Using long division, determine which of the following polynomials divides evenly for a divisor of x+4 .(1 point) Responses 3x2−19x−28 3 x squared minus 19 x minus 28 - no response given −3x2−19x−28 negative 3 x squared minus 19 x minus 28 - no response given −3x2−19x+28 negative 3 x squared minus 19 x plus 28 - no response given 3x2+19x−28

To determine which of the given polynomials divides evenly by \( x + 4 \) using polynomial long division, we can take each polynomial and divide it by \( x + 4 \).

**Step 1: Dividing \( 3x^2 - 19x - 28 \) by \( x + 4 \)**

1. Divide the leading term of the dividend by the leading term of the divisor:
\[
\frac{3x^2}{x} = 3x
\]
2. Multiply \( 3x \) by \( x + 4 \):
\[
3x(x + 4) = 3x^2 + 12x
\]
3. Subtract from the original polynomial:
\[
(3x^2 - 19x - 28) - (3x^2 + 12x) = -31x - 28
\]
4. Now divide \(-31x\) by \(x\):
\[
\frac{-31x}{x} = -31
\]
5. Multiply \(-31\) by \(x + 4\):
\[
-31(x + 4) = -31x - 124
\]
6. Subtract:
\[
(-31x - 28) - (-31x - 124) = 96
\]

The remainder is \(96\), so \(3x^2 - 19x - 28\) does not divide evenly by \(x + 4\).

---

**Step 2: Dividing \(-3x^2 - 19x - 28\) by \(x + 4\)**

1. Divide the leading term:
\[
\frac{-3x^2}{x} = -3x
\]
2. Multiply:
\[
-3x(x + 4) = -3x^2 - 12x
\]
3. Subtract:
\[
(-3x^2 - 19x - 28) - (-3x^2 - 12x) = -7x - 28
\]
4. Now divide \(-7x\):
\[
\frac{-7x}{x} = -7
\]
5. Multiply:
\[
-7(x + 4) = -7x - 28
\]
6. Subtract:
\[
(-7x - 28) - (-7x - 28) = 0
\]

The remainder is \(0\). Therefore, \(-3x^2 - 19x - 28\) divides evenly by \(x + 4\).

---

**Step 3: Dividing \(-3x^2 - 19x + 28\) by \(x + 4\)**

1. Leading term:
\[
\frac{-3x^2}{x} = -3x
\]
2. Multiply:
\[
-3x(x + 4) = -3x^2 - 12x
\]
3. Subtract:
\[
(-3x^2 - 19x + 28) - (-3x^2 - 12x) = -7x + 28
\]
4. Now divide \(-7x\):
\[
\frac{-7x}{x} = -7
\]
5. Multiply:
\[
-7(x + 4) = -7x - 28
\]
6. Subtract:
\[
(-7x + 28) - (-7x - 28) = 56
\]

The remainder is \(56\), so \(-3x^2 - 19x + 28\) does not divide evenly by \(x + 4\).

---

**Step 4: Dividing \(3x^2 + 19x - 28\) by \(x + 4\)**

1. Leading term:
\[
\frac{3x^2}{x} = 3x
\]
2. Multiply:
\[
3x(x + 4) = 3x^2 + 12x
\]
3. Subtract:
\[
(3x^2 + 19x - 28) - (3x^2 + 12x) = 7x - 28
\]
4. Now divide \(7x\):
\[
\frac{7x}{x} = 7
\]
5. Multiply:
\[
7(x + 4) = 7x + 28
\]
6. Subtract:
\[
(7x - 28) - (7x + 28) = -56
\]

The remainder is \(-56\), so \(3x^2 + 19x - 28\) does not divide evenly by \(x + 4\).

---

**Conclusion:**
The only polynomial among the given options that divides evenly by \(x + 4\) is:

\[
\boxed{-3x^2 - 19x - 28}
\]