Answer:
1) D. [tex]y = -\frac{3}{2}\cdot x^{12} -7\cdot x^{5}+\frac{2}{3}\cdot x -10[/tex]
2) E. The coefficient of [tex]x[/tex] is -16.
Step-by-step explanation:
1) A polynomial is an algebraic expression of the form [tex]p(x) = \Sigma \limits_{i = 0}^{n} c_{i}\cdot x^{i}[/tex], where [tex]n[/tex] is the grade of the polynomial. In this case, the only equation that satisfies this definition is:
[tex]y = -\frac{3}{2}\cdot x^{12} -7\cdot x^{5}+\frac{2}{3}\cdot x -10[/tex]
Correct answer: D
2) Let [tex]p(x) = (2\cdot x + 1) \cdot (5\cdot x^{3}-8\cdot x +4)[/tex], we proceed to expand the expression by algebraic means:
[tex]p(x) = (2\cdot x + 1)\cdot (5\cdot x^{3}) -(2\cdot x +1)\cdot (8\cdot x) + 4\cdot (2\cdot x + 1)[/tex]
[tex]p(x) = 10\cdot x^{4}+5\cdot x^{3}-16\cdot x^{2}+4[/tex]
We see that coefficients for [tex]x^{2}[/tex] and [tex]x[/tex] are -16 and 0, respectively. Hence, the incorrect answer is E.
