The polynomial in the form p(x) = d(x)q(x) + r(x) is
p(x) = (x + 3)(4x - 17) + 54
Step-by-step explanation:
In synthetic division we equate the divisor by 0 to find the value of x
x + 3 = 0 ⇒ x = -3
Step 1 : Write down the coefficients of the f(x) , put x = -3 at the left
-3 4 -5 3
____________
Step 2 : Bring down the first coefficient to the bottom row.
-3 4 -5 3
________________
4
Step 3 : Multiply it by -3, and carry the result into the next column.
-3 4 -5 3
____-12________
4
Step 4 : Add down the column
-3 4 -5 3
____-12________
4 -17
Step 5 : Multiply it by -3, and carry the result into the next column
-3 4 -5 3
_____-12___51_____
4 -17
Step 6 : Add down the column
-3 4 -5 3
_____-12____51___
4 -17 54
The quotient is (4x - 17) and the remainder is 54
The factors of (4x² - 5x + 3) are:
d(x) = (x + 3) and q(x) = (4x - 17)
The remainder r(x) = 54
The polynomial in the form p(x) = d(x)q(x) + r(x) is
p(x) = (x + 3)(4x - 17) + 54
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