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Factor.
x, squared, plus, 4, x, minus, 21
x
2
+4x−21

Answer 1

To factor the quadratic expression \( x^2 + 4x - 21 \), we can follow these steps:

1. **Identify the coefficients**:
- The coefficient of \( x^2 \) (which is \( a \)) is 1.
- The coefficient of \( x \) (which is \( b \)) is 4.
- The constant term (which is \( c \)) is -21.

2. **Factor the expression**:
We are looking for two numbers that multiply to \( ac = 1 \times -21 = -21 \) and add to \( b = 4 \).

The two numbers that meet these conditions are \( 7 \) and \( -3 \) because:
- \( 7 \times -3 = -21 \)
- \( 7 + (-3) = 4 \)

3. **Rewrite the middle term**:
We can rewrite the expression as:
\[
x^2 + 7x - 3x - 21
\]

4. **Group the terms**:
Now, group the terms:
\[
(x^2 + 7x) + (-3x - 21)
\]

5. **Factor by grouping**:
Factor out the common factors from each group:
\[
x(x + 7) - 3(x + 7)
\]

6. **Factor out the common binomial**:
Now, we can factor out \( (x + 7) \):
\[
(x + 7)(x - 3)
\]

So, the factored form of \( x^2 + 4x - 21 \) is:
\[
(x + 7)(x - 3)
\]