Q 58E - Intermediate Algebra

Question

 How do you check result after factoring a polynomial?

Step-by-Step Solution

Answer

• Multiply the factors obtained from the polynomial equation.
• If we get the same polynomial equation on multiplying the factors, then the obtained factors are correct.

Step 1 Let us consider a polynomial equation,

$x^3+x^2-x-1$.

The factors for this equation are,

$\left(x^2-1\right)\left(x+1\right)$.

Step 2 Now multiply both the factors.

$$\begin{gathered} \left(x^2-1\right)\left(x+1\right)=x^2\left(x\right)+\left(-1\right)\left(x\right)+x^2\left(1\right)\left(-1\right)\left(1\right) \\ =x^3-x+x^2-1 \\ =x^3+x^2-x-1 \end{gathered}$$

which is same as the given polynomial equation.

So, if we need to check whether the obtained factors are correct or not, just multiply the factors and on multyiplying them if we get the given polynomial equation then it is correct otherwise, it is wrong answer.