Question

Consider the expression 8-6x+x^2, Is the expression equivalent to (x-4)(x-2)?​

Answer 1

Yes

Explanation:

Factoring is the process of breaking a polynomial into its factors.

Standard Form

It is easiest to factor when in standard form. Standard form is when the terms are listed from highest power to lowest.

• Standard form is
  `x^2-6x+8`

Factoring

To find if two expressions are equal we can either factor the quadratic or multiply out the binomials. I find factoring to be faster and easier, so I will show that.

There are multiple techniques to factor; I will be explaining one of them. One way to factor quadratics is to find 2 numbers that multiply to c (the constant) and sum to b (the second term). In this case, the numbers -4 and -2 fit these requirements.

• -4 * -2 = 8
• -4 + -2 = -6

This means that
`x^2-6x+8` factored is
`(x-4)(x-2)`. Thus, they are equivalent.