What is syntheticdivision ((3x^4-2x^3-10x^2+15))/((x-2)) ?

The solution to syntheticdivision ((3x^4-2x^3-10x^2+15))/((x-2)) is 3x^3+4x^2-2x-4+7/((x-2))

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Divide Using Synthetic Division (3x^4-2x^3-10x^2+15)/(x-2)

synthetic division

\frac{( 3 x ^{4} - 2 x ^{3} - 10 x ^{2} + 15 )}{( x - 2 )}

3 x^{3} + 4 x^{2} - 2 x - 4 + \frac{7}{( x - 2 )}

Solution steps

\frac{( 3 x ^{4} - 2 x ^{3} - 10 x ^{2} + 15 )}{( x - 2 )}

Coefficients of the numerator polynom

3 - 2 - 1015

Find the zeros of the denominator:

x = 2

Write the problem in synthetic division format

2 ¦ 3 - 2 - 10015 ¦

Carry down the leading coefficient, unchanged, to below the division symbol

2 ¦ 3 - 2 - 10015 ¦ 3

Multiply the carry-down value by the zero of the denominator, and carry the result up into the next column:

3 \cdot 2 = 6

2 ¦ 3 - 2 - 10015 ¦ \underline{6} 3

Add down the column:

- 2 + 6 = 4

2 ¦ 3 - 2 - 10015 ¦ \underline{6} 34

Multiply the carry-down value by the zero of the denominator, and carry the result up into the next column:

4 \cdot 2 = 8

2 ¦ 3 - 2 - 10015 ¦ \underline{68} 34

Add down the column:

- 10 + 8 = - 2

2 ¦ 3 - 2 - 10015 ¦ \underline{68} 34 - 2

Multiply the carry-down value by the zero of the denominator, and carry the result up into the next column:

(- 2) 2 = - 4

2 ¦ 3 - 2 - 10015 ¦ \underline{68 - 4} 34 - 2

Add down the column:

0 - 4 = - 4

2 ¦ 3 - 2 - 10015 ¦ \underline{68 - 4} 34 - 2 - 4

Multiply the carry-down value by the zero of the denominator, and carry the result up into the next column:

(- 4) 2 = - 8

2 ¦ 3 - 2 - 10015 ¦ \underline{68 - 4 - 8} 34 - 2 - 4

Add down the column:

15 - 8 = 7

2 ¦ 3 - 2 - 10015 ¦ \underline{68 - 4 - 8} 34 - 2 - 47

The last carry-down value is the remainder

7

Write the result in polynom format

3 x^{3} + 4 x^{2} - 2 x - 4 + \frac{7}{( x - 2 )}

x, \frac{1}{3} x = 9

1.06 \cdot 1 0^{- 1} 0

x, ∣ 3 x - 1 ∣ = 2

- \frac{225}{49}

0/2

What is syntheticdivision ((3x^4-2x^3-10x^2+15))/((x-2)) ?
The solution to syntheticdivision ((3x^4-2x^3-10x^2+15))/((x-2)) is 3x^3+4x^2-2x-4+7/((x-2))