Factor 4x^2+19x-5

Problem

4*x2+19*x−5

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=4 b=19 and c=−5

2. Find two numbers that multiply to a⋅c=4⋅(−5)=−20 and add to b=19

3. Determine the pair of numbers, which are 20 and −1 since 20⋅(−1)=−20 and 20 + (-1) = 19$.

4. Rewrite the middle term 19*x using the two numbers found: 20*x−x

4*x2+20*x−x−5

5. Factor by grouping the first two terms and the last two terms.

(4*x2+20*x)−(x+5)

6. Factor out the greatest common factor from each group.

4*x*(x+5)−1*(x+5)

7. Factor out the common binomial (x+5)

(4*x−1)*(x+5)

Final Answer

4*x2+19*x−5=(4*x−1)*(x+5)

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