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(7x^2 + 19x - 36) divided by (x+4)

Sagot :

Rvkacademicidn

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]



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