Question

divide 27x⁴ − 24x³ + 12x² −18x by -3x​

Answer 1

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We need to use a technique called factoring by grouping

Will write as 2 groups of terms 8x^3 -12x^2 and 18x -27 and factor each group separately

The first group has a common factor of 4x^2 so this factors to 4x^2( 2x -3)

The second group has a common factor of 9 so this factors to 9(2x -3) so now I have

(4x^2)(2x-3) +9(2x -3) Both groups have a common factor of (2x -3) so can rewrite as

(4x^2 +9)(2x -3) This is as far as we can factor. If we want to solve we set the equation equal to zero and get 4x^2 +9=0 2x -3 = 0

4x^2 = -9 2x =3

x^2 = -9/4 x=1.5

x= +/- (3/2)i

So have i real and 2 imaginary solutions. You can graph and confirm that there is only 1 zero