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# x*(x+1)*(x+2) + x*(x+3) = ?

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Re: x*(x+1)*(x+2) + x*(x+3) = ? [#permalink]
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Given: x(x+1)(x+2)+x(x+3)

Method 1: for those who hate rearranging algebraic terms :D

Let's plugin x=-1(or any other number) and calculate:
The value = 0+(-1)(2)= -2
Let's check the options: we plugin x=-1 in each and check which one gives the value as '-2':

A: -1 + 4 - 5 = -2
B: -1 + 3 - 2 = 0
C: -1 + 6 - 3 = 2
D: -2 + 3 - 5 = -4
Also, D is wrong since the coefficient of x³ should have been 1, not 2

Option E is clearly wrong because there is no x³ term at all!

Only A matches - hence is the correct option

Method 2: x(x+1)(x+2) + x(x+3)
= x(x² + 3x + 2) + x² + 3x
= x³ + 3x² + 2x + x² + 3x
= x³ + 4x² + 5x

Option A

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Re: x*(x+1)*(x+2) + x*(x+3) = ? [#permalink]
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Bunuel wrote:
$$x*(x+1)*(x+2)+x*(x+3) = ?$$

(A) $$x^3+4x^2+5x$$

(B) $$x^3+3x^2+2x$$

(C) $$x^3+6x^2+3x$$

(D) $$2x^3+3x^2+5x$$

(E) $$2x^2+6x+2$$

Simplifying, we have:

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

x^3 + 3x^2 + 2x + x^2 + 3x

x^3 + 4x^2 + 5x

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x*(x+1)*(x+2) + x*(x+3) = ? [#permalink]
Bunuel wrote:
$$x*(x+1)*(x+2)+x*(x+3) = ?$$

(A) $$x^3+4x^2+5x$$

(B) $$x^3+3x^2+2x$$

(C) $$x^3+6x^2+3x$$

(D) $$2x^3+3x^2+5x$$

(E) $$2x^2+6x+2$$

$$x* \{ x^2 + 3x + 2 + x + 3 \} = x * \{x^2 + 4x + 5\}= x^3 + 4x^2 + 5x$$

IMO A

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Re: x*(x+1)*(x+2) + x*(x+3) = ? [#permalink]

Solution

To find
We need to determine
• The simplified value of the given expression $$x * (x + 1) * (x + 2) + x * (x + 3)$$

Approach and Working out
$$x * (x + 1) * (x + 2) + x * (x + 3)$$
$$= x [(x + 1) * (x + 2) + (x + 3)]$$
$$= x [ x^2 + 3x + 2 + x + 3]$$
$$= x [x^2 + 4x + 5]$$
$$= x^3 + 4x^2 + 5x$$

Thus, option A is the correct answer.

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Re: x*(x+1)*(x+2) + x*(x+3) = ? [#permalink]
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Re: x*(x+1)*(x+2) + x*(x+3) = ? [#permalink]
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