Question

Find the zeros of the polynomial
$p\left(x\right)=x^2-6x+9$

Answer 1

In the given polynomial $x^2-6x+9$,

The first term is $x^2$ and its coefficient is $1$.

The middle term is $-6x$ and its coefficient is $-6$.

The last term is a constant term $9$.

Multiply the coefficient of the first term by the constant $1\times 9=9$.

We now find the factor of $9$ whose sum equals the coefficient of the middle term, which is $-6$ and then factorize the polynomial $x^2-6x+9$ as shown below:

$x^2-6x+9=x^2-3x-3x+9=x(x-3)-3(x-3)=(x-3)(x-3)$

Therefore, $x^2-6x+9=(x-3)(x-3)$.

so the zero of the polynomial is 3.