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Answer:
- (p, q, r) = (-1, -3/2, 1/2)
- f(x) = (2x -1)(2x +1)
- g(x) = (x -2)(x +1/2)
Explanation:
Substituting for p in the equation for f(x), we can use synthetic division to find the value of r that makes the remainder zero from division by (x +r).
To make (x+r) be a factor, the remainder (4r² -2r) must be zero. That factors as ...
2r(2r -1) = 0 ⇒ r = 1/2; r = 0 is disallowed by the problem statement
Then p = -2r = -1, and q = -3r = -3/2.
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The functions with the values filled in are ...
f(x) = 4x² -1 = (2x -1)(2x +1)
g(x) = x² -3/2x -1 = (x -2)(x +1/2)