Question

Show that (x-1) is a factor of X3

- 7X2 + 14X - 8. Hence completely factorize the given

expression.​

Answer 1

Answer:

$\huge{\underline{\mathtt{\red{❥A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$If (x – 1) is a factor of x3 – 7x2 + 14x – 8 then on putting x – 1 = 0

x = 1

f(1) = 0

= 13 – 7(1)2 + 14(1) - 8

= 1 – 7 + 14 – 8 = 0

Hence x – 1 is one factor.

To find other factors = x3 – 7x2 + 14x – 8

= x2(x – 1) – 6x(x – 1) + 8(x – 1)

= (x – 1)(x2 – 6x + 8)

= (x – 1)(x2 – 4x – 2x + 8)

= (x – 1){x(x – 4) – 2(x – 4)}

= (x – 1)(x – 2)(x – 4).

Answer 2

If (x – 1) is a factor of x3 – 7x2 + 14x – 8 then on putting x – 1 = 0

x = 1

f(1) = 0

= 13 – 7(1)2 + 14(1) - 8

= 1 – 7 + 14 – 8 = 0

Hence x – 1 is one factor.

To find other factors = x3 – 7x2 + 14x – 8

= x2(x – 1) – 6x(x – 1) + 8(x – 1)

= (x – 1)(x2 – 6x + 8)

= (x – 1)(x2 – 4x – 2x + 8)

= (x – 1){x(x – 4) – 2(x – 4)}

= (x – 1)(x – 2)(x – 4).

I hope this helps you.