Simplify the expression 1 over 4 to the negative fourth power.
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Since the questions are in multiple choice, I'll only provide the answers.
1: 4th degree polynomial
2: 10x3 + 14x2 − 4x4 + x
4: 10x + 1
5: −7x3 + 4x2 − 4x
6: 10a2 + 9a − 10
7: 1 over x to the 5th power
12: A polynomial in standard form is to arrange the monomials in decreasing powers. For instance, if we have 3x + x3 + 2 - 4x2, the standard form is x3 - 4x2 + 3x + 2.
13: To simplify the expression (8x2 + 5) − (3x2 − x + 7):
First, we look at the first term of the first polynomial and find if there are like terms with the other polynomial. In this case, we have 8x2 and 3x2, when subtracted would give us 5x2.
Second, we look at the next power of x. Only the second polynomial has an x with power 1. Thus, we have x (since negative of negative x provides a positive x).
Third, we subtract the numerical constants for both polynomials, 5 - 7, yielding -2.
Finally, we combine the results for each step: 5x2 + x - 2
a negative exponent means a reciprocal
so 1 / 4^(-4) = 4^4