factoring by grouping practice

Front

What is factoring by grouping?

Back

Factoring by grouping is a method used to factor polynomials by grouping terms with common factors and then factoring out the common binomial.

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 expression 5n³-10n²+3n-6?

Back

Group the terms: (5n³-10n²) + (3n-6), then factor out common factors: 5n²(n-2) + 3(n-2) = (5n²+3)(n-2).

Front

What is the factored form of x³+7x²-2x-14?

Back

Group the terms: (x³+7x²) + (-2x-14), then factor out common factors: x²(x+7) - 2(x+7) = (x²-2)(x+7).

Front

What is the factored form of 8x³-28x²+14x-49?

Back

Group the terms: (8x³-28x²) + (14x-49), then factor out common factors: 4x²(2x-7) + 7(2x-7) = (4x²+7)(2x-7).

Front

How do you factor the expression 20x³-25x²+4x-5?

Back

Group the terms: (20x³-25x²) + (4x-5), then factor out common factors: 5x²(4x-5) + 1(4x-5) = (5x²+1)(4x-5).

Front

What is the factored form of x²+3x+7x+21?

Back

Group the terms: (x²+3x) + (7x+21), then factor out common factors: x(x+3) + 7(x+3) = (x+3)(x+7).

Front

What is a common factor in a polynomial?

Back

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

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms, such as a + b.

Front

What is the difference between factoring and expanding?

Back

Factoring is the process of breaking down a polynomial into simpler components (factors), while expanding is the process of multiplying out the factors to obtain the polynomial.