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Sub 505 Level|   Algebra|      
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x*(x+1)*(x+2) + x*(x+3) = ? 13 Feb 2020, 07:35
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A
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\(x*(x+1)*(x+2)+x*(x+3) = ?\)


(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) \(2x^2+6x+2\)
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A
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x*(x+1)*(x+2) + x*(x+3) = ? 13 Feb 2020, 07:40
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Bunuel
\(x*(x+1)*(x+2)+x*(x+3) = ?\)


(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) \(2x^2+6x+2\)
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Given: \(x*(x+1)*(x+2)+x*(x+3) \)
Expand to get: \(x^3+3x^2+2x+x^2 + 3x\)
Combine like terms to get: \(x^3+4x^2+5x\)

Answer: A

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x*(x+1)*(x+2) + x*(x+3) = ? 13 Feb 2020, 08:20
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Bunuel
\(x*(x+1)*(x+2)+x*(x+3) = ?\)


(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) \(2x^2+6x+2\)
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Please refer to my attachment below:
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algebra 1.JPG
algebra 1.JPG [ 64.05 KiB | Viewed 5433 times ]

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x*(x+1)*(x+2) + x*(x+3) = ? 14 Feb 2020, 03:04
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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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x*(x+1)*(x+2) + x*(x+3) = ? 21 Feb 2020, 09:17
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Bunuel
\(x*(x+1)*(x+2)+x*(x+3) = ?\)


(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) \(2x^2+6x+2\)
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Simplifying, we have:

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

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

x^3 + 4x^2 + 5x

Answer: A
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x*(x+1)*(x+2) + x*(x+3) = ? 21 Feb 2020, 09:22
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Bunuel
\(x*(x+1)*(x+2)+x*(x+3) = ?\)


(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) \(2x^2+6x+2\)
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\(x* \{ x^2 + 3x + 2 + x + 3 \} = x * \{x^2 + 4x + 5\}= x^3 + 4x^2 + 5x\)

IMO A

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x*(x+1)*(x+2) + x*(x+3) = ? 21 Feb 2020, 10:05
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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.

Correct Answer: Option A
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x*(x+1)*(x+2) + x*(x+3) = ? 26 Nov 2024, 19:44
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