Warm up Solutions

Factor to solve.

Note

Problems 1–2
To solve, you need to set each expression in your factored answer equal to zero and solve for the value of the variable. You should use mental math when possible. 

$2 x^{2} - 10 x = 0$

$2 x (x - 5) = 0 \begin{matrix} 2 x = 0 & x - 5 = 0 \\ x = 0 & x = 5 \end{matrix}$

$4 x^{2} + 12 x + 9 = 0$

$\begin{array}{rcl} (2 x + 3) (2 x + 3) & = & 0 \\ {(2 x + 3)}^{2} & = & 0 \\ 2 x + 3 & = & 0 \\ x & = & - \frac{3}{2} \end{array}$

Simplify.

Note

Problems 3–4
Simplify coefficients as numerical fractions. Because all terms are monomials, simplify variables using the exponent rules.

$\frac{5 a^{3} b}{15 a b^{2}}$

$\frac{a^{2}}{3 b}$

$\frac{4 x^{2}}{9 y^{2}} \cdot \frac{y}{24 x}$

$\frac{4 x^{2} y}{(9 \cdot 24) x y^{2}} \frac{x}{54 y}$