Use synthetic division to divide the following problems. Show your work for full credit. You may use the synthetic division template to show your work.
(x2 + 13x + 40) ÷ (x + 8) (1 point)
(2x2 – 23x + 63) ÷ (x – 7) (1 point)
Let f(x) = 4x3 + 7x2 – 13x – 3 and g(x) = x + 3. Find (1 point)
Let f(x) = 3x3 – 4x – 1 and g(x) = x + 1. Find (1 point)
Let f(x) = x4 – 8x3 + 16x2 – 19 and g(x) = x – 5. Find (1 point)
(x2 + 13x + 40) ÷ (x + 8) (1 point)
(2x2 – 23x + 63) ÷ (x – 7) (1 point)
Let f(x) = 4x3 + 7x2 – 13x – 3 and g(x) = x + 3. Find (1 point)
Let f(x) = 3x3 – 4x – 1 and g(x) = x + 1. Find (1 point)
Let f(x) = x4 – 8x3 + 16x2 – 19 and g(x) = x – 5. Find (1 point)
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x + 8 = x – (-8) so you use –8 in the "box." You just bring down, multiply by the number "under the line." Then the answer goes in the next column above the line. Add; repeat.
͢͢-͢8͢│1 13 40
......... -8 -40
─────────
..... 1.. 5.. 0
Read off the answer: 1x + 5, R=0. So just x + 5 is the answer.
You do the same thing for the 2nd one.
You have not completed the question for the others. Find WHAT? I will assume f(x)/g(x). For these you do exactly the same thing.
You just have to be careful about "missing" powers. You will need to insert the "missing" term with a zero coefficient.
For example, f(x) = 3x³ –4x – 1 is missing the x² term. So you re-write it as f(x) = 3x³ +0x² –4x – 1 and the coefficients in the synthetic division will become:
-1 ) 3 0-4 - 1 and you proceed as in the above worked example.
For the last problem with g(x) = x–5, you put +5 in the "box." Note that the linear term, 0x, is "missing."
͢͢-͢8͢│1 13 40
......... -8 -40
─────────
..... 1.. 5.. 0
Read off the answer: 1x + 5, R=0. So just x + 5 is the answer.
You do the same thing for the 2nd one.
You have not completed the question for the others. Find WHAT? I will assume f(x)/g(x). For these you do exactly the same thing.
You just have to be careful about "missing" powers. You will need to insert the "missing" term with a zero coefficient.
For example, f(x) = 3x³ –4x – 1 is missing the x² term. So you re-write it as f(x) = 3x³ +0x² –4x – 1 and the coefficients in the synthetic division will become:
-1 ) 3 0-4 - 1 and you proceed as in the above worked example.
For the last problem with g(x) = x–5, you put +5 in the "box." Note that the linear term, 0x, is "missing."
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I'll do the last one, because I'm sure others are working on the other four.
(x^4 - 8x^3 + 16x^2 - 19) / (x-5)
How many times does x go into x^4? x^3. What is x^3 times x? x^4. What is x^3 times -5? -5x^3. What is -8x^3 - -5x^3? -3x^3. How many times does x go into -3x^3? -3x^2. And so on. Just like regular long division, but with multiple terms. When done right, you'll get:
x^3 - 3x^2 + x + 5 + (6/(x-5)).
If you can't follow this, look it up on a webpage... I'm sure there's plenty of tutorial ones.
(x^4 - 8x^3 + 16x^2 - 19) / (x-5)
How many times does x go into x^4? x^3. What is x^3 times x? x^4. What is x^3 times -5? -5x^3. What is -8x^3 - -5x^3? -3x^3. How many times does x go into -3x^3? -3x^2. And so on. Just like regular long division, but with multiple terms. When done right, you'll get:
x^3 - 3x^2 + x + 5 + (6/(x-5)).
If you can't follow this, look it up on a webpage... I'm sure there's plenty of tutorial ones.
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x^4 – 8*x^3 + 16*x^2 + 0*x – 19 Ix - 5
......................................…
......................................… - 3*x^2 + x + 5
-x^4 +5*x^3
------------------------
- 3*x^3 + 16*x^2
+3*x^3 - 15*x^2
------------------------
x^2 + 0*x
-x^2 + 5*x
---------------
-5*x - 19
5*x + 25
-------------
6
Answer = x^3 - 3*x^2 + x + 5 + 6/(x-5)
......................................…
......................................… - 3*x^2 + x + 5
-x^4 +5*x^3
------------------------
- 3*x^3 + 16*x^2
+3*x^3 - 15*x^2
------------------------
x^2 + 0*x
-x^2 + 5*x
---------------
-5*x - 19
5*x + 25
-------------
6
Answer = x^3 - 3*x^2 + x + 5 + 6/(x-5)