Question

question
factor completely.
5x² - 12x + 7
answer attempt 1 out of 2

Explanation:

Step1: Identify the quadratic form

We have a quadratic trinomial \(5x^2 - 12x + 7\). For a quadratic \(ax^2+bx + c\) (\(a = 5\), \(b=- 12\), \(c = 7\)), we use the factoring method by finding two numbers that multiply to \(a\times c=5\times7 = 35\) and add up to \(b=-12\). The numbers are \(-5\) and \(-7\) since \((-5)\times(-7)=35\) and \(-5 + (-7)=-12\).

Step2: Rewrite the middle term

Rewrite \(-12x\) as \(-5x-7x\):
\[5x^2-5x - 7x + 7\]

Step3: Group and factor

Group the first two terms and the last two terms:
\((5x^2 - 5x)+(-7x + 7)\)
Factor out the GCF from each group:
\(5x(x - 1)-7(x - 1)\)

Step4: Factor out the common binomial

Now, factor out \((x - 1)\):
\((5x - 7)(x - 1)\)

Answer:

\((5x - 7)(x - 1)\)