Question

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

Thanks!!

Answer 1

1) D.
`y = -(3)/(2)\cdot x^(12) -7\cdot x^(5)+(2)/(3)\cdot x -10`

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

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 = -(3)/(2)\cdot x^(12) -7\cdot x^(5)+(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.