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Q: What is the factorization of the polynomial graphed below Assume it has no constant factor.?

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I assume you meant x^4 + 5x^2 +10x + 12. The remainder is 28

I assume x2 + 5x - 36 is the polynomial in the question. First, look for two factors of 36 that have a difference of 5, which would be 9 and 4. It would factor into (x + 9)(x - 4). To double check, multiplying them together results in x2 - 4x + 9x - 36 = x2 + 5x - 36. If the polynomial is 5x2 +7x +2

If you have the zeros of a polynomial, it is easy, almost trivial, to find an expression with those zeros. I am not sure I understood the question correctly, but let's assume you have the zero 2 with multiplicity 2, and other zeros at 3 and 5. Just write the expression: (x-2)(x-2)(x-3)(x-5). (Example with a negative zero: if there is a zero at "-5", the factor becomes (x- -5) = (x + 5).) You can multiply this out to get the polynomial if you like. For example, if you multiply every term in the first factor with every term in the second factor, you get x2 -2x -2x + 4 = x2 -4x + 4. Next, multiply each term of this polynomial with each term of the next factor, etc.

I assume you mean a polynomial of degree 4. In general, a polynomial of degree "n" can be separated into "n" linear factors. As a result, a polynomial of degree "n" has exactly "n" solutions - unless two or more of the factors are repeated; in which case the corresponding solution is said to be a multiple solution. As an example: (x - 2)(x - 5) = 0 has two solutions, namely 2 and 5; while (x - 3)(x - 3)(x + 5) = 0 is of degree three, but has only two solutions, since the solution "3" is repeated. An equation such as x2 + 1 = 0 cannot be factored in the real numbers, so if you insist that the solutions be real, there are zero solutions. However, the polynomial can be factored in the complex numbers; in this case: (x + i)(x - i) = 0, resulting in the two complex solutions, -i and +i.

Its average acceleration is (40-8)/(8) = 32/8 = 4 m/s2

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yes

A lot of mathematical problems about travelling distances, assume that you are travelling at a constant speed.

I'm going to assume the polynomial in question is 2x7+(3-2x3)+(5x8-4x) Expanding out the polynomial: 2x7+3-2x3+5x8-4x Order the terms by powers of x: 5x8+2x7-2x3-4x+3 Since 8 is the highest power of x, the degree of the polynomial is 8.

The net force acting on it is zero.

I would assume -1, which is not prime and must be part of the factorization to make the negative number negative.

I would assume that the use of the constant in this scenario is in a formula. Generally, it would act as a proportionality factor, where when everything is kept constant, the result will be increased on decreased proportionately based on that constant.

since PV=nRT and we assume that the number of moles and temperature remains constant, we can assume that PV=R as R the gas constant will not change, if pressure is increased, then volume must decrease to counteract the change in pressure

I assume you meant x^4 + 5x^2 +10x + 12. The remainder is 28

It really is not constant, but to solve problems that want you to only use Boyle's Law and not the combined gas law it is important that you assume that volume is constant. The change in volume is not really that great.

It depends on your setting. If the net force on an object is zero than the object will move with a constant speed. It will also move with a constant speed (but not velocity!) if a force forces the object to move in a circular motion.

I assume you mean to find the prime factorization of 405. If so: 34 x 5

There is not enough information. You can't calculate one root on the basis of another root. HOWEVER, if we assume that all the polynomial's coefficients are real, then if the polynomial has a complex root, then the complex conjugate of that root (in this case, 4 - 17i) must also be a root.