Question

Factor the trinomial below.
x2 - 12x+ 35

Answer 1

The factors of the expression
`x^(2)-12x+35` are (x – 7) and (x – 5).

SOLUTION:

Given, Trinomial expression is
`x^(2)-12x+35`

Trinomial is nothing but an expression or equation having three terms in it.

Given expression is quadratic expression.

Now, to factorize any quadratic expression we need to write the constant term as product of two numbers, such that sum two number should equal to coefficient of x, in order to take common.

`x^(2)-12 x+35`

By writing constant as product of two numbers, we get

`x^(2)-12 x+5 * 7`

By writing the “x” term as sum of two number coefficients, we get

`x^(2)-7 x-5 x+5 * 7`

By taking x and -5 as common

x(x – 7) –5(x – 7)

By taking (x – 7) as common, the above expression becomes,

(x – 7)(x – 5)

Thus factors of the expression
`X^(2)-12 X+35` are (x – 7) and (x – 5).

Answer 2

Explanation:

x2 - 12x+ 35 = x^2 - 7x -5x +35

= x ( x-7) - 5(x - 7)

= (x-7)(x-5)