Question

(26v3 + 18v + 6v4 – 8 + 13v2) = (v + 4)

Synthetic Division style.

Answer 1

The quotient is 6v³ + 2v² + 5v - 2

Explanation:

To solve using the synthetic Division

1. Arrange the variable according to its powers from greatest to smallest

2. Equate the divisor by 0 to find the value of the variable

3. Use the coefficients of the terms with it to find the quotient

Let us do that

∵ The dividend is
`26v^(3)+18v+6v^(4)-8+13v^(2)`

→ Arrange the terms from greatest power to the smallest power

∴ The dividend is
`6v^(4)+26v^(3)+13v^(2)+18v-6`

∵ The divisor is v + 4

→ Equate it by 0 to find v

∵ v + 4 = 0

→ Subtract 4 from both sides

∴ v + 4 - 4 = 0 - 4

∴ v = -4

→ Now use the coefficient of the terms with it

-4 → 6 26 13 18 -8

-------------------------------------- Multiply 6 by -4 and put the answer under 26

6 -24 13 18 -8

-------------------------------------- Add 26 and -24

6 2 13 18 -8

-------------------------------------- Multiply 2 by -4 and put the answer under 13

6 2 -8 18 -8

-------------------------------------- Add 13 and -8

6 2 5 18 -8

-------------------------------------- Multiply 5 by -4 and put the answer under 18

6 2 5 -20 -8

-------------------------------------- Add 18 and -20

6 2 5 -2 -8

-------------------------------------- Multiply -2 by -4 and put the answer under -8

6 2 5 -2 8

-------------------------------------- Add -8 and 8

6 2 5 -2 0

• The coefficients of the terms of the quotients are 6, 2, 5, -2

• The degree of the quotient is less than the degree of the dividend by 1

• The power of the greatest term of the quotient is v³

∴ The quotient is 6v³ + 2v² + 5v - 2