1.
Factor completely: \(2n^2+5n-12\)
Solution: 2×(-12)=-24. Numbers 8 and -3 add to 5. Therefore \((2n-3)(n+4)\).
2.
Factor: \(121a^2+110a+25\)
Solution: Perfect square trinomial: \((11a+5)^2\).
3.
Factor the following: \(-\frac{1}{3}x^2-2x-3\)
Solution: Factor out \(-\frac13\): \(-\frac13(x^2+6x+9)=-\frac13(x+3)^2\).
4.
Find all three factors of \(6x^2+9xy-6y^2\).
Solution: Factor out 3 first, then factor the trinomial. Result: \(3(x+2y)(2x-y)\).
5.
Factor completely: \(4x^2+23x+15\)
Solution: 4×15=60. Numbers 20 and 3 add to 23. Therefore \((4x+3)(x+5)\).
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