HSA.SSE.A.2 Math Practice Questions

Practice playeasy

Which is the completely factored form of $10x^{2} - 15x$ ?

The greatest common factor of $10x^{2}$ and $15x$ is $5x\textsf{.}$ Factoring gives $5x(2x - 3)$ .

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Which expression is equivalent to $81 - x^{2}$ ?

$81 - x^{2} = 9^{2} - x^{2} = (9 - x)(9 + x)$ .

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Which expression is equivalent to $\dfrac{15p}{r} + 15p$ , where $r > 0$ ?

Write $15p$ with denominator $r$ : $\dfrac{15p}{r} + \dfrac{15pr}{r} = \dfrac{15p + 15pr}{r} = \dfrac{15p(r + 1)}{r}$ .

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$x^3 - 8 = 0$ . What is the real root?

$x^3 - 8 = (x - 2)(x^2 + 2x + 4) = 0$ . The quadratic factor has no real roots, so the only real root is $x = 2$ .

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Factor: $x^{2} - 16$ .

$x^{2} - 16$ is a difference of squares: $x^{2} - 4^{2}$ . So $x^{2} - 16 = (x + 4)(x - 4)$ .

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Which is the completely factored form of $5x^{2} + 10x$ ?

The greatest common factor of $5x^{2}$ and $10x$ is $5x\textsf{.}$ Factoring gives $5x(x + 2)$ .

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Which expression is equivalent to $x^{2} - 64$ ?

$x^{2} - 64 = x^{2} - 8^{2} = (x - 8)(x + 8)$ .

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Which expression is equivalent to $\dfrac{24n}{w} + 24n$ , where $w > 0$ ?

Write $24n$ with denominator $w$ : $\dfrac{24n}{w} + \dfrac{24nw}{w} = \dfrac{24n + 24nw}{w} = \dfrac{24n(w + 1)}{w}$ .

HSA.SSE.A.2 math practice. Learn by doing.