Question

question
factor completely:
\\(x^2(4x^2 - 7) + 3x(4x^2 - 7) - 70(4x^2 - 7)\\)

Explanation:

Step1: Factor out the common binomial factor

Notice that each term has a common factor of \((4x^{2}-7)\). Factor it out:
\[
(4x^{2}-7)(x^{2}+3x - 70)
\]

Step2: Factor the quadratic trinomial

Now, factor the quadratic \(x^{2}+3x - 70\). We need two numbers that multiply to \(-70\) and add to \(3\). The numbers are \(10\) and \(-7\) because \(10\times(-7)=-70\) and \(10+(-7)=3\). So,
\[
x^{2}+3x - 70=(x + 10)(x - 7)
\]

Step3: Combine the factors

Putting it all together, the completely factored form is:
\[
(4x^{2}-7)(x + 10)(x - 7)
\]

Answer:

\((4x^{2}-7)(x + 10)(x - 7)\)