Q. 276 - Intermediate Algebra

Question

Create three factoring problems that would be good test questions to measure your knowledge of factoring. Show the solutions. 

Step-by-Step Solution

Answer

The factoring problems are

 $$\begin{gathered} x^2-6x+5=0 \\ 16x^2=25 \\ {x}^2-5xy+6y=0 \end{gathered}$$

Step 1: Given information

Given the three polynomials

Step 2: Write the polynomial and calculate the solution

The polynomial is, $x^2-6x+5=0$, calculating using factorisation method, we get

$$\begin{gathered} x^2-5x-x+5=0 \\ x(x-5)-1(x-5)=0 \\ (x-1)(x-5)=0 \\ x=1,5 \end{gathered}$$

Step 3: Check for another polynomial

The polynomial is, $16x^2=25$ using zero factor principle, we have

 $$\begin{gathered} 16x^2=25 \\ 16x^2-25=0 \\ (4x-5)(4x+5)=0 \\ x=\frac{5}{4},\frac{-5}{4} \end{gathered}$$

Step 4: Check for another polynomial

The polynomial is $x^2-5xy+6y=0$ so using the splitting method, we have

$$\begin{gathered} x^2-3xy-2xy+6y=0 \\ x(x-3y)-2y(x-3y)=0 \\ (x-2y)(x-3y)=0 \\ x=2y,3y \end{gathered}$$