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 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 factor.

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 expression 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.

Front

What is the difference between a zero and a factor of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero, while a factor is a polynomial that divides another polynomial without a remainder.

Front

How do you factor the expression 4x^2 - 16?

Back

4x^2 - 16 can be factored as 4(x^2 - 4), which further factors to 4(x + 2)(x - 2) using the difference of squares.

Front

What is the lead coefficient of a polynomial?

Back

The lead coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

What is the inverse of a function?

Back

The inverse of a function is a function that reverses the effect of the original function. If f(x) = y, then the inverse function f^(-1)(y) = x.

Front

How do you find the inverse of the function y = (2x + 4)/8?

Back

To find the inverse, swap x and y and solve for y: x = (2y + 4)/8. Rearranging gives y = (8x - 4)/2.