Factor the polynomial and use the factored form to find the zeros. (Enter your answers as a comma-separated list. Enter all
answers including repetitions.)

Ask by Spencer Riley. in the United States

Mar 28,2025

Question

Factor the polynomial and use the factored form to find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) $$ P(x)=x^{3}-x^{2}-20 x $$ $$ x=\square $$

UpStudy AI · Accepted Answer

1. Factor out the common factor:
   $$
   P(x)=x^{3}-x^{2}-20x=x\left(x^{2}-x-20\right)
   $$

2. Factor the quadratic $$ x^{2}-x-20 $$:
   We need two numbers that multiply to $$-20$$ and add to $$-1$$. These numbers are $$-5$$ and $$4$$. Therefore,
   $$
   x^{2}-x-20=\left(x-5\right)\left(x+4\right)
   $$

3. Write the completely factored form of $$ P(x) $$:
   $$
   P(x)=x\left(x-5\right)\left(x+4\right)
   $$

4. Find the zeros by setting each factor equal to zero:
   - From $$ x=0 $$
   - From $$ x-5=0 $$: $$ x=5 $$
   - From $$ x+4=0 $$: $$ x=-4 $$

The zeros are: $$ -4, 0, 5 $$.
The zeros are: -4, 0, 5.

Factor the polynomial and use the factored form to find the zeros. (Enter your answers as a comma-separated list. Enter all
answers including repetitions.)

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