1. Describe the end behavior of the graph y = 2x 5 – 3x 2 + 5. 2. Sketch a graph of 3 rd degree...
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Transcript of 1. Describe the end behavior of the graph y = 2x 5 – 3x 2 + 5. 2. Sketch a graph of 3 rd degree...
1. Describe the end behavior of the graph y = 2x5 – 3x2 + 5.
2. Sketch a graph of 3rd degree with a zero at -5 (multiplicity 2) and a zero at 0 (multiplicity 1).
1
To solve, you factor the problem, each factor must be factored down to at most a quadratic.
To solve, put each factor equal to zero.
3
1. 2x5 + 24x = 14x3
2x5 – 14x3 + 24x = 0
2x(x4 – 7x2 + 12) = 0
2x(x2 – 3)(x2 – 4) = 0
2x=0 x2–3=0 x2–4=0
x=0 x2=3 x2= 4
x=±√3 x = ±2
2. 2y5 – 18y = 0
2y(y4 – 9) = 0
2y(y2 – 3)(y2 + 3) = 0
2y=0 y2–3=0 y2+3=0
y=0 y2 = 3 y2 = –3
y=±√3 y=±i√3
4
Divide 3x3 – 5x2 + 10x – 3 by 3x + 1
3x + 1 ) 3x3 – 5x2 + 10x – 3
6Algebra II
x2
3x3 + x2
-6x2+ 10x
- 2x
-6x2 - 2x
12x - 3
+ 4
12x + 4
-7
-7 . 3x + 1
+
Divide 2x3 – 7x2 – 17x – 3 by 2x + 3
2x + 3 ) 2x3 – 7x2 – 17x – 3
7
x2
2x3 + 3x2
-10x2
- 17x
- 5x
-10x2 - 15x
- 2x - 3
- 1
-2x - 3
0
Divide 4x3 + 5x2 - 3x + 10 by x2 + 3
x2 + 0x + 3 ) 4x3 + 5x2 – 3x + 10
9
4x
4x3 + 0x2 + 12x
5x2 – 15x + 10
+ 5
5X2 + 0x + 15
-15x – 5
- 15x – 5 x2 + 3
Divide -3x3 + 4x – 1 by x - 1
x - 1 ) -3x3 + 0x2 + 4x – 1
10
-3x2
-3x3+ 3x2
-3x2+ 4x
- 3x
-3x2 + 3x
1x - 1
+ 1
1x - 1
0
Divide a polynomial by a binomial
The polynomial must be in standard form
Be sure to add zeros when needed for missing placeholders
The divisor must be a linear binomial with a leading coefficient of 1 and in the form x + k
11Algebra II
12
Divide x3 + 2x2 – 3x - 6 by x + 2.
X = -2
-2 1 2 - 3 -6
times
1 0
0
-3
6
Now solve x2 – 3 = 0 to find the remaining zeros.
- + +2
13
Divide 6x3 – 19x2 + 16x - 4 by x - 2.
X = 2
2 6 -19 16 -4
times 12
6 -7
-14
2
4
0
Now solve 6x2 – 7x + 2 = 0
+ + +