## Discussion

If

*This question is included in Nova Math - Problem Set A: Substitution, question #11

*x*is an integer, then which of the following is the product of the next two integers greater than 2(*x*+ 1)?(A) | 4x^{2} + 14x + 12 |

(B) | ... |

(C) | ... |

(D) | ... |

(E) | ... |

(F) | ... |

The solution is

Posted: 10/28/2013 15:51

Are there any fast shortcuts to this problem?

Max, I didn't use substitution for this one. I found this way to be easier:

2(x+1) can also be written as 2x +2. So you want the next two integers (doesn't matter even or odd), and then find the product of the two. The integer after 2x+2 would be 2x+2+1, or 2x+3, and the one after that would be 2x+3+1, or 2x+4. So then we need the product of these two, so the answer would be (2x+3)(2x+4), or 4x^2+14x+12. Does that help?

2(x+1) can also be written as 2x +2. So you want the next two integers (doesn't matter even or odd), and then find the product of the two. The integer after 2x+2 would be 2x+2+1, or 2x+3, and the one after that would be 2x+3+1, or 2x+4. So then we need the product of these two, so the answer would be (2x+3)(2x+4), or 4x^2+14x+12. Does that help?

This is wrong....4 squared is 16 and 16 plus 14 is 30 so answer E is right. Answer A adds 12 which would equal 42 which is wrong.

Hi Katie,

We chose x to equal 1, not 4.

But we can go through the same steps with x = 4. Then 2(x + 1) = 2(4 + 1) = 10. The next two integers greater than 10 are 11 and 12, and their product is 132. Now, check which of the answer-choices equal 132 when x = 4. Begin with (A): 4(4^2) + 14(4) + 12 = 4(16) + 14(4) + 12 = 64 + 56 +12 = 132. No other answer-choice equals 132 when x = 4. Hence, the answer is (A).

Nova Press

We chose x to equal 1, not 4.

But we can go through the same steps with x = 4. Then 2(x + 1) = 2(4 + 1) = 10. The next two integers greater than 10 are 11 and 12, and their product is 132. Now, check which of the answer-choices equal 132 when x = 4. Begin with (A): 4(4^2) + 14(4) + 12 = 4(16) + 14(4) + 12 = 64 + 56 +12 = 132. No other answer-choice equals 132 when x = 4. Hence, the answer is (A).

Nova Press

Yes I am referring to x=1. The equation given in A is 4x squared. 4*1=4 and 4 squared is 16.

4(1)^2+14(1)+12=42

According to the order of operations, parentheses come first so you multiply 4 by 1 to get 4 and then compute 4 squared which is 16.

4(1)^2+14(1)+12=42

According to the order of operations, parentheses come first so you multiply 4 by 1 to get 4 and then compute 4 squared which is 16.

Posted: 12/14/2015 20:56

Just kidding, I see where I went wrong! Thanks!

I chose the number 6. The next two integers greater than 6 was 7&8 which gave me 56. So I chose D because it totaled out to be 54 and that was the closest. So why does my answer have to be wrong because the substitute in the problem was chosen to be 1? Not everyone is going to automatically assume or choose 1. Some might chose 2,3,4 etc

Hi Lexi,

The problem is not asking for the product of the next 2 integers larger than the number you choose. It is asking for the product of the next 2 integers larger than the expression 2(x + 1).

If x = 6, then 2(x + 1) = 2(6 + 1) = 2(7) = 14. The next two numbers greater than 14 are 15 and 16. And their product is 240. Now, the expression in Choice A gives

4x^2 + 14x + 12 = 4(6)^2 + 14(6) + 12 = 4(36) + 14(6) + 12 = 144 + 84 + 12 = 240.

Nova Press

The problem is not asking for the product of the next 2 integers larger than the number you choose. It is asking for the product of the next 2 integers larger than the expression 2(x + 1).

If x = 6, then 2(x + 1) = 2(6 + 1) = 2(7) = 14. The next two numbers greater than 14 are 15 and 16. And their product is 240. Now, the expression in Choice A gives

4x^2 + 14x + 12 = 4(6)^2 + 14(6) + 12 = 4(36) + 14(6) + 12 = 144 + 84 + 12 = 240.

Nova Press