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

2022
Views:

166

Pages:

2
Author:

lorenzops0

Workshop #10 1. (a) Divide the following i. 23 2789 ii. 2x + 3 2x3 + 7x2 + 8x + 9 (b) What are the similarities and diﬀerences between part i and ii? (c) Based on your answers to part (a) try and guess the result of the polynomial long division by using the standard division in part i below. i. 23 4479 ii. 2x + 3 4x3 + 4x2 + 7x + 9 (d) Compute the polynomial long division in ii. Does it match your guess? 2. Divide the following, check your answers (a) 6x2 − x − 7 x+1 (b) 3x4 + 2x3 + x2 + 2x + 9 x+3 (c) 4x3 − 12x2 + 17x + 12 2x − 3 3. Let f (x) = x − 2 and g(x) = 2x2 − 1. Multiply out, simplify and write each polynomial with the powers of x in descending order (a) g(x) + f (x) (b) g(x) · f (x) (c) (f (x))2 · 3 − 2 · g(x) 4. Multiply out the following products and simplify as much as possible (a) (x − 2)(x + 12) (c) (2x + 4)(4 − 2x) (b) (x + 7)(x − 7) (d) (x + a)(x + b) 5. A student wants to ﬁnd two integers which multiply together to be 36 but add together to be as big as possible. Which integers should they choose? 6. The number 12 can be factored into the product of two integers in the following 6 ways 1, 12 -1, -12 2, 6 -2, -6 3, 4 -3, -4 (a) Which of the above pairs makes the following expression true (x + )(x + ) = x2 − 8x + 12 (b) Find all the pairs of integers whose product is 45, using these pairs ﬁll in the blanks with integers which make the following equation true (x + )(x + (c) Do the same for −32 and the equation (x + ) = x2 + 14x + 45 )(x + ) = x2 − 14x − 32 (d) Do the same for −20 and the equation (2x + )(x + ) = 2x2 + 6x − 20 (e) Do the same for 32 · b2 and the equation (x + )(x + ) = x2 + 6bx + 32 b2 7. Multiply out the following products and simplify as much as possible (a) (x2 − 2x + 1)(x + 1) (b) (x − 1)(x2 + x + 1) (c) (a + b)2 + (a − b)2