Question

find the value of a if x + 6 is a factor of x3 – 3x2 + 2x - 6
without actually calculating the cubes find the value of
(28)3 + (-15)3 + (-13)3
factorise : 6 "x"3 – 5 "x"2 – 13x + 12
please fast!!!!

Answer 1

We have to find the value of (28)³ + (-15)³ + (-13)³ without calculating the cube.

And factorise 6x³ - 5x² - 13x + 12

Solution : We know, if a + b + c = 0 then a³ + b³ + c³ = 3abc

Here a = 28, b = -15 and c = -13

so, a + b + c = 28 - 15 - 13 = 0

now, (28)³ + (-15)³ + (-13)³ = 3(28)(-15)(-13) = 16,380

Now let's factorise 6x³ - 5x² - 13x + 12

putting x = 1 we get, P(1) = 6 - 5 - 13 + 12 = 0

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

Now let's arrange it in which (x -1) is included

6x³ - 6x² + x² - x - 12x + 12

= 6x²(x - 1) + x(x - 1) - 12(x - 1)

= (6x² + x - 12)(x - 1)

= (6x² + 3x - 2x - 1)(x - 1)

= {3x(2x + 1) - (2x + 1)}(x - 1)

= (3x - 1)(2x + 1)(x - 1)

Answer 2

Answer:

Meaing of this question