The quotient and remainder when the first polynomial is divided by the second are -4w^2 - 7w - 21 and -71 respectively
How to determine the quotient and remainder when the first polynomial is divided by the second?
The polynomials are given as:
-4w^3 + 5w^2 - 8, w - 3
Set the divisor to 0.
So, we have
w - 3 = 0
Add 3 to both sides
w = 3
Substitute w = 3 in -4w^3 + 5w^2 - 8 to determine the remainder
-4(3)^3 + 5(3)^2 - 8
Evaluate the expression
-71
This means that the remainder when -4w^3 + 5w^2 - 8 is divided by w - 3 is -71
The quotient (Q) is calculated as follows:
Q = [-4w^3 + 5w^2 - 8]/[w - 3]
The numerator can be expressed as follows:
Numerator = -4w^3 + 5w^2 - 8
Subtract the remainder.
So, we have:
Numerator = -4w^3 + 5w^2 - 8 + 71
This gives
Numerator = -4w^3 + 5w^2 + 61
So, the quotient becomes
Q = [-4w^3 + 5w^2 + 61]/[w - 3]
Expand
Q = [(w - 3)(-4w^2 - 7w - 21)]/[w - 3]
Evaluate
Q = -4w^2 - 7w - 21
Hence, the quotient and remainder when the first polynomial is divided by the second are -4w^2 - 7w - 21 and -71 respectively
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