of 3x^3 - 4x^2 + 9x - 12?

Back

(x^2 + 3)(3x - 4)

Front

How do you factor the polynomial 12x^3 - 21x^2 + 28x - 49?

Back

(3x^2 + 7)(4x - 7)

Front

What is the factored form of 63x^3 + 54x^2 - 105x - 90?

Back

3(3x^2 - 5)(7x + 6)

Front

What is a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means to express it as a product of its factors, which are polynomials of lower degrees.

Front

What is the significance of the distributive property in factoring?

Back

The distributive property allows us to factor out common terms from a polynomial, making it easier to simplify and solve.

Tags

CCSS.7.EE.A.1