Dividing Polynomials: Long Division and Synthetic Methods

What is the first step in dividing polynomials using long division?

• Multiply the divisor by the dividend

• Subtract the divisor from the dividend

• Add the divisor to the dividend

• Ask what to multiply the divisor by to get the leading term of the dividend

In the first example, what is the remainder when 2n^2 - 16n + 19 is divided by n - 7?

• 5

• 0

• -5

• 7

In the second example, what is the leading term of the quotient when k^3 - 17k + 32 is divided by k + 5?

• k^2

• k

• 5k

• k^3

What is the remainder when k^3 - 17k + 32 is divided by k + 5?

• 5

• 0

• -8

• 8

In the third example, what indicates that x - 2 is a factor of x^4 - 16?

• The dividend is a factor

• The divisor is a factor

• The remainder is zero

• The quotient is a polynomial

What is the first step in synthetic division?

• Add the divisor to the dividend

• Subtract the divisor from the dividend

• List the coefficients of the polynomial

• Multiply the divisor by the dividend

In synthetic division, what do you do after listing the coefficients?

• Add the divisor to the first coefficient

• Multiply the divisor by the first coefficient

• Bring down the first coefficient

• Subtract the divisor from the first coefficient

What is the remainder when x^2 + 3x - 43 is divided by x + 8 using synthetic division?

• 5

• 0

• 3

• -3

According to the Remainder Theorem, what is P(3) for the polynomial x^4 + 0x^3 - 2x^2 - x + 122?

• 60

• 122

• 182

• 21

What does the Remainder Theorem state about the remainder of a polynomial division?

• It is always zero

• It is equal to the value of the polynomial at the divisor

• It is always positive

• It is equal to the leading coefficient