Simplifying Polynomials
What are the degree and leading coefficient of the polynomial shown when in standard form?
x2 + 4x - 3x4 + 2 - 7x3
Degree: 4
Leading Coefficient: -3
Factor
x2 + 5x + 6
(x + 3)(x + 2)
Factor
x2 - 1
(x + 1)(x - 1)
Factor out a GCF
24x5 + 20x
4x(6x4 + 5)
Identify the vertex of the function given in vertex form below.
f(x) = (x - 7)2 + 15
(7, 15)
Write the expression below as a polynomial in standard form.
4 - x2 +2x3 + 6x
2x3 - x2 + 6x + 4
Factor
x2 - 10x + 16
(x - 8)(x - 2)
Factor
x2 - 49
(x + 7)(x - 7)
Factor completely.
2x2 - 12x + 16
2(x - 4)(x - 2)
Write a function in vertex form given the vertex below.
(3, -2)
Answers vary
Ex: f(x) = (x - 3)2 - 2
How can you tell if an expression represents a polynomial?
When simplified, all terms contain exponents that are non-negative integers.
x2 - x - 12
(x - 4)(x + 3)
Factor
4x2 - 25
(2x + 5)(2x - 5)
Factor completely
3x3 + 12x2 - 63x
3x(x + 7)(x - 3)
Use the method of completing the square to write the function below in vertex form.
f(x) = x2 + 8x - 1
f(x) = (x + 4)2 - 17
Write the expression below as a polynomial in standard form.
(x + 4)(2x - 3)
2x2 + 5x - 12
Factor
x2 + 5x - 84
(x + 12)(x - 7)
Factor
9x2 - 16
(3x + 4)(3x - 4)
Factor completely
5x2 - 20
5(x + 2)(x - 2)
Use the method of completing the square to identify the vertex of the function below.
f(x) = x2 - 24x + 4
(12, -100)
Write the expression below as a polynomial in standard form.
(x - 3)2 + 1
x2 - 6x + 10
Factor
x4 + 3x2 - 40
(x2 + 8)(x2 - 5)
Factor
16x6 - 81
(4x3 + 9)(4x3 - 9)
Factor completely
2x4 - 10x2 + 8
2(x + 2)(x - 2)(x + 1)(x - 1)
f(x) = x2 - 30x - 27
(15, -252)