Use synthetic division to divide $2x^3-12x^2+12x-6$ by $x-5$. What are the quotient and remainder?

$P(x)=x^3+12x^2+47x+60$, and dividing by $x+3$ gives the quotient $x^2+9x+20$ with remainder 0. What is $P(x)$ factored completely?

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

Before dividing $x^5-1$ by $x-2$ with long division, how must the dividend be written?

Factor completely: $8x^3-125$.

$P(x)=4x^3+5x^2-4x-6$. Which list gives every possible rational zero?

A student subtracts $x^3-5x+4$ from $8x^3-5x-9$ and writes $7x^3-10x-5$, changing the sign of only the first term of the second polynomial. What is the correct difference in standard form?

$f(x)=(x+2{)}^2(x-5)(x-7{)}^2$. What are the zeros of f and their multiplicities?

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

$f(x)=x^3+4x$. What are all the zeros of f, written in a + bi form where they are not real?

Divide $12x^2+13x-3$ by $4x-1$. Write the answer as quotient plus remainder over divisor.

$f(x)=(x-4{)}^2(x-1)(x+6{)}^2$. What are the zeros of f and their multiplicities?

A student factors $8x^3-1$ as $(2x-1)(4x^2-2x+1)$, copying the minus sign of the binomial into the middle term of the trinomial. What is the correct complete factorization?

Write a degree-4 polynomial function with leading coefficient 1 whose only zeros are -2 with multiplicity 3 and 1 with multiplicity 1. Give the answer in factored form.

Divide $2x^3+8x^2+10x+4$ by $x+2$. What is the quotient?

$f(x)=2x^3+6x-1$. Which describes the end behavior of the graph of f?

$P(x)=2x^3-6x^2-7x-5$. What is the remainder when $P(x)$ is divided by $x+4$?

Synthetic division of a degree-three polynomial by x - 2 produces the bottom row 2, -5, 4, 0. What is the quotient?

$P(x)=2x^3+4x^2-3x+6$. Is $x-3$ a factor of $P(x)$?

Use synthetic division to divide $x^3-8x^2+17x-12$ by $x-3$. What are the quotient and remainder?

Factor completely: $x^4-26x^2+25$.

A student subtracts $3x^3+6x+4$ from $6x^3+3x-9$ and writes $3x^3+9x-5$, changing the sign of only the first term of the second polynomial. What is the correct difference in standard form?

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

A student divides $x^3+5x^2+11x-50$ by $x-2$ but places -2 in the division box and gets a remainder of -60. What is the correct remainder?

A polynomial function with real coefficients has least degree and has 2 and 2 + 3i among its zeros. Write it with leading coefficient 1, in standard form.

Before dividing $x^4-1$ by $x-2$ with long division, how must the dividend be written?

A student subtracts $x^3+6x+4$ from $4x^3-5x+7$ and writes $3x^3+x+11$, changing the sign of only the first term of the second polynomial. What is the correct difference in standard form?

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

$x+1$ is a factor of $P(x)=x^3+k{x}^2+4x+3$. What is the value of k?

$f(x)=7x^2+5x^3+9-x$. What are the degree and the leading coefficient of f?

Factor completely: $27x^3+27$.

What is the first step in factoring $4x^3-24x^2+7x-42$?

$f(x)=3x^2-2x^3+9-x$. What are the degree and the leading coefficient of f?

Factor completely: $2x^4+128x$.

Factor completely: $x^4-40x^2+144$.

A student subtracts $3x^3-5x+4$ from $2x^3-5x-9$ and writes $-x^3-10x-5$, changing the sign of only the first term of the second polynomial. What is the correct difference in standard form?

A polynomial function with real coefficients has least degree and has -1 and 1 + 3i among its zeros. Write it with leading coefficient 1, in standard form.

A polynomial function of least degree has only the zeros 1 and 4 and passes through the point (5, 8). Write it in factored form.

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are 2, 1 and 6. Give the answer in standard form.

Factor completely: $x^4-37x^2+36$.