Question

factor each completely. 2r² + 11r + 12 options: 2(r + 3)(r - 4), (3r + 7)(r - 8), (2r + 3)(r + 4), (5r - 6)(r - 7), (2r + 5)(r - 7)

Explanation:

Step1: Expand each option

For option 1: \(2(r + 3)(r - 4)=2(r^{2}-4r + 3r-12)=2(r^{2}-r - 12)=2r^{2}-2r - 24\)
For option 2: \((3r + 7)(r - 8)=3r^{2}-24r+7r - 56=3r^{2}-17r - 56\)
For option 3: \((2r + 3)(r + 4)=2r^{2}+8r+3r + 12=2r^{2}+11r + 12\)
For option 4: \((5r - 6)(r - 7)=5r^{2}-35r-6r + 42=5r^{2}-41r + 42\)
For option 5: \((2r + 5)(r - 7)=2r^{2}-14r+5r - 35=2r^{2}-9r - 35\)

Step2: Compare with the original quadratic

The original quadratic is \(2r^{2}+11r + 12\), which matches the expansion of \((2r + 3)(r + 4)\)

Answer:

(2r + 3)(r + 4)