Answer:
[tex]7x - 9[/tex]
Step-by-step explanation:
We are asked to calculate
[tex](7x^2 + 19x - 36) \div (x + 4)[/tex]
Let's factor out the numerator [tex]7x^2+19x-36[/tex] as follows:
- Break the expression into two groups:
[tex]=\left(7x^2-9x\right)+\left(28x-36\right)[/tex] - Factor out x from [tex]\left(7x^2-9x\right):[/tex]
[tex]x(7x - 9)[/tex] - Factor out 4 from [tex]28x-36[/tex]
[tex]4\left(7x-9\right)[/tex] - Original numerator expression becomes
[tex]x\left(7x-9\right)+4\left(7x-9\right)[/tex] - Factor out common term [tex]7x-9[/tex]:
[tex]\left(7x-9\right)\left(x+4\right)[/tex]
- Now the division becomes:
[tex]\dfrac{\left(7x-9\right)\left(x+4\right)}{x+4}[/tex] - The x + 4 term on numerator and denominator cancel out giving the final result as
[tex]7x - 9[/tex]
