He uses 15 gallons. Because 270/6 = 45. Meaning he drives 45 miles per gallon. So 675/45=15. 15 gallons he will need to use to drive 675 miles.
Answer:
-1
Step-by-step explanation:
See the attachment for the polynomial long division. The constant in the quotient is -1.
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Here, there is a remainder of -x. If there were no remainder the constant in the quotient is the ratio of the constant in the dividend to the constant in the divisor: -2/2 = -1.
That could be a first guess in a "guess and check" solution approach.
<em>Guess</em>: first term of binomial quotient is (2x^3)/x^2 = 2x; last term of binomial quotient is -2/2 = -1. So, the quotient is guessed to be (2x -1).
<em>Check</em>: (2x -1)(x^2 -x +2) = 2x^3 -3x^2 +5x -2
Subtracting this from the actual dividend gives a remainder of -x. This has a lower degree than the divisor, so no further adjustment of the quotient is required.
The second degree polynomial with leading coefficient of -2 and root 4 with multiplicity of 2 is:

<h3>
How to write the polynomial?</h3>
A polynomial of degree N, with the N roots {x₁, ..., xₙ} and a leading coefficient a is written as:

Here we know that the degree is 2, the only root is 4 (with a multiplicity of 2, this is equivalent to say that we have two roots at x = 4) and a leading coefficient equal to -2.
Then this polynomial is equal to:

If you want to learn more about polynomials:
brainly.com/question/4142886
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