2 years ago

Consider the table of the powers of 8.

Mathematics

1 answer:

garri49 [273]2 years ago

8 0

C loser that’s the correct number

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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.

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