Adding Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number exponents and coefficients, combined using addition, subtraction, and multiplication.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions to form a single polynomial.

Front

What are like terms in polynomials?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3a^2 and 5a^2 are like terms.

Front

How do you simplify the expression (4a^3 - 8a - 4a^2) + (7a^3 - 7 - 6a)?

Back

Combine like terms: 4a^3 + 7a^3 = 11a^3, -4a^2, -8a - 6a = -14a, and -7. The simplified expression is 11a^3 - 4a^2 - 14a - 7.

Front

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

Back

Combine like terms: -2x^3 + 5x^3 = 3x^3, 4x - 4x = 0, and +5. The result is 3x^3 + 5.

Front

How do you find the sum of (3y^2 + y^3 - 5) + (4y^2 - 4y + 2y^3 + 8)?

Back

Combine like terms: y^3 + 2y^3 = 3y^3, 3y^2 + 4y^2 = 7y^2, -4y, and -5 + 8 = 3. The sum is 3y^3 + 7y^2 - 4y + 3.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a parenthesis.

Front

Simplify -3(x - 4).

Back

Using the distributive property: -3x + 12.

Front

What is the formula for the perimeter of a rectangle?

Back

The perimeter P of a rectangle is given by P = 2(length + width).

Front

If a rectangle has width (2x + 3) and length (2x - 4), what is its perimeter?

Back

P = 2((2x + 3) + (2x - 4)) = 2(4x - 1) = 8x - 2.