Question

question 1-2
factor completely.
$2a^2 + 5a - 7$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(2\times(-7)= -14\) and add up to \(5\). The numbers are \(7\) and \(-2\) since \(7\times(-2)=-14\) and \(7 + (-2)=5\).

Step2: Rewrite the middle term

Rewrite \(5a\) as \(7a-2a\) in the expression \(2a^{2}+5a - 7\), so we get \(2a^{2}+7a-2a - 7\).

Step3: Group and factor

Group the first two terms and the last two terms: \((2a^{2}+7a)+(-2a - 7)\). Factor out the greatest common factor from each group: \(a(2a + 7)-1(2a + 7)\).

Step4: Factor out the common binomial

Now, factor out the common binomial \((2a + 7)\) to get \((2a + 7)(a - 1)\).

Answer:

\((2a + 7)(a - 1)\)