Quiz 11:Creative Problem Solving

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Created by Isabelle Yeong on July 15th 2015

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Please answer the following questions based on the equation 4x²+5xy-6y²-4x+3y-1=0

Solve for integer solutions of 4x²+5xy-6y²-4x+3y-1=0

Question 1: Do you think we can factor part of the expression in the given equation 4x²+5xy-6y²-4x+3y-1=0?

A. Yes.

B. No.

C. Perhaps.

Clear selection

Question 2: Would you group 4x²-4x and -6y²+3y together if you're ask to factorize 4x²+5xy-6y²-4x+3y?

You can select more than one answer correct.

Yes, the hints are clear that we could factor out 4x from 4x²-4x and also 3y from -6y²+3y.

No.

Question 3: If you're told to substitute x=3 and y=4 simultaneously into the given equation 4x²+5xy-6y²-4x+3y-1=0, what would you have observed?

A. We obtained 0-1=0, which is ridiculous.

B. x=3 and y=4 are roots of 4x²+5xy-6y²-4x+3y-1=0

C. x=3 and y=4 are roots of 4x²+5xy-6y²-4x+3y=0

Clear selection

Question 4: If you've picked the choice C for question 2, how would you factorize 4x²+5xy-6y²-4x+3y?

A. Polynomial long division to divide 4x²+5xy-6y²-4x+3y by (x-3).

B. Polynomial long division to divide 4x²+5xy-6y²-4x+3y by (y-4).

C. Polynomial long division to divide 4x²+5xy-6y²-4x+3y by (x-3)(y-4)..

D. Neither of the above.

Clear selection

Question 5: If you've failed to factorize 4x²+5xy-6y²-4x+3y, what else could you do to factorize it completely by making full use of the info that substituting x=3 and y=4 into 4x²+5xy-6y²-4x+3y yields a zero?

A. I would try to divide 4x²+5xy-6y²-4x+3y by (x+y-7).

B. I would try to divide 4x²+5xy-6y²-4x+3y by (xy-12).

C. I would try to divide 4x²+5xy-6y²-4x+3y by (4x-3y).

D. We could not factorize the expression 4x²+5xy-6y²-4x+3y.

Clear selection

Question 6: Solve for integer solutions of 4x²+5xy-6y²-4x+3y-1=0.

A. No integer solution.

B. There are 3 solutions.

C. There are 4 solutions.

D. There are infinite solutions.

Clear selection

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