Multiplying and Factoring Polynomials

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 to factor a polynomial?

Back

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

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms, such as a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last.

Front

What is the result of multiplying (x + 2)(x + 3)?

Back

x^2 + 5x + 6.

Front

What is the result of multiplying (2x + 3)(3x + 4)?

Back

6x^2 + 17x + 12.

Front

What is the process of expanding a polynomial?

Back

Expanding a polynomial involves multiplying out the factors and combining like terms.

Front

What is a common factor in polynomials?

Back

A common factor is a polynomial that divides two or more polynomials without leaving a remainder.

Front

How do you factor the polynomial n^2 + 16n + 63?

Back

(n + 7)(n + 9).