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.

Question

Zain Cruz

Mathematics

27 January, 14:34

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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Answers (1)

Know the Answer?

Christine Yu · Answer 1

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)