Operations with Polynomials and Factoring 2024

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, from the highest degree to the lowest.

Front

What is the degree of a polynomial?

Back

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

Front

How do you factor a quadratic polynomial of the form ax² + bx + c?

Back

To factor a quadratic polynomial, find two numbers that multiply to ac (the product of a and c) and add to b. Then, rewrite the polynomial using these numbers.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern expressed as a² - b² = (a + b)(a - b).

Tags

CCSS.HSA.APR.C.4

Front

What is the factored form of x² - 10x + 24?

Back

(x - 4)(x - 6) is the factored form of x² - 10x + 24.

Front

How do you multiply two binomials?

Back

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

Tags

CCSS.HSA.APR.A.1

Front

What is the result of (4x + 1)(5x - 2)?

Back

The result is 20x² - 3x - 2.

Tags

CCSS.HSA.APR.A.1

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.