Question

Hi, can someone help with these two questions ASAP! (Ignore the multiple choice I circled, not sure if it’s correct)

Answer 1

Answer:

1) D. $y = -\frac{3}{2}\cdot x^{12} -7\cdot x^{5}+\frac{2}{3}\cdot x -10$

2) E. The coefficient of $x$ is -16.

Step-by-step explanation:

1) A polynomial is an algebraic expression of the form $p(x) = \Sigma \limits_{i = 0}^{n} c_{i}\cdot x^{i}$, where $n$ is the grade of the polynomial. In this case, the only equation that satisfies this definition is:

$y = -\frac{3}{2}\cdot x^{12} -7\cdot x^{5}+\frac{2}{3}\cdot x -10$

Correct answer: D

2) Let $p(x) = (2\cdot x + 1) \cdot (5\cdot x^{3}-8\cdot x +4)$, we proceed to expand the expression by algebraic means:

$p(x) = (2\cdot x + 1)\cdot (5\cdot x^{3}) -(2\cdot x +1)\cdot (8\cdot x) + 4\cdot (2\cdot x + 1)$

$p(x) = 10\cdot x^{4}+5\cdot x^{3}-16\cdot x^{2}+4$

We see that coefficients for $x^{2}$ and $x$ are -16 and 0, respectively. Hence, the incorrect answer is E.