In this question, we have to Find The Zeros of The Polynomial p(x)=(x-2)^2-(x+2)^2 by the factorization method. Also, we will see some related p(x) = 0 examples.

Let’s find the zeros of the polynomial p(x)=(x-2)^2-(x+2)^2.

**p(x) = (x-2) ^{2} – (x+2)^{2}**

**Note:** For solving this we need 2 formuleas as follow:

(a+b)^{2} = a^{2}+b^{2}+2ab

(a-b)^{2} = a^{2}+b^{2}-2ab

So we will consider a = x and b = 2 and will solve this polynomial

Let’s see:

p(x) = **(x-2) ^{2} – (x+2)^{2}**

= (x^{2}+4-4x) – (x^{2}+4+4x)

= x^{2}+4-4x – x^{2}-4-4x

= x^{2}-x^{2}+4-4-4x-4x

= 0+0-8x

= 0-8x

= -8x

## Find The Zeros of The Polynomial p(x)=(x-2)^2-(x+2)^2

So, p(x) = **(x-2) ^{2} – (x+2)^{2}**

**(x-2)**= 0

^{2}– (x+2)^{2}-8x = 0

x = 0

So, the zeros of the Polynomial p(x)=(x-2)^2-(x+2)^2 will be zero when x = 0.

8×2-22x-21=0 By Factorization Method

Find The Zeros of The Quadratic Polynomial x2-2x-8 = 0

Factorization of 3×2-8x+5

## Question 2. Which are the zeros of p(x)=(x-1)(x-2)

Now we will solve which are the zeros of p(x)=(x-1)(x-2). Here we know that polynomial is equal to zero.

So, we will verify the relation.

**p(x)=(x-1)(x-2)**

p(x)=(x-1)(x-2) = 0

(x-1)(x-2) = 0

(x-1) = 0**x = 1**

(x-2) = 0

x – 2 = 0**x = 2**

Here we find the zeros of p(x)=(x-1)(x-2)**x = 1 x = 2**

**Que. 3. **Find the zeros of (x2 -1)

Here we will expand this polynomial by the a^{2} – b^{2} formula.

( a^{2} – b^{2} ) = (a – b)(a + b)

Find the zeros of (x2 -1)

(x2-1) = (x^{2} – 1^{2})

(x^{2} – 1) = (x+1)(x-1)

For finding the zeros of (x^{2} – 1) we will use the standard relationship

p(x) = 0

(x^{2} – 1) = 0

(x+1)(x-1) = 0

(x+1) = 0

x = -1

Similarly, (x -1 ) = 0

x = 1

Here we find the zeros of (x2-1), x = +1, -1.

Que. 4 Which are the zeros of p(x)=(x+5)(x-2)

Sol. Here we can see that polynomial is already in factorize form.

now we will use standard relationship p(x) = 0

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

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

now

(x+5) = 0

(x-2) = 0

Hence

x = -5

x= 2

This is our answer.

### Conclusion

In this question we see **Find The Zeros of The Polynomial p(x)=(x-2)^2-(x+2)^2** along with w**hich are the zeros of p(x)=(x+5)(x-2)**, **Which are the zeros of p(x)=(x-1)(x-2)** and Find the zeros of (x2 -1).

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