1.
Item 1. Which expression is equivalent to \((m+7)(2m-1)\)?
Solution: \((m+7)(2m-1)=2m^2-m+14m-7=2m^2+13m-7\). Answer: A
2.
Item 2. Factor the following completely. \(17m(2q-r)-5d(2q-r)\)
Solution: The common binomial factor is \((2q-r)\). Therefore \(17m(2q-r)-5d(2q-r)=(2q-r)(17m-5d)\). Answer: A
3.
Item 4. Factor the following completely. \(a^2+13ab+30b^2\). Which is one factor?
Solution: Find two numbers that multiply to \(30\) and add to \(13\): \(10\) and \(3\). So \(a^2+13ab+30b^2=(a+10b)(a+3b)\). Answer: B
4.
Item 3. Factor completely. \(6x^2+12x-48\)
Solution: Factor out 6: \(6(x^2+2x-8)\). Then \(x^2+2x-8=(x+4)(x-2)\). Answer: D
5.
Item 5. Factor the following completely. \(100x^2y^2-169z^2\)
Solution: This is a difference of squares: \((10xy)^2-(13z)^2=(10xy-13z)(10xy+13z)\). Answer: A
6.
Item 6. Factor the following completely. \(\frac{x^2}{25}-\frac{y^2}{81}\)
Solution: \(\frac{x^2}{25}-\frac{y^2}{81}=\left(\frac{x}{5}\right)^2-\left(\frac{y}{9}\right)^2=\left(\frac{x}{5}-\frac{y}{9}\right)\left(\frac{x}{5}+\frac{y}{9}\right)\). Answer: D
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