Question

Describe the first step when factoring any polynomial. Why is this the first step? Explain.

Answer 1

Answer with explanation:

→Consider a Polynomial

   $\rightarrow ax^n+bx^{n-1}+cx^{n-2}+...........+d$

→We will use rational root theorem to find out the factors of the polynomial.

  $\rightarrow ax^n+bx^{n-1}+cx^{n-2}+...........+d\\\\\rightarrow a(x^n+\frac{bx^{n-1}}{a} +\frac{cx^{n-1}}{a}+..........+\frac{d}{a})$

→Factors of d are

        $=\pm 1 , .....\pm d\\\\ \text{Factors of a are}=\pm 1,.....\pm a\\\\ \pm\frac{d}{a}$  

⇒Now,substitute these integers that is factors into Polynomial expression to find which expression is equal to Zero.These integers will be factor of Polynomial expression.

For example

 f(x)=x²-3 x+2

By rational root theorem ,roots of the polynomial can be , -1,1,2,-2.

f(1)=1²-3×1+2

   =1-3+2

   =0

f(2)=2²-3×2+2

   =4-6+2

  =0

So, 1 and 2 are root of the polynomial expression.

Answer 2

Step 1: If there is a common factor, factor out the GCF. Step 2: Identify the number of terms: (i) If polynomial has two terms, convert polynomial into difference of two squares or sum of two cubes or difference of two cubes.