II. Perform the indicated operations.
2. (2x + 4) (x + 2) = 2x^2+8x+8
5.(x3 + 7x-6)÷ (x - 2) = [tex] {x}^{2} + 2x + 11 + \frac{16}{x - 2} [/tex]
Step-by-step explanation:
2. Use the FOIL Method
[tex](2x + 4)(x + 2) = 2 {x}^{2} + 8x + 8 \\ \\ 2xx + 2x \times 2 + 4x + 4 \times 2 \\ 2xx = 2 {x}^{2} \\ 2x \times 2 = 4x \\ 4 \times 2 = 8 \\ 2 {x }^{2} + 4x + 4x + 8 \\ \underline \green{ 2 {x}^{2} + 8x + 8}[/tex]
5. Long Division
[tex] \frac{( {x}^{3 } + 7x - 6)}{x - 2} = {x}^{2} + 2x + 11 + \frac{16}{x - 2} \\ \\ {x}^{2} + \frac{2 {x}^{2} + 7x - 6 }{x - 2} \begin{cases} qoutient = {x}^{2} \\remainder = 2 {x}^{2} + 7x - 6 \end{cases} \\ 2x + \frac{11x - 6}{x - 6} \begin{cases} quotient = 2x \\ remainder = 11x - 6\end{cases} \\ {x}^{2} + 2x + \frac{11x - 6}{x - 2} \\ 11 + \frac{16}{x - 2} \begin{cases} quotient = 11 \: \: \: \: \: \: \: \: \: \: \\ remainder = 16\end{cases} \\ \underline \green{{x}^{2} + 2x + 11 + \frac{16}{x - 2} }[/tex]
[tex] \\ [/tex]
Hope it's help
#CarryOnLearning!
