A2 Review 5.1-5.3

Front

If \( f(x) = x^2 + x \), find \( 2f(a - 3) \).

Back

\( 2f(a - 3) = 2((a - 3)^2 + (a - 3)) = 2(a^2 - 6a + 9 + a - 3) = 2a^2 - 10a + 12 \)

Front

If \( f(x) = 5 - 3x \), what is \( f(x - 1) \)?

Back

\( f(x - 1) = 5 - 3(x - 1) = 5 - 3x + 3 = -3x + 8 \)

Front

Divide using synthetic division: \( 2x^3 + 4x^2 - 5 \) by \( x + 3 \).

Back

The result is \( 2x^2 - 2x + 6 \) with a remainder of \( -23 \)

Front

Divide \( 2x^2 + 6x - 20 \) by \( 2x - 4 \) using long division.

Back

The result is \( x + 5 \)

Front

Find the sum: \( (3y^2 + y^3 - 5) + (4y^2 - 4y + 2y^3 + 8) \).

Back

The sum is \( 3y^3 + 7y^2 - 4y + 3 \)

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor of the form \( x - c \).

Front

Define polynomial degree.

Back

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

Front

What is the remainder theorem?

Back

The remainder theorem states that the remainder of the division of a polynomial \( f(x) \) by \( x - c \) is equal to \( f(c) \).

Front

Explain the concept of factoring polynomials.

Back

Factoring polynomials involves expressing the polynomial as a product of its factors, which can be simpler polynomials.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a single term, while a polynomial is a sum of two or more monomials.