To find the quotient represented by the expression, we need to perform polynomial long division.
8w^2 - 20w - 12 / 2w + 1
First, divide the 2w into 8w^2 to get 4w. This gives us 4w(2w + 1) = 8w^2 + 4w.
Next, multiply 4w by 2w and 1 to get 8w + 4. Subtract this from the original expression:
(8w^2 - 20w - 12) - (8w + 4) = -24w - 16
Since the degree of -24w is lower than the degree of 2w, we stop here. The quotient is 4w - 2 with a remainder of -24w - 16.
Therefore, the quotient represented by the expression 8w^2 - 20w - 12 / 2w + 1 is 4w - 2.
What is the quotient represented by the expression
8w^2 - 20w -12/2w+1 for all values of w where the
Expression is defined
4w +12
4W-12
W-3
W+3
3 answers
That’s not an option
Apologies for the confusion. Let's try solving the division again:
\[
\frac{{8w^2 - 20w - 12}}{{2w + 1}}
\]
Dividing \(8w^2\) by \(2w\) gives \(4w\). Multiply \(4w\) by \(2w + 1\) to get \(4w(2w + 1) = 8w^2 + 4w\).
Subtract \(8w^2 + 4w\) from \(8w^2 - 20w - 12\) to get \(-24w - 12\).
Now, divide \(-24w\) by \(2w\) to get \(-12\). This gives us \(-12(2w + 1) = -24w - 12\).
The division result is \(4w - 12\).
Therefore, the quotient represented by the expression is \(4w - 12\).
\[
\frac{{8w^2 - 20w - 12}}{{2w + 1}}
\]
Dividing \(8w^2\) by \(2w\) gives \(4w\). Multiply \(4w\) by \(2w + 1\) to get \(4w(2w + 1) = 8w^2 + 4w\).
Subtract \(8w^2 + 4w\) from \(8w^2 - 20w - 12\) to get \(-24w - 12\).
Now, divide \(-24w\) by \(2w\) to get \(-12\). This gives us \(-12(2w + 1) = -24w - 12\).
The division result is \(4w - 12\).
Therefore, the quotient represented by the expression is \(4w - 12\).
1 answer