Question

imaginary). show proper work to receiv

1. f(x) = x³ + 2x² + 5x +10

factored form:
solutions:

Explanation:

Step1: Group Terms

Group the first two terms and the last two terms: $f(x) = (x^3 + 2x^2) + (5x + 10)$

Step2: Factor Each Group

Factor out the greatest common factor from each group: $f(x) = x^2(x + 2) + 5(x + 2)$

Step3: Factor Out Common Binomial

Factor out the common binomial factor $(x + 2)$: $f(x) = (x^2 + 5)(x + 2)$

Step4: Find Solutions

Set $f(x) = 0$:

• For $x + 2 = 0$, we get $x = -2$
• For $x^2 + 5 = 0$, we have $x^2 = -5$, so $x = \pm\sqrt{-5} = \pm i\sqrt{5}$

Answer:

Factored Form: $(x + 2)(x^2 + 5)$
Solutions: $x = -2$, $x = i\sqrt{5}$, $x = -i\sqrt{5}$