Cards In This Deck

• $$\begin{gathered} \text{True or False?} \\ \text{To simplify the algebraic fraction }\frac{x^2+5x+6}{x+2}\text{, you can simply cancel the }x\text{ terms to get }x+5x+3\text{.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{You cannot cancel individual terms added or subtracted in the numerator and denominator. } \\ \text{✅ Correct Method: You must factorise the numerator first:} \\ \frac{(x+3)(x+2)}{x+2}=x+3 \end{gathered}$$
• $\text{When performing algebraic long division for }{x}^3-7x+2\text{ divided by }x-1\text{, what is the crucial first step regarding the setup?}$
  $$\begin{gathered} \text{You must include the missing term with a zero coefficient.} \\ \text{Write the dividend as: }{x}^3+0{\mathbf{x}}^2-7x+2\text{.} \end{gathered}$$
• $\text{If a polynomial }f(x)\text{ is divided by }(ax-b)\text{ and leaves a remainder }R\text{, how do you express }f(x)\text{ in the form involving the quotient }Q(x)\text{?}$
  $f(x)=(ax-b)Q(x)+R$