Factor Theorem and Long Division

Apply long division to find the remainder when dividing 2x^4 - 5x^3 + 3x^2 - 7x + 1 by x - 3.

• The remainder is -3

• The remainder is 25

• The remainder is 145

• The remainder is 10

Apply long division to divide 3x^3 - 6x^2 + 9x - 12 by x + 2.

• The quotient is 3x^2 - 12x + 33 with a remainder of -78.

• The quotient is 4x^2 - 16x + 44 with a remainder of -112.

• The quotient is 2x^2 - 8x + 22 with a remainder of -56.

• The quotient is 5x^2 - 20x + 55 with a remainder of -110.

Apply long division to divide 4x^4 - 8x^3 + 12x^2 - 16x + 20 by 2x - 4.

• x^3 - 2x^2 + 4x - 6

• 4x^3 - 8x^2 + 12x - 16

• 3x^3 - 6x^2 + 9x - 10

• 2x^3 - 4x^2 + 8x - 12

Apply long division to find the quotient and remainder when dividing 5x^5 - 10x^4 + 15x^3 - 20x^2 + 25x - 30 by x - 1.

• The quotient is 5x^4 - 5x^3 + 10x^2 - 10x + 15 and the remainder is 30

• The quotient is 5x^4 - 5x^3 + 10x^2 - 10x + 15 and the remainder is -15.

• The quotient is 5x^3 - 5x^2 + 10x - 10 and the remainder is 15

• The quotient is 5x^5 - 10x^4 + 15x^3 - 20x^2 + 25x - 30 and the remainder is 0

Use the factor theorem to determine if x - 3 is a factor of 2x^3 - 5x^2 + 3x - 6.

• No

• Not sure

• Yes

• Maybe

Use the factor theorem to determine if x + 2 is a factor of 3x^4 + 2x^3 - 5x^2 + 4x - 8.

• Yes

• Not sure

• No

• Maybe

Use the factor theorem to determine if x + 4 is a factor of 5x^6 + 3x^5 - 2x^4 + 7x^3 - 4x^2 + 9x - 6.

• Not sure

• Yes

• No

• Maybe

Use the factor theorem to determine if x - 2 is a factor of 6x^7 - 5x^6 + 4x^5 - 3x^4 + 2x^3 - x^2 + 8x - 7.

• Maybe

• Yes

• Not sure

• No

Is (x-3) a factor of
(x³ - 3x² + 2x + 2)?

• Yes

• No

4x⁴+4x³-9x²-x+2 ÷ x-1

• 4x³+8x²-7x-2

• 4x³+19x²-x-2

• 4x³+8x²-x-9

• 4x³+8x²-x-2