Factoring Polynomials

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler factors that, when multiplied together, give the original expression.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication.

Front

What is a trinomial?

Back

A trinomial is a polynomial that consists of three terms.

Front

What does GCF stand for in factoring?

Back

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

Front

How do you factor a trinomial of the form ax^2 + bx + c?

Back

To factor a trinomial of the form ax^2 + bx + c, find two numbers that multiply to ac and add to b, then rewrite the trinomial as a product of two binomials.

Front

What is the difference between factoring by grouping and factoring by GCF?

Back

Factoring by grouping involves rearranging terms and factoring out common factors from groups of terms, while factoring by GCF involves finding the largest common factor from all terms in the polynomial.

Front

What is the factored form of the polynomial 9x^2 - 6x - 8?

Back

The factored form is (3x + 2)(3x - 4).

Front

What is the factored form of the polynomial x^2 - 17x + 72?

Back

The factored form is (x - 9)(x - 8).

Front

What is the factored form of the polynomial 8n^3 + 2n^2?

Back

The factored form is 2n^2(4n + 1).

Front

What is the factored form of the polynomial 4b^5 + 4b^3 + 16b^2?

Back

The factored form is 4b^2(b^3 + b + 4).