## find the value of a if x + 6 is a factor of x3 – 3×2 + 2x – 6 without actually calculating the cubes find the value of (28)3 + (

Question

find the value of a if x + 6 is a factor of x3 – 3×2 + 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

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1 month 2021-08-13T17:27:28+00:00 2 Answers 0 views 0

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)