Question

factor completely.
(2q^2 - q - 10)

Explanation:

Step1: Identify coefficients and constant

We have the quadratic expression \(2q^{2}-q - 10\). The coefficient of \(q^{2}\) is \(a = 2\), the coefficient of \(q\) is \(b=- 1\) and the constant term \(c=-10\).

Step2: Find two numbers

We need to find two numbers \(m\) and \(n\) such that \(m\times n=a\times c = 2\times(- 10)=-20\) and \(m + n=b=-1\). The numbers are \(-5\) and \(4\) since \(-5\times4=-20\) and \(-5 + 4=-1\).

Step3: Split the middle term

Rewrite the middle term using these two numbers:
\(2q^{2}-5q + 4q-10\)

Step4: Group and factor

Group the first two terms and the last two terms:
\((2q^{2}-5q)+(4q - 10)\)
Factor out the greatest common factor from each group:
\(q(2q - 5)+2(2q - 5)\)

Step5: Factor out the common binomial

Now, factor out the common binomial \((2q - 5)\):
\((2q - 5)(q + 2)\)

Answer:

\((2q - 5)(q + 2)\)