Mastering Polynomials

Factor the polynomial: x^2 - 5x + 6.

• (x + 2)(x + 3)

• (x - 1)(x - 6)

• (x - 2)(x - 3)

• (x - 4)(x - 2)

Evaluate the polynomial: P(x) = 2x^3 - 3x + 1 at x = 2.

• 11

• 5

• 9

• 15

Graph the polynomial function: f(x) = x^2 - 4.

• The vertex of the graph is at (2, 0) and opens downwards.

• The graph of f(x) = x^2 - 4 is a parabola opening upwards with vertex at (0, -4) and x-intercepts at (-2, 0) and (2, 0).

• The x-intercepts are at (-1, 0) and (1, 0).

• The graph of f(x) = x^2 - 4 is a straight line with a slope of 2.

Factor the polynomial: 3x^2 + 12x + 12.

• 3(x + 2)^2

• 3(x + 4)(x + 1)

• (3x + 6)(x + 2)

• (x + 3)(3x + 4)

Evaluate the polynomial: Q(x) = x^4 - 2x^2 + 1 at x = -1.

• 1

• 2

• 0

• -1

Graph the polynomial function: g(x) = -x^3 + 3x.

• The graph of g(x) = -x^3 + 3x has a local minimum at (0, 0) and is symmetric about the x-axis.

• The graph of g(x) = -x^3 + 3x is a cubic curve with a local maximum at (0, 0) and symmetric behavior about the y-axis.

• The graph of g(x) = -x^3 + 3x is a quadratic curve with a minimum at (0, 0).

• The graph of g(x) = -x^3 + 3x is a linear function with no maximum points.

Factor the polynomial: x^2 + 7x + 10.

• (x + 1)(x + 10)

• (x + 3)(x + 4)

• (x + 2)(x + 5)

• (x - 2)(x - 5)

Evaluate the polynomial: R(x) = 5x^2 - 4x + 3 at x = 0.

• 0

• 5

• 3

• -4

Graph the polynomial function: h(x) = 2x^4 - x^2 + 1.

• The graph of h(x) = 2x^4 - x^2 + 1 is a quartic polynomial that opens upwards with a minimum point and no x-intercepts.

• The graph of h(x) = 2x^4 - x^2 + 1 is a linear function with one x-intercept.

• The graph of h(x) = 2x^4 - x^2 + 1 has two x-intercepts and no minimum point.

• The graph of h(x) = 2x^4 - x^2 + 1 is a cubic polynomial that opens downwards.

Factor the polynomial: 4x^2 - 16.

• 4(x - 2)(x + 2)

• 4(x - 4)(x + 4)

• 2(x - 2)(x + 2)

• (x - 2)(x - 2)