Factor 4x^2+8x-5

Problem

4*x2+8*x−5

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=4 b=8 and c=−5

2. Find two numbers that multiply to a⋅c=4⋅(−5)=−20 and add to b=8

3. Determine the pair of numbers, which are 10 and −2 because 10⋅(−2)=−20 and 10 + (-2) = 8$.

4. Rewrite the middle term 8*x using the two numbers found: 10*x−2*x

4*x2+10*x−2*x−5

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

2*x*(2*x+5)−1*(2*x+5)

6. Factor out the common binomial (2*x+5)

(2*x+5)*(2*x−1)

Final Answer

4*x2+8*x−5=(2*x+5)*(2*x−1)

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