Question

(1) If width is taken as x, which of the following polynomial represents
volume of box?
a) x2 - 5x - 6
b) x3 + x2 - 6x
c) x3 - 6x2 - 6x
d) x2 + x - 6​

Answer 1

x³+x²-6x

=x(x²+x-6)

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

lbh

so b is the answer

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

If width is taken as x, which of the following polynomial represents volume of box

$\sf{a) \: \: {x}^{2} - 5x - 6}$

$\sf{b) \: \: {x}^{3} + {x}^{2} - 6x}$

$\sf{c) \: \: {x}^{3} - 6 {x}^{2} - 6x }$

$\sf{d) \: \: {x}^{2} + x - 6}$

EVALUATION

We are aware of the formula of volume of a box

Volume = Length × Width × Height

Here width is taken as x

So volume must be a polynomial of degree 3

So option (a) & (c) is not true

$\sf{{x}^{3} - 6 {x}^{2} - 6x} \: can \: not \: be \: factorised$

Now

$\sf{{x}^{3} + {x}^{2} - 6x}$

$\sf{ = x({x}^{2} + x - 6)}$

$\sf{ = x \{{x}^{2} + 3x - 2x - 6 \}}$

$\sf{ = x \{x(x + 3) - 2(x + 3) \}}$

$\sf{ = x (x + 3)(x - 2)}$

$\sf{{x}^{3} + {x}^{2} - 6x} \: \: \: is \: the \: volume$

FINAL ANSWER

Hence the correct option is

$\sf{b) \: \: {x}^{3} + {x}^{2} - 6x}$

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