By Nancy Hall, Rena Price
Explode The Code presents a sequential, systematic method of phonics within which scholars mix sounds to construct vocabulary and skim phrases, words, sentences, and tales. common assessment of formerly
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Notice that 2/2 simplifies to 1, which is the same as 1/1, and 6/2 simplifies to 3, which is the same as 3/1. That’s why our set of 8 potential roots turned out to be only 6 distinct potential roots. p(1/2) = 2(1/2)3 − (1/2)2 − 7(1/2) + 6 = 1/4 − 1/4 − 7/2 + 6 = 5/2 Not a root p(−1/2) = 2(−1/2)3 − (−1/2)2 − 7(−1/2) + 6 = −1/4 − 1/4 + 7/2 + 6 = 9 Not a root p(3/2) = 2(3/2)3 − (3/2)2 − 7(3/2) + 6 = 27/4 − 9/4 − 21/2 + 6 = 9/2 − 21/2 + 6 = 0 Aha! 3/2 is a root, so (2x − 3) is one factor of the polynomial.
The Rational Root Theorem provides a set of potential roots, narrowing down our choices from any possible rational numbers to a smaller number of possibilities. The Rational Root Theorem states that if a polynomial has any rational roots, they must be in the form ± . If we were trying to find the roots of x4 − x3 − 12x2 − 4x + 16, we would know that any rational roots would be a positive or negative ratio of a factor of 16 (the constant term) to a factor of 1 (the coefficient of x4). Factors of 16 include 1, 2, 4, 8, and 16.
A company manufactures solar chargers. They have discovered that the demand curve for this particular solar charger is described by the equation q = −1/10 p2 + 490, where q is the number of chargers sold in a month at a price of p dollars. It costs the company $10 per charger to manufacture them. Write and graph a polynomial function representing the company’s monthly profit, t, in terms of p. Using graphing technology, find the solar charger price that will maximize the company’s profits. Profit is equal to total revenue minus costs.