Answer:
(a) -2 (multiplicity 2) and +2
(b) ±√2
Step-by-step explanation:
(a) Factor by grouping:
f(x) = (x^3 +2x^2) -(4x +8)
= x^2(x +2) -4(x +2) . . . . . remove the common factor from each group
= (x^2 -4)(x +2) . . . . . . . . .collect the factors
= (x -2)(x +2)(x +2) . . . . . . factor the difference of squares
Zeros are the values of x that make these factors be zero: {2, -2, -2}.
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(b) g(x) = 0 = -x^2 +2
You can factor this as the difference of squares:
(√2 -x)(√2 +x) = 0
The zeros are the values of x that make these factors be zero: {√2, -√2}.
