Final answer:
To divide the polynomial by another polynomial, arrange both in descending powers of x and use polynomial division methods. Verify using the division algorithm. Equations in the form ax^2 + bx + c = 0 can be solved using the quadratic formula.
Step-by-step explanation:
To carry out the division of the polynomial 19x+6+x2−6x3 by 5x+3−3x2, we first need to arrange both the numerator and the denominator in descending powers of x. Then, we apply long division, polynomial division, or synthetic division (if applicable) method to divide the polynomials and find the quotient and the remainder.
To verify the result by the division algorithm, we ensure that the product of the divisor and the quotient, plus the remainder, equals the original dividend (the numerator). That is, if P(x) is the original polynomial and D(x) is the divisor, then the division algorithm states that P(x) = D(x) • Q(x) + R(x), where Q(x) is the quotient and R(x) is the remainder.
It is important to note that when dealing with Division of Exponentials, the process involves dividing the coefficient terms and subtracting the exponents of like bases.
Regarding the equations provided, like x2 + 1.2 x 10−2x −6.0 × 10−3 = 0, these can be solved using the quadratic formula when rearranged into the form of ax2 + bx + c = 0.