Using the Fundamental Theorem of Algebra, complete the following exercises. Show your work. 1. Determine how many, what type, and find the roots for f(x) = x4 + 21x2 − 100.

2. Determine how many, what type, and find the roots for f(x) = x3 − 5x2 − 25x + 125.

3. The following graph below shows a seventh-degree polynomial:

Part 1: List the polynomial’s zeroes with possible multiplicities.

Part 2: Write a possible factored form of the seventh-degree function.

4. Without plotting any points other than intercepts, draw a possible graph of the following polynomial: f(x) = (x + 8)3 (x + 6)2 (x + 2)(x − 1)3 (x − 3)4 (x − 6).

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

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