Flashcard 7.1-7.3

Front

What is the result of multiplying the polynomials \( (2a+4)(a+1) \)?

Back

The result is \( 2a^2 + 6a + 4 \).

Front

How do you add the polynomials \( (-3x + 4) + (8x - 5) \)?

Back

The sum is \( 5x - 1 \).

Front

What is the result of multiplying the polynomials \( (2x+9)(x-2) \)?

Back

The result is \( 2x^2 + 5x - 18 \).

Front

What is the result of multiplying the polynomials \( (n+2)(n^2+5n-3) \)?

Back

The result is \( n^3 + 7n^2 + 7n - 6 \).

Front

What is the sum of the polynomials \( (3x^2+4x+5) + (2x^2-x+3) \)?

Back

The sum is \( 5x^2 + 3x + 8 \).

Front

Define a polynomial.

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents of variables.

Front

What is the degree of the polynomial \( 4x^3 + 3x^2 - 2x + 1 \)?

Back

The degree is 3, which is the highest exponent of the variable x.

Front

What is the leading coefficient of the polynomial \( 5x^4 - 2x^3 + 3 \)?

Back

The leading coefficient is 5, which is the coefficient of the term with the highest degree.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms.

Front

What is the result of \( (x + 3)(x - 3) \)?

Back

The result is \( x^2 - 9 \), which is a difference of squares.