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gr.10 math!

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factor the equation: -6x^2+15x+36

please show me the steps in answering this problem.


  • gr.10 math! -

    What are the factors of 1000

  • gr.10 math! -

    -6x^2+15x+36 is an expression. An equation has an equal sign.

    First take out common factors
    Now concentrate on the part in parentheses.
    Make a table of possible combinations of factors that multiply to the constant term (-12) and put them in the first two columns. For example, -1 and 12.
    Multiply the first column by the coefficient of the term in x² (2) and add to the second column. Put the result in the third column (-1*2 + 12 = 10):
    -1 12 10
    Compare the third column with the coefficient of the term in x, i.e. -5. If they compare, you have found the factors: (x+A)(2x+B) where A and B are the numbers in the first and second columns.
    Let's continue:
    A B 2*A+B
    #-1 12
    12 -1 12*2+(-1)=23
    #2 -6
    4 -3 2*4-3=5 (Found, but wrong sign)
    -4 3 2*(-4)+3=-5 (switched sign)
    # Since we have already taken out all common factors, we do not have to check cases where B is even, which makes 2x+2k (k=integer).

    The intermediate answer is (x-4)(2x+3).
    Check by expanding: 2x²-8x+3x-12=x²-5x-12
    The final answer is -3(x-4)(2x+3).

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