1.
Item 1. Which expression is equivalent to \((4n-3)(3n+4)\)?
Solution: \((4n-3)(3n+4)=12n^2+16n-9n-12=12n^2+7n-12\). This is not listed. Answer: E
2.
Item 5. Factor the following completely. \(144x^2y^2-121z^2\)
Solution: This is a difference of squares: \((12xy)^2-(11z)^2=(12xy-11z)(12xy+11z)\). Answer: C
3.
Item 3. Factor completely. \(2x^4-10x^3+8x^2\)
Solution: Factor out \(2x^2\): \(2x^2(x^2-5x+4)\). Then factor the trinomial: \(x^2-5x+4=(x-1)(x-4)\). Answer: C
4.
Item 2. Factor the following completely. \(4x(3x-1)+5(3x-1)\)
Solution: Both terms have common factor \((3x-1)\). So \(4x(3x-1)+5(3x-1)=(3x-1)(4x+5)\). Answer: D
5.
Item 6. Factor the following completely. \(\frac{x^2}{64}-\frac{2y^2}{50}\)
Solution: \(\frac{x^2}{64}-\frac{2y^2}{50}=\frac{x^2}{64}-\frac{y^2}{25}=\left(\frac{x}{8}-\frac{y}{5}\right)\left(\frac{x}{8}+\frac{y}{5}\right)\). Answer: D
6.
Item 4. Factor the following completely. \(ca^2+9abc-10cb^2\)
Solution: Factor out \(c\): \(c(a^2+9ab-10b^2)\). Then \(a^2+9ab-10b^2=(a+10b)(a-b)\). Answer: C
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