consider the following quadratic equation x^2-10x+25=0 using the standard form ax^(2)+bx+c=0 of the given quadratic equation factor the left hand side of the equation into two linear factors
To factor the quadratic equation x^2 -10x + 25 = 0, we need to find two linear factors that, when multiplied, give us the quadratic equation.
First, let's take a look at the quadratic equation in the standard form: ax^2 + bx + c = 0. In our case, we have:
a = 1
b = -10
c = 25
Now, let's find the linear factors. We can do this by factoring the quadratic equation. However, in this case, we notice that the equation is already in a perfect square form: (x - 5)^2 = 0.
When we expand (x - 5)^2, we get x^2 - 10x + 25, which matches our original quadratic equation. Therefore, the two linear factors are (x - 5)(x - 5) or simply (x - 5)^2.
So, the quadratic equation x^2 - 10x + 25 = 0 can be factored into the two linear factors (x - 5)(x - 5) or (x - 5)^2.