REMAINDER THEOREM, FACTOR THEOREM AND THE RATIONAL ROOT THEOREM

Using factor theorem, find the roots of the polynomial f(x) = x^3 - 2x^2 - 5x + 6.

• x = 0, x = 1, and x = -6

• x = 4, x = -2, and x = 1

• x = -3, x = 2, and x = 5

• The roots of the polynomial f(x) = x^3 - 2x^2 - 5x + 6 are x = 2, x = -1, and x = 3.

Using factor theorem, find the roots of the polynomial f(x) = 2x^3 - 5x^2 - 3x + 2.

• x = -4, x = 1, and x = 3

• x = -3, x = 0, and x = 4

• x = -2, x = 0, and x = 3

• The roots of the polynomial f(x) = 2x^3 - 5x^2 - 3x + 2 are x = -1, x = 1, and x = 2.

Using factor theorem, find the roots of the polynomial f(x) = x^4 - 5x^3 + 8x^2 - 4x - 4.

• The roots are x = -2, x = 3, x = 4, and x = 5

• The roots are x = 0, x = 1, x = 2, and x = 3

• The roots are x = -1, x = 1, x = 2, and x = 2

• The roots are x = -1, x = 0, x = 1, and x = 3

Using factor theorem, find the roots of the polynomial f(x) = 3x^3 - 7x^2 + 4x - 8.

• The roots of the polynomial f(x) = 3x^3 - 7x^2 + 4x - 8 are x = 2, x = -1, and x = 4/3.

• x = 1, x = -3, and x = 5

• x = 0, x = -4, and x = 2

• x = 5, x = -2, and x = 1/3

Apply remainder theorem to find the remainder when f(x) = 2x^3 - 5x^2 + 3x - 7 is divided by (x - 2).

• 2x^3 - 5x^2 + 3x - 7

• -11

• 5

• 0

Apply remainder theorem to find the remainder when f(x) = x^4 - 3x^3 + 2x^2 - 5x + 6 is divided by (x + 1).

• 0

• 2

• 5

• -3

Apply remainder theorem to find the remainder when f(x) = 3x^3 - 7x^2 + 4x - 8 is divided by (x - 3).

• The remainder is 5

• The remainder is 0

• The remainder is 13

• The remainder is -2

Solve the problem using factor theorem: If f(x) = x^3 - 3x^2 - 4x + 12, find all the roots of the polynomial.

• The roots of the polynomial are x = 1, x = 5, and x = -4.

• The roots of the polynomial are x = -2, x = 2, and x = 3.

• The roots of the polynomial are x = -1, x = 2, and x = 6.

• The roots of the polynomial are x = 0, x = 4, and x = -3.

Solve the problem using factor theorem: If f(x) = 2x^3 - 5x^2 + 3x - 7, find all the roots of the polynomial.

• The roots of the polynomial are x = -1, x = 1, and x = 7/2.

• The roots of the polynomial are x = 2, x = 5, and x = -7

• The roots of the polynomial are x = 0, x = -3, and x = 4

• The roots of the polynomial are x = 3, x = -4, and x = 6

Solve the problem using factor theorem: If f(x) = x^4 - 3x^3 + 2x^2 - 5x + 6, find all the roots of the polynomial.

• The roots are x = 5, x = -6, x = 7, and x = -8

• The roots are x = 0, x = 4, x = -3, and x = 2

• The roots are x = 2, x = -1, x = 4, and x = -3

• The roots are x = 1, x = -2, x = 3, and x = -1