A parabola with real coefficients lies entirely below the x-axis. What must be true of its discriminant?

$f(x)=x^3-9x^2+8x$. What are the zeros of f and their multiplicities?

Writing (2 + 2i)/(3 + i) in a + bi form, a student multiplied by 3 - i over itself but treated $i^2$ as 1 in the numerator, getting 2/5 + (2/5)i. What is the correct answer?

What value of c makes $x^2+8x+c$ a perfect square trinomial?

Simplify $i^{25}$.

Solve $3x^2+16x+5\le 0$. Write the solution in interval notation.

A student factors $27x^3-64$ as $(3x-4)(9x^2-12x+16)$, copying the minus sign of the binomial into the middle term of the trinomial. What is the correct complete factorization?

Write (3 + 4i) - (3 + 5i) in a + bi form.

f(x) = (x - 6)(x + 2). At x = 6, what does the graph of f do?

Use synthetic division to divide $3x^3-11x^2+10x-6$ by $x-2$. What are the quotient and remainder?

Rewrite $y=-2x^2+16x-43$ in vertex form.

Write (-5 + 7i)(-7 + 4i) in a + bi form.

A quadratic function with real coefficients has a positive discriminant. What must be true of its graph?

$f(x)=5x^3+x^2+5$ and $g(x)=2x^3+4x^2-3x+1$. What is $f(x)-g(x)$ in standard form?

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are -5, 3 and -6. Give the answer in standard form.

Solve $x^2+9x+4=0$. What is the greater solution, rounded to the nearest hundredth?

Factor completely: $x^3+2x^2-x-2$.

Solve $2x^2+x-6<0$. Write the solution in interval notation.

$f(x)=(x-1{)}^2(x+1)(4x-5{)}^1$. What are the degree and the leading coefficient of f when it is expanded?

For a polynomial P, P(3) = 0. Which statement must be true?

Solve $5x^2+9x+4=0$ by factoring.

For what value of c does $x^2-6x+c=0$ have exactly one real solution?

Simplify $i^{53}+i^{48}$. Write the answer in a + bi form.

Every possible rational zero of $P(x)=a{x}^3-4x^2+x+5$ is in the list +/-1, +/-5, +/-1/8, +/-1/4, +/-1/2, +/-5/8, +/-5/4, +/-5/2, and a is positive. What is the value of a?

A parabola opens downward and crosses the x-axis at -2 and 5. For which x-values is y < 0? Write the answer in interval notation.

$P(x)=3x^3-x+6$. Which value is NOT a possible rational zero of P?

$f(x)=-2x^6-5x+2$. Which describes the end behavior of the graph of f?

$x-1$ is a factor of $P(x)=2x^3+k{x}^2+6x+1$. What is the value of k?

$f(x)=x^3-13x^2+40x$. What are the zeros of f and their multiplicities?

A polynomial with leading coefficient 1 has the zero -6 with multiplicity 2 and the zero 1 with multiplicity 1, and no other zeros. What is its factored form?

Solve $x^2+18x+90=0$. Give the answer in a + bi form.

A punted football has height $h(t)=-16t^2+96t+5$, where h is in feet and t is in seconds. What is the greatest height the ball reaches?

What is $(x-3)(x^2+2x-7)$ in standard form?

Use synthetic division to divide $2x^3+0x^2+7x+0$ by $x-3$. What are the quotient and remainder?

$P(x)=2x^3+5x^2-4x-9$. Which list gives every possible rational zero?

Factor completely: $x^3+x^2-4x-4$.

How many and what kind of solutions does $-2x^2-6x+6=0$ have?

Use synthetic division to divide $2x^3-3x^2+4x-12$ by $x-2$. What are the quotient and remainder?

Rewrite $y=-3x^2+30x-86$ in vertex form.

Use synthetic division to divide $x^4+0x^3+0x^2+0x-81$ by $x-3$. What are the quotient and remainder?

A student factors $8x^3-64$ as $(2x-4)(4x^2-8x+16)$, copying the minus sign of the binomial into the middle term of the trinomial. What is the correct complete factorization?

$P(x)=x^3-19x+30$, and dividing by $x-2$ gives the quotient $x^2+2x-15$ with remainder 0. What is P(x) factored completely?

Factor completely: $6x^4-1536$.

What is the first step in factoring $4x^3-20x^2+5x-25$?

Solve $x^2+8x+12<0$. Write the solution in interval notation.

Multiplying $(2+5i)(2-5i)$, a student wrote $4-25i^2$ and then $4-25=-21$. What is the correct product in a + bi form?

Write (6 - 4i)/(2 - 3i) in a + bi form.

For $-x^2-6x-9=0$ a student computed $b^2-4ac$ as $36-4(1)(-9)=72$ and concluded two irrational solutions. What is the correct discriminant and conclusion?

$f(x)=-x^2-x^3-5-x$. What are the degree and the leading coefficient of f?

$P(x)=5x^3-x+6$. Which value is NOT a possible rational zero of P?

$f(x)=(x-1{)}^1(x+1)(2x-5{)}^2$. What are the degree and the leading coefficient of f when it is expanded?

What is $(x+2)(x^2-6x-7)$ in standard form?

A student says the graph of $f(x)=3-6x^6$ rises on both ends because the highest exponent is even. Which statement corrects the student?

Factor completely: $5x^4-320x$.

A gardener encloses a rectangular plot with 40 meters of fence on all four sides. The area is A(w) = w(20 - w), where w is the width in meters. What is the greatest area the plot can have?

A quadratic function with real coefficients has a negative discriminant. What must be true of its graph?

One solution of $4x^2+bx+12=0$ is x = -1/2. What is the value of b?

Solve $x^2+8x+4=0$ with the quadratic formula. Give the answer in simplest radical form.

Solve $x^2-10x+30>0$. Write the solution in interval notation.

For $-x^2-4x-4=0$ a student computed $b^2-4ac$ as $16-4(1)(-4)=32$ and concluded two irrational solutions. What is the correct discriminant and conclusion?