Use the method of your choice to factor the trinomial, or state that the trin

Select the correct choice below and if necessary, fill in the answer box to
A.
B. The polynomial is prime

Ask by Ramirez Deleon. in the United States

Jan 27,2025

Question

Use the method of your choice to factor the trinomial, or state that the trin

Select the correct choice below and if necessary, fill in the answer box to
A.
B. The polynomial is prime

Ask by Ramirez Deleon. in the United States

Jan 27,2025

UpStudy AI · Accepted Answer

To factor the trinomial $$ 5x^{2} + 19x - 4 $$, we can use the **ac method**.

1. **Identify coefficients**:
   - $$ a = 5 $$
   - $$ b = 19 $$
   - $$ c = -4 $$

2. **Multiply $$ a $$ and $$ c $$**:
   $$
   a \times c = 5 \times (-4) = -20
   $$

3. **Find two numbers that multiply to $$ -20 $$ and add to $$ 19 $$**:
   - The numbers are $$ 20 $$ and $$ -1 $$ because:
     $$
     20 \times (-1) = -20 \quad \text{and} \quad 20 + (-1) = 19
     $$

4. **Rewrite the middle term using these numbers**:
   $$
   5x^{2} + 20x - x - 4
   $$

5. **Factor by grouping**:
   $$
   (5x^{2} + 20x) - (x + 4) = 5x(x + 4) - 1(x + 4)
   $$

6. **Factor out the common binomial**:
   $$
   (x + 4)(5x - 1)
   $$

**Answer Choice A is correct**:
$$
5x^{2} + 19x - 4 = (x + 4)(5x - 1)
$$

**Answer**:
**A.** $$5 x^{2}+19 x-4 = (x + 4)(5x - 1)$$
$$5x^{2} + 19x - 4 = (x + 4)(5x - 1)$$

Use the method of your choice to factor the trinomial, or state that the trin

Select the correct choice below and if necessary, fill in the answer box to
A.
B. The polynomial is prime

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Use the method of your choice to factor the trinomial, or state that the trin Select the correct choice below and if necessary, fill in the answer box to A. B. The polynomial is prime

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