Question

Divide. Divide \(b^{2}-7 b-12\) by \(4 b+4\)

Short answer

The division result is \(\frac{b}{4} - \frac{7}{4} - \frac{12}{(4b+4)}\)

Step-by-step solution

Factorize the denominator

Factorize the denominator \(4b+4\), this can be rewritten as \(4*(b+1)\). This is done by identifying the greatest common factor of the binomial, which is 4 in this case.

Divide each term

Now we divide each term of the numerator \(b^{2}-7b-12\) by \(4*(b+1)\). We get \(\frac{b^{2}}{4*(b+1)} - \frac{7b}{4*(b+1)} - \frac{12}{4*(b+1)}\)

Simplify

The result can be further simplified to: \(\frac{b}{4} - \frac{7}{4} - \frac{12}{(4b+4)}\).

Final Answer

The simplified version of the polynomial division is \(\frac{b}{4} - \frac{7}{4} - \frac{12}{(4b+4)}\).