Polynomials: Adding Subtracting Multiplying

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. For example, 2x^2 + 3x - 5 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions. For example, (2x + 3) + (3x + 5) = 5x + 8.

Tags

CCSS.HSA.APR.A.1

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves taking the second polynomial away from the first, which includes changing the signs of the second polynomial's terms before combining like terms. For example, (5x + 3) - (2x + 1) = 3x + 2.

Tags

CCSS.HSA.APR.A.1

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property to multiply each term in the first polynomial by each term in the second polynomial, then combine like terms. For example, (x + 2)(x + 3) = x^2 + 5x + 6.

Tags

CCSS.HSA.APR.A.1

Front

What is a like term?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms, while 3x^2 and 4x are not.

Tags

CCSS.6.EE.A.2B

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest exponent of the variable in the polynomial. For example, in the polynomial 4x^3 + 2x^2 - x, the degree is 3.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 5x^4 + 3x^2 - 2, the leading coefficient is 5.

Front

What is the result of multiplying (p - 8)²?

Back

The result is p² - 16p + 64.

Tags

CCSS.HSA.APR.C.4

Front

What is the result of subtracting (5x^4 - 2x^2 + 4x - 3) - (5x^4 + 3x^3 - 4x + 3)?

Back

The result is -3x^3 - 2x^2 + 8x - 6.

Tags

CCSS.HSA.APR.A.1

Front

What is the result of multiplying 7x²y³(2x⁴y⁵ + 6xy³)?

Back

The result is 14x^6y^8 + 42x^3y^6.

Tags

CCSS.HSA.APR.A.1