Math for College Algebra: 5.2 & 5.3 Flashcard

Front

What is the result of multiplying the polynomials \( (2x+7)(2x^2+5x-4) \)?

Back

The result is \( 4x^3 + 24x^2 + 27x - 28 \).

Front

Simplify the expression \( (3y^2+y^3-5)+(4y^2-4y+2y^3+8) \).

Back

The simplified expression is \( 3y^3 + 7y^2 - 4y + 3 \).

Front

What is the expanded form of \( (2x-3)^3 \)?

Back

The expanded form is \( 8x^3 - 36x^2 + 54x - 27 \).

Front

Multiply the polynomials \( (m+5)(m^2+4m-8) \).

Back

The result is \( m^3 + 9m^2 + 12m - 40 \).

Front

Simplify the expression \( 2x(-2x-3) \).

Back

The simplified expression is \( -4x^2 - 6x \).

Front

What is the distributive property in algebra?

Back

The distributive property states that \( a(b+c) = ab + ac \).

Front

Define a polynomial. Give an example.

Back

A polynomial is an expression consisting of variables and coefficients, involving only addition, subtraction, multiplication, and non-negative integer exponents. Example: \( 3x^2 + 2x - 5 \).

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in \( 4x^3 + 2x^2 + 7 \), the degree is 3.

Front

Explain how to combine like terms in an expression.

Back

To combine like terms, add or subtract the coefficients of terms that have the same variable raised to the same power. For example, \( 3x + 4x = 7x \).

Front

What is the formula for the cube of a binomial \( (a-b)^3 \)?

Back

The formula is \( (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 \).