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25 February, 14:53

F left parenthesis x right parenthesis equals 9 x cubed plus 2 x squared minus 5 x plus 4 and g left parenthesis x right parenthesis equals 5 x cubed minus 7 x plus 4. what is f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis? show all of your steps and write your final answer in factored form.

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  1. 25 February, 17:08
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    The answer is 2x (2x²+x+1).

    When we subtract polynomials we combine like terms:

    (9x³+2x²-5x+4) - (5x³-7x+4)

    9x³-5x³=4x³

    2x² - 0 = 2x²

    -5x--7x=-5x+7x=2x

    4-4=0

    This gives us

    4x³+2x²+2x

    Each of these is divisible by 2, and each has an x, so we factor those out:

    2x ()

    4x³/2x = 2x²:

    2x (2x²)

    2x²/2x=x:

    2x (2x²+x)

    2x/2x = 1:

    2x (2x²+x+1)
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