Question

Using synthetic division, what is the quotient (2x3 + 3x − 22) ÷ (x − 2)? (16 points)

Answer 1

2x³ + 0x² + 3x - 22

2 | 2 + 0 + 3 - 22
... . . .+ 4 + 8 + 22
.. . 2 + 4 + 11 + 0

Therefore, the quotient is 2x² + 4x + 11.

Answer 2

( 2x² + 4x + 11 )

Explanation:

We have to find the quotient by synthetic division

( 2x³ + 3x - 22 ) ÷ ( x - 2 )

Numerator can be written as 2x³ + 0.x² + 3x - 22

Since ( x - 2 ) is a zero factor of this equation then we have to divide the coefficients by x = 2

2 | 2 0 3 -22

- 4 8 22

2 4[(0+4)=4] 11[(3+8)=11] 0[(-22+22)=20]

Now the quotient will be ( 2x² + 4x + 11 )