Summative Polynomials

Which of the following is a polynomial?

• iii only

• i and ii

• ii only

• i and iii

Ryan divided (7x³ – 10x + 11x² – 5) by (x + 3) and obtained –317 as remainder. Here is his solution. What is his error?

i. He did not change the sign of the divisor.

ii. He did not arrange the terms of the polynomial in decreasing powers of x.

iii. The sum in the third row is incorrect.

iv. The numerical coefficients in the first row were not properly arrange.

• i only

• ii only

• ii and iv only

• i and iii only

If (x⁴ – 5x² +4) is divided by (x - 2) using synthetic division, the numbers in the first row would be

• 1 -5 4

• 1 0 -5 4

• 1 0 -5 0 4

• 1 0 -5 4 0

Which is the quotient?

• 5x + 5

• 25x² – 50x + 25

• 5x – 5

• 0

Which is the dividend?

• 5x + 5

• 25x² – 50x + 25

• 5x – 5

• 0

Using the Remainder Theorem, what is the remainder when (3x³ - 2x² - 150) is divided by (x - 4) ?

• 15

• 5

• 10

• 1

1.) If P(-2) = 0, which of the following statements is true about P(x)?

• (x+2) is a factor of P(x)

• 2 is a root of P(x)=0

• P(x)=0, has two negative roots

• P(0) = -2

What is the remainder when (x³ - x² + x - 50) is divided by (x - 4)?

• -15

• -50

• -64

• -46

Which of the following binomials is a factor of the quadratic x² + 2x - 3?

• x - 1

• x + 1

• x + 2

• x - 2

1.) Using the Rational Root Theorem, what are the possible roots of the polynomial equation 3x⁴ - 16x³ + 21x² + 4x - 12 = 0?

• ±1

• ±2

• ±4

• All of the above