Question

The volume of a cuboid is polynomial p(x)=4x3+20x2+33x+18. Find the possible expressions for the dimensions of the cuboid.

Answer 1

P(x) = 4x³ + 20x² + 33x + 18
We try at x = -1 and x = -2 , we get
P ( - 2 ) = 0
=> P(x) = ( x + 2 )( 4x² + 12x + 9 )
= ( x + 2 )(4x²+6x+6x+9)
= ( x + 2 ){2x(2x+3)+3(2x+3)}
= ( x + 2 )(2x+3)(2x+3)
Volume of a cuboid is => Length ×Breadth × Height
Possible expressions for cuboid => ( x + 2) (2x + 3) (2x + 3 )units

Answer 2

Answer:

the answer is (x+2)(2x+3)(2x+3)

Step-by-step explanation: first factor of 4x^3+20x^2+33x+18 is (x+2) which we have got by the remainder theorm.

now we will find the other two factors by long division=

                                                                            4x^3+20x^2+33x+18/x+2

                                                                          = (4x^2+12x+9)

now we will get the two factors by splitt the middle term method=

4x^2 +12x+9

4x^2+6x+6x+9

2x(2x+3)+3(2x+3)

=(2x+3)(2x+3)

hence, the three factors are (x+2)(2x+3)(2x+3)

therefore the dimentions are length *breadth * height= (x+2)(2x+3)(2x+3)

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