Digital SAT Practice Questions

Determine the value of $k$ if $(x + 3)$ is a factor of $x^3 + 2x^2 - kx + 6$....

For the polynomial $f(x) = 2x^3 - kx^2 + 5x - 6$, if $f(1) = 0$, what is the value of $k$?...

Which value is a root of the polynomial $g(x) = x^3 - 7x - 6$?...

When $x^4 - 2x^2 + 3$ is divided by $(x - 1)$, the remainder is:...

If $p(x)$ is a polynomial and $p(-5) = 0$, which must be a factor of $p(x)$?...

The polynomial $P(x) = x^3 - 3x^2 - 10x + 24$ has a known zero at $x = 2$. What are the other two zeros?...

Calculate the remainder when $2x^3 + 5x^2 - 4x - 1$ is divided by $(x + 2)$....

A polynomial $q(x)$ satisfies $q(4) = -7$. What is the remainder when $q(x)$ is divided by $(x - 4)$?...

If $(x - 1)^2$ divides $x^3 - 3x + 2$, what is the quotient?...

Simplify $\frac{x^2 - 16}{x^2 + 7x + 12}$ for all defined values of $x$....

For which value of $x$ is the expression $\frac{5x}{2x - 8}$ undefined?...

Simplify $\frac{3}{x - 1} + \frac{2}{x + 2}$ into a single rational expression....

Find the solution to $\frac{x}{x - 3} = \frac{2}{x - 3} + 4$ for $x \ne 3$....

Which expression is equivalent to $\frac{x^2 - 9}{x - 3}$ for $x \ne 3$?...

What are the values of $x$ for which $\frac{x + 1}{x^2 - 5x + 6}$ is undefined?...

Divide $\frac{2x}{x^2 - 4} \div \frac{4}{x - 2}$ and express in simplest form....

Solve $\frac{1}{x} + \frac{1}{2x} = \frac{3}{4}$ for $x$....

Simplify the compound fraction $\frac{\frac{1}{x} + \frac{1}{y}}{\frac{1}{xy}}$....

If $\frac{x^2 - c}{x - 4} = x + 4$ for all $x \ne 4$, what is the value of $c$?...

Consider $P(x) = -3x^4 + 2x^2 - 5$. As $x \to \infty$, what does $P(x)$ approach?...

How many real zeros does the graph of $f(x) = (x - 1)^2(x + 3)(x - 5)^3$ have?...

At which zero does the graph of $y = (x - 2)^2(x + 1)$ touch the $x$-axis without crossing?...

What is the degree of the polynomial $f(x) = (x^2 + 1)(x - 3)^3(x + 2)$?...

Which of the following functions has a graph that crosses the $x$-axis at $(-3, 0), (0, 0),$ and $(4, 0)$?...