Polynomials: assorted problems
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(Please see the attached file for the full question detains)
Please solve and explain these questions:
1, 2 , 7, 17 19 21
1. Write the polynomial in standard form, identify the degree of the polynomial, identify the leading coefficient, and then classify it according to its degree and number of teams.
2y - 3y^2 + 2y^3 + 3
2. Simplify.
(6a^4 + (4a + 6) - a^2) - (7a - (6a^3 - 4a^2 +5a) - 8(a + 6))
7. Factor completely.
8y^3 + 3y^2 - 80y - 30
17. Solve.
x^2 = -8x - 15
19. Find the discriminant and identify the best description of the equation's root(s0.
3z^2 + sqrt(11z) = 5z^2 + 2
21. A ladder of length 4x + 1 feet is positioned against a wall such that the bottom is x - 1 feet away from a wall. The distance between the floor and the top of the ladder is 4x feet.
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Solution Summary
This solution offers detailed step-wise calculations to some problems related to polynomials, where one example of each type is worked out.
Solution Preview
Please see the attachment.
Answer to 582217
1) The standard form for writing down a polynomial is to put the terms with the highest degree first and then in gradually decreasing order.
a) So, here the standard form will be: 2y3 - 3y2 + 2y + 3
b) The degree of polynomial (or the largest exponent of the variable) is: 3
c) The leading coefficient (or the coefficient of the leading term) is: 2
d) This polynomial is a (classification): Cubic Polynomial
2) (4x2 - 7) (3x2 + 3)
= 12x4 + 12x2 - 21x2 - 21
= ...
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