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Exercise

$f\left(x\right)=\frac{8-x}{x^2-7x+12}$

Step-by-step Solution

1

Factor the trinomial $x^2-7x+12$ finding two numbers that multiply to form $12$ and added form $-7$

$\begin{matrix}\left(-3\right)\left(-4\right)=12\\ \left(-3\right)+\left(-4\right)=-7\end{matrix}$
2

Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values

$f\left(x\right)=\frac{8-x}{\left(x-3\right)\left(x-4\right)}$

Final answer to the exercise

$f\left(x\right)=\frac{8-x}{\left(x-3\right)\left(x-4\right)}$

Try other ways to solve this exercise

  • Choose an option
  • Write in simplest form
  • Solve by quadratic formula (general formula)
  • Find the derivative using the definition
  • Simplify
  • Find the integral
  • Find the derivative
  • Factor
  • Factor by completing the square
  • Find the roots
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Main Topic: Factorization

In mathematics, factorization or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original.

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