Math 3 Midterm Review Unit 6

Front

What is a factor in algebra?

Back

A factor is a number or expression that divides another number or expression evenly, without leaving a remainder.

Front

How do you determine if (x-8) is a factor of a polynomial?

Back

You can use polynomial division or the Factor Theorem, which states that (x-c) is a factor of a polynomial if the polynomial evaluates to zero at x=c.

Front

Solve for x: x^2 - 4 = 0

Back

x = 2, -2

Front

What is synthetic division?

Back

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

Front

If f(x) = x^3 + 8x + 24, what is f(-2) using synthetic division?

Back

f(-2) = 0 (the remainder when dividing by (x + 2)).

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

Perform synthetic division on 5p^2 + 5p - 26 by p + 3.

Back

5p - 10 + \frac{4}{p + 3}.

Front

What is the purpose of synthetic division?

Back

Synthetic division is used to divide polynomials and find remainders quickly without performing long division.

Front

Solve for x using synthetic division: 5x^2 + 2x - 3 = 0

Back

x = 1, -\frac{3}{5}.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial function and its degree.