Question

factorise

x²-22x+120​

Answer 1

Answer:

(x-12)(x-10)

Step-by-step explanation:

${x}^{2} - 22x + 120 \\ = {x}^{2} - 10x - 12x + 120 \\ = x(x - 10) - 12(x - 10) \\ = (x - 12)(x - 10)$

Thank you for 50 points

Answer 2

Answer:

$\huge\star\underline\mathbb{HELLO}$

Using reasoning:

x2−22x+120 = (x−10)(x−12)

Explanation:

Lets try and reason this out.

The coefficient of x2 is +1 so as a starting point we have the form

(x±?1)(x±?2)

The constant of 120 is positive So both of the ? are the same sign.

The x term has negative 22 so both ? are negative giving

(x−?1)(x−?2)

Note that √120→just under 11

Stating the obvious, the constant of 120 ends in zero so it has to be the product of two numbers where one of them ends in either 5 or 0.

As the square root is close to 11 lets consider the possibility one of the factors as being 10.

10×12=120and(−10)+(−12)=−22 ← It works

So we have:

x2−22x+120 = (x−10)(x−12)