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2. Polynomials
easy
What are the possible expressions for the dimensions of the cuboids whose volumes are given below ?$\boxed{\rm {Volume}\,:3x^2-12x}$
Option A
Option B
Option C
Option D
Solution
Volume of a cuboid $=($ Length $) \times($ Breadth $) \times($ Height $)$
Volume $=3 x^{2}-12 x$
On factorising $3 x ^{2}-12 x ,$ we have
$3 x ^{2}-12 x =3\left[ x ^{2}-4 x \right]=3 \times[ x ( x -4)]=3 \times x \times( x -4)$
$\therefore$ The possible dimensions of the cuboid are: $3, x$ and $(x-4)$ units.
Standard 9
Mathematics
