Factor the following trinomial $$ x^{2}-4 x-32 $$ Select the correct choce below and, il necessary, fill in the answer box to complete your choice. A. $$ x^{2}-4 x-32= $$ (Type your answer in factored form.) B. The polynomial is prime.

Question

UpStudy AI · Accepted Answer

1. We need to factor the trinomial
   $$
   x^{2}-4x-32.
   $$

2. Look for two numbers $$ m $$ and $$ n $$ such that
   $$
   m \cdot n = -32 \quad \text{and} \quad m+n = -4.
   $$

3. Testing possible pairs, we find that $$ 4 $$ and $$ -8 $$ work because
   $$
   4 \cdot (-8) = -32 \quad \text{and} \quad 4+(-8)=-4.
   $$

4. Rewrite the trinomial by splitting the middle term:
   $$
   x^{2}-4x-32 = x^{2}+4x-8x-32.
   $$

5. Factor by grouping:
   $$
   (x^{2}+4x) + (-8x-32).
   $$

6. Factor out the greatest common factor from each group:
   $$
   x(x+4) - 8(x+4).
   $$

7. Factor out the common binomial factor $$(x+4)$$:
   $$
   (x+4)(x-8).
   $$

Thus, the correct choice is A with the factored form:
$$
x^{2}-4x-32=(x+4)(x-8).
$$
The trinomial $$ x^{2}-4x-32 $$ factors to $$ (x+4)(x-8) $$.

Factor the following trinomial \[ x^{2}-4 x-32 \] Select the correct choce below and, il necessary, fill in the answer box to complete your choice. A. \( x^{2}-4 x-32= \) (Type your answer in factored form.) B. The polynomial is prime.

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Algebra Questions