Question

Factorise : x 3 - 23x 2 + 142x - 120

Answer 1

x3 - 23x2 +142x -120

If we put x=1 the value of the expression becomes zero.

Thus by the factor theorem (x-1) is a factor of the given polynomial.

The polynomial is a 3 degree polynomial and hence has 3 factors.

To get the other 2 factors divide the given polynomial by (x-1) and factorize the 2 degree polynomial obtained by middle term splitting.

Answer 2

Answer:

We know that if the sum of the coefficients is equal to 0 then (x-1) is one of the factors of given polynomial.

x-1 = 0

x = 1

Put x=1,

(1)³-23(1)²+142(1)-120

→ 1-23+142-120

→ 120-120

→ 0

Therefore,(x-1) is a factor of the given polynomial.

Now the factors are (x-1) and (x²-22x+120) {see pic for knowing how (x²-22x+120) is a factor}

Now factorise x²-22x+120

x²-22x+120

→ x²-12x-10x+120

→ x(x-12)-10(x-12)

→ (x-12)(x-10)

Therefore, x²-22x+120 = (x-12)(x-10)

The factors of x³-23x²+142x-120 = (x-1)(x-12)(x-10)

Hope it helps....…