Answer:
See below.
Step-by-step explanation:
I'll show you step by step how to do the synthetic division.
You are dividing polynomial -6x^4 + 22x^3 + 3x^2 + 15x + 20 by x - 4.
From the polynomial, you only need the coefficients in descending order of degree as they are written.
-6 22 3 15 20
In synthetic division, you divide by x - b. You are dividing by x - 4, so b = 4.
The 4 is written to the left of the coefficients of the polynomial.
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4 | -6 22 3 15 20
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This is what the setup looks like. You can see it in the problem you were given.
The first step is to just copy the leftmost coefficient straight down to below the line.
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4 | -6 22 3 15 20
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-6
Now multiply b, which is 4, by -6 and write it above and to the right.
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4 | -6 22 3 15 20
-24
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-6
Add 22 and -24 and write it next to -6.
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4 | -6 22 3 15 20
-24
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-6 -2
Multiply 4 by -2 and write it above and to the right. Add vertically.
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4 | -6 22 3 15 20
-24 -8
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-6 -2 -5
Multiply 4 by -5 and write it above and to the right. Add vertically.
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4 | -6 22 3 15 20
-24 -8 -10
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-6 -2 -5 -5
Multiply 4 by -5 and write it above and to the right. Add vertically.
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4 | -6 22 3 15 20
-24 -8 -10 -20
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-6 -2 -5 -5 0
The 4 numbers in the second line are the coefficients of the quotient.
The quotient is 1 degree less than the original polynomial.
The quotient is: -24x^3 - 8x^2 - 10x - 20
The last number on the third line is the remainder. Since here the reminder is zero, that means that this division has no remainder. The remainder is 0/(x - 4)
Fill in the boxes with:
-24, -8, -10, -20
-6, -2, -5, -5, 0
-24x^3 - 8x^2 - 10x - 20
0
