The polynomial p(x) in the form of p(x) = d(x)q(x) + r(x) is
p(x) = (x + 1)(-2x - 2) + 5
Step-by-step explanation:
(3 - 4x - 2x²) ÷ (x + 1) ⇒ rearrange the terms from greatest power to smallest power
(-2x² - 4x + 3) ÷ (x + 1)
In the synthetic division we use the coefficient of the dividend
with one factor of the function
Equate the divisor by 0 to find the value of x
∵ x + 1 = 0 ⇒ x = -1
Step 1 : Write down the coefficients of the f(x) , put x = -1 at the left
-1 -2 -4 3
_____________
Step 2 : Bring down the first coefficient to the bottom row.
-1 -2 -4 3
________________
-2
Step 3 : Multiply it by -1, and carry the result into the next column.
-1 -2 -4 3
_____2__________
-2
Step 4 : Add down the column
-1 -2 -4 3
_____2__________
-2 -2
Step 5 : Multiply it by -1, and carry the result into the next column
-1 -2 -4 3
_____2____2____
-2 -2
Step 6 : Add down the column
-1 -2 -4 3
_____2____2______
-2 -2 5
∴ The quotient is (-2x - 2) and the remainder is 5
The factors of (-2x² - 4x + 3) are:
d(x) = (x + 1) and q(x) = (-2x - 2)
The remainder r(x) = 5
The polynomial p(x) in the form of p(x) = d(x)q(x) + r(x) is
p(x) = (x + 1)(-2x - 2) + 5
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