Algebra 2 Unit Test #5

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Part 1: Calculator Allowed

 1 Add. $\left(4x-3{x}^{2}\right)+\left(4{x}^{5}-3x+{x}^{2}\right)$ (3)

$4{x}^{5}-2{x}^{2}+x$

 2 Subtract. $\left(7+{x}^{5}\right)-\left(4+6{x}^{3}\right)$ (3)

${x}^{5}-6{x}^{3}+3$

 3 Multiply. $\left(7x+2\right)\left(2x+3\right)$ (4)

$14{x}^{2}+25x+6$

 4 The roots of a polynomial are 2 (with multiplicity 3) and 1. What are the factors of this polynomial? (4)

${\left(x-2\right)}^{3}\left(x-1\right)$

 Algebra 2 Unit Test #5

Part 2: No Calculator Allowed

 5 Simplify. $\frac{{5}^{3}\cdot {5}^{-3}}{{\left(5\cdot {5}^{4}\right)}^{2}}$ (5)

$\frac{1}{{5}^{10}}$

 6 Simplify. Assume that the variable has a positive value. ${\left(\frac{{x}^{-1}}{{x}^{-3}{y}^{-2}\cdot {x}^{0}{y}^{3}}\right)}^{2}$ (6)

$\frac{{x}^{4}}{{y}^{2}}$

 7 Identify the degree, leading coefficient, and end behavior of $y=-5{x}^{3}+2{x}^{2}-3$ (5)

Degree: 3

End Behavior: $\left(+\infty ,-\infty \right)$

 8 Identify the degree, leading coefficient, and end behavior of $y=2{x}^{4}-{x}^{3}+3{x}^{2}-3$ (5)

Degree: 4

End Behavior: $\left(+\infty ,+\infty \right)$

 9 List the roots (and their multiplicities) of ${x}^{3}-3{x}^{2}-10x=0$ (7)

${x}^{3}-3{x}^{2}-10x=0⇒\left(x\right)\left({x}^{2}-3x-10\right)=0⇒\left(x\right)\left(x-5\right)\left(x+2\right)=0$, so the roots are $x\in \left\{-2,0,5\right\}$ (all of which have multiplicity 1).

 10 Factor. $y=4{x}^{3}-12{x}^{2}-x+3$ (7)

$y=\left(x-3\right)\left(2x-1\right)\left(2x+1\right)$

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