# FIND THE ROOTS OF FACTORED POLYNOMIALS

## About "Find the roots of factored polynomials"

Find the roots of factored polynomials :

To find the roots of the factored polynomials, we have to write each and every factor as p(x) = 0.

Here P(x) stands for linear factors of the given polynomial.

Let us see some example problems to understand the above concept.

Example 1 :

Find the zeroes of the function f(x).

f(x)=(x–2)(x+5)

Solution :

Let f(x) = 0

(x - 2) (x + 5) = 0

 x - 2 = 0Add 2 on both sidesx - 2 + 2 = 0 + 2 x = 2 x + 5 = 0Subtract 5 on both sidesx + 5 - 5 = 0 - 5x = -5

Hence the roots are 2 and 5.

Example 2 :

Find the roots of the factored polynomial.

f (x) = (x+8)(x+6)

Solution :

Let f(x) = 0

(x + 8) (x + 6) = 0

 x + 8 = 0Subtract 8 on both sidesx + 8 - 8 = 0 - 8 x = -8 x + 6 = 0Subtract 6 on both sidesx + 6 - 6 = 0 - 6x = -6

Hence the roots are -8 and -6.

Example 3 :

Find the zeroes of the function g(x).

g(x) = x (x–5)

Solution :

Let g(x) = 0

x(x -5) = 0

 x = 0 x - 5 = 0Add 5 on both sidesx - 5 + 5  = 0 + 5x = 5

Hence the roots are 0 and -5.

Example 4 :

Find the zeroes of the function g(x).

g(x) = (x - 4)²

Solution :

Let g(x) = 0

(x - 4)² = 0

We can write (x - 4)² as (x - 4) (x - 4)

 x - 4 = 0 x - 4 = 0Add 4 on both sidesx - 4 + 4  = 0 + 4x = 4

Hence the roots are 4 and 4.

Example 5 :

Find the zeroes of the function g(x).

g(x) = (2x - 3) (5x - 7)

Solution :

Let g(x) = 0

(2x - 3) (5x - 7) = 0

 2x - 3 = 0Add 3 on both sides2x - 3 + 3  = 0 + 32x = 3Divide by 2 on both sides2x/2 = 3/2x = 3/2 5x - 7 = 0Add 7 on both sides5x - 7 + 7  = 0 + 75x = 7Divide by 5 on both sides5x/5 = 7/5x = 7/5

After having gone through the stuff given above, we hope that the students would have understood "Find the roots of factored polynomials".

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