## Discussion

If x is an integer, then which of the following is the product of the next two integers greater than 2(x + 1)?

 (A) 4x2 + 14x + 12 (B) ... (C) ... (D) ... (E) ... (F) ...
*This question is included in Nova Math - Problem Set A: Substitution, question #11

The solution is

Posted: 12/29/2011 22:41
How is it equal to thirty?
Posted: 12/30/2011 07:33
Tanisha, I guess you refer to the example 5 times 6 is product 30.

Another example would be x=5:
2(5+1)=12 -> the next two integers greater than this are 13 and 14.
13 times 14 gives us product 182

Now, if we take choice A and plug in x=5:
4(5^2)+14(5)+12=
4(25)+70+12=
100+82=182

Niels

Greetings from Holland
Posted: 03/28/2012 19:59
How do we know to use 5 as the integer? Would we be able to use 1 or 3?
Posted: 03/28/2012 20:12
Joana, you could.
Posted: 09/14/2012 10:38
How is E not the answer? If I used 1=x in 4x^2+14. Was I supposed to use 1^2 first or 4*1 first ?
Posted: 09/14/2012 11:26
Tyra, power / exponential operation is first, before multiplication. Remember PEMDAS: parentheses, exponent, multiplication, division, addition, subtraction.
Posted: 11/30/2012 10:18
what do they mean by next 2 integers ?
Posted: 11/30/2012 12:18
Pattyl,

When I refer to 12 then the next integer is 13 and the next integer 14, thus 'the next 2 integers' of N is N+1 and N+2.

Niels
Posted: 11/30/2012 12:56
Pattyl, the next 2 integers are simply x+1 and x+2.
Posted: 01/01/2013 07:07
Can somebody explain the question for me .. Thank you .
Posted: 01/01/2013 11:23
If x is an integer, then which of the following is the product of the next two integers greater than 2(x+1)?

We start by creating our definitions:
Def.1 x is from set N(atural numbers)
Def.2 a product is the result of a multiplication
Def.3 'the next two integers' are n+1 and n+2
Def.4 n > 2(x+1)

If def.4 says this is n, we can use it for def.3 to substitute for n, thus
2(x+1)+1 and 2(x+1)+2 instead of n+1 and n+2
Def.2 tells us to multiply the two thus (n+1)*(n+2) which we just found is equal to:
( 2(x+1)+1 ) * ( 2(x+1)+2 )
( 2x+2+1 ) * ( 2x+2+2 )
( 2x+3 ) * ( 2x+4 )
4x^2 + 8x + 6x + 12
4x^2 + 14x + 12

Niels
Posted: 08/09/2014 10:19
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