1.
Factor completely: \(2x^2-16xy+30y^2\)
Solution: Factor out 2: \(2(x^2-8xy+15y^2)\)=\(2(x-5y)(x-3y)\).
2.
Factor completely: \(3x^3-48x^2-108x\)
Solution: Factor out \(3x\): \(3x(x^2-16x-36)\). Since \((-18)(2)=-36\) and sum = -16, answer is \(3x(x-18)(x+2)\).
3.
Factor: \(7n^2-14n-105\)
Solution: Factor out 7: \(7(n^2-2n-15)\). Since \((3)(-5)=-15\) and sum = -2, answer is \(7(n-5)(n+3)\).
4.
Factor completely: \(2x^3-12x^2-54x\)
Solution: Factor out \(2x\): \(2x(x^2-6x-27)\). Since \((-9)(3)=-27\) and sum = -6, answer is \(2x(x+3)(x-9)\).
5.
What are all the possible values for k in \(x^2+kx-15\) ?
Solution: Factor pairs of -15 give k values +2, -2, +14, -14. Therefore answer A.
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