Mathematics: Factorise x 3 - 2 3 x 2 + 142x - 120

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Factorise x 3 - 2 3 x 2 + 142x - 120 - id32321421207226143, LanaParrilla

joco3625

31.01.2022

(x - 1)(x - 12)(x - 10)

Step-by-step explanation:

Given

Factorize:

x^3 - 23x^2 + 142x - 120

Required

Factorize

We start by checking for the factors of the given polynomial;

Check x - 1 = 0;

This implies that x = 1

Substitute 1 for x in x^3 - 23x^2 + 142x - 120

(1)^3 - 23(1)^2 + 142(1) - 120

= 1 - 23 + 142 - 120

= 0

Since the result is 0, then x - 1 = 0 is a factor

Divide the polynomial by x - 1

(See attachment for long division)

The result is: x^2 - 22x + 120

Hence, the factor is

(x - 1)(x^2 - 22x + 120)

Expand the quadratic function

(x - 1)(x^2 - 12x - 10x + 120)

Factorize

(x - 1)(x(x - 12) - 10(x - 12))

(x - 1)(x - 12)(x - 10)

Hence;

Factorizing x^3 - 23x^2 + 142x - 120 gives (x - 1)(x - 12)(x - 10)

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