Math 3 EOC Review 1

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number powers and multiplied by coefficients. For example, y = x^3 + 4x^2 - 11x + k is a polynomial.

Front

What does it mean for (x + 5) to be a factor of a polynomial?

Back

If (x + 5) is a factor of a polynomial, it means that when the polynomial is divided by (x + 5), the remainder is zero.

Front

How do you find another factor of a polynomial when one factor is known?

Back

You can use polynomial long division or synthetic division to divide the polynomial by the known factor to find the other factors.

Front

What is the process to expand (2x - 3y)^2?

Back

To expand (2x - 3y)^2, use the formula (a - b)^2 = a^2 - 2ab + b^2. Thus, (2x - 3y)^2 = (2x)^2 - 2(2x)(3y) + (3y)^2 = 4x^2 - 12xy + 9y^2.

Front

What are the coefficients in the polynomial ax^2 + bxy + cy^2?

Back

The coefficients are the numerical factors in front of the variables: a is the coefficient of x^2, b is the coefficient of xy, and c is the coefficient of y^2.

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What does it mean for a function to be decreasing on an interval?

Back

A function is decreasing on an interval if, as the input values increase, the output values decrease.

Front

How can you determine the intervals where a function is increasing or decreasing?

Back

You can determine the intervals by finding the derivative of the function and analyzing where the derivative is positive (increasing) or negative (decreasing).

Front

What is the significance of the roots of a polynomial?

Back

The roots of a polynomial are the values of x for which the polynomial equals zero. They represent the x-intercepts of the graph of the polynomial.

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).

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What is the Remainder Theorem?

Back

The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), the remainder of that division is f(c).