Topic 1: Be able to combine functions and determine the resulting function.
Topic 2: Be able to find the product of functions and determine the resulting function.Topic 3: Be able to perform multiple operations on functions.
Topic 4: Determine if two given functions represent equivalent forms of the same function..
I. Multiplying Polynomial Functions
Example 1: 3(2x + 6)
(3)(2x) + (3)(6)
6x + 18
Example 2: -5(3x2 – 6x + 4)
(-5)(3x2) + (-5)(– 6x) + (-5)(4)
-15x2 + 30x - 20
Concept: Constant x Linear = Linear
Concept: Constant x Quadratic = Quadratic
Example 3: 3(-4x3 - 7x2 + x + 2)
(3)(-4x3) + (3)(– 7x2) + (3)(x) + (3)(2)
-12x3 - 21x2 + 3x + 6
Concept: Constant x Cubic = Cubic
I. Multiplying Polynomial Functions
Example 4: (3x + 4)(2x - 1)
(3x)(2x - 1) + (4)(2x - 1)
(3x)(2x ) + (3x)(-1) (4)(2x ) + (4)(-1)+
6x2 - 3x + 8x - 4
6x2 + 5x - 4
3x 4
2x
-1
6x2 8x
-3x -4
6x2 + 5x - 4
Concept: Linear x Linear= Quadratic
Example 5: (-2x - 3)(6x + 7)
(-2x)(6x + 7) + (-3)(6x + 7)
(-2x)(6x ) + (-2x)(7) (-3)(6x ) + (-3)(7)+
-12x2 - 14x - 18x - 21
-12x2 - 32x - 21
-2x -3
6x
7
-12x2 -18x
-14x -21
-12x2 -32x - 21
Concept: Linear x Linear= Quadratic
I. Multiplying Polynomial Functions
Example 6: (x - 3)(2x2 – 7x + 5)
(x)(2x2 – 7x + 5) + (-3)(2x2 - 7x + 5)
(x)(2x2 )+ (x)(– 7x) + (x)( 5) (-3)(2x2 )+ (-3)(– 7x) + (-3)( 5) +
2x3 – 7x2 + 5x -6x2 + 21x - 15
2x3 – 13x2 + 26x - 15
2x2 -7x 5
x
-3
2x3 -7x2 5x
-6x2 21x -15
2x3 – 13x2 + 26x - 15
Concept: Linear x Quadratic = Cubic
I. Multiplying Polynomial Functions
Example 7: (5x2 - 3)(3x2 – 4x + 2)
5x2 0x -3
3x2
-4x
2
15x4 0x3 -9x2
-20x3 0x2 12x
10x2 0x -6
15x4 - 20x3 + x2 + 12x - 6
Concept: Quadratic x Quadratic = Quartic
Special Note: When setting up your table, be sure that you account for all terms of the polynomial.