University:
Highline College
Course:
MATHP 141 | Precalculus I Plus Extra Support
Academic year:

2022
Views:

302

Pages:

2
Author:

Origbo2ol

Workshop #9 1. Consider the polynomial p(x) = 4x4 − 2x5 + 3x + 6 (a) What is the degree of this polynomial? (b) Write the polynomial in descending powers of x. (c) Identify the leading coeﬃcient and the constant coeﬃcient of p(x). (d) Without a calculator ﬁnd p(0), p(1), p(−1), p(2) and p(−2). 2. Let f (x) = x + 2 and g(x) = 2x + 3 (a) Find f (x) − g(x) (b) What is f (3) − g(3)? (c) Check your answer by computing f (3) and g(3) and then subtracting. 3. Create a polynomial with variable r which describes the area of the shaded region 3 2r r Simplify as much as possible. 4. Suppose the directions on a problem were to simplify the left hand side of the following equation. The right hand side represents the ﬁrst step in an attempted solution. Identify the error(s) in the work. (3x + 2)2 − (2x + 1) = 9x2 + 4 − 2x + 1 5. Perform the operation and simplify completely (a) 3t + 7 − 2t + 4 (d) (3a + 2b)(2 − a) (b) 4x(3y + z) (e) −3(t − 8)2 − 12(t − 4)2 (c) 2x2 + 3 − x(3x + 1) (f) 3xy 2 z(x2 − 2y + z 3 ) 6. The cost of producing x units of an item is given by the function C(x) = 2x + 200 in dollars, where the revenue for selling x units is given by R(x) = 10x + 300 in dollars. (a) What is C(7)? Explain your result in context. (b) What is R(15)? Explain your result in context. (c) Create a simpliﬁed polynomial P (x) which gives proﬁt in dollars. What is the proﬁt if we produce and sell exactly 44 units? 7. Suppose you have a two squares. The larger square has sides 2 units longer than the sides of the smaller square. (a) Give a polynomial which gives the cumulative perimeter of both squares where the variable is the length of a side of the smaller square. Simplify as much as possible. (b) Suppose the squares from the previous problem are connected like so: Give a polynomial which gives the perimeter of the above ﬁgure where the variable is the length of a side of the smaller square. Simplify as much as possible.