Question

Choose + or - in each blank to complete the examples of each rule.
Rules for Factoring x'+ bx + c x+bx+C= (x+p)(x+q)
Rule
If b and c are both
positive, then pand q are (x choose your answer...




く
both positive.

If b and c are both
have opposite signs.
negative, then pand a (x choose your answer...

く

If b is positive and c is negative, then p and q have opposite signs.


(x choose your answer...
く

If b is negative and c is
positive, then p and q are (X choose your answer...
both negative.




Example x2+6x+9=
3) (x
3)
x'-4x-12=
2) (x
6)
x?+4x-12=
2) (x
6)
x'-6x+9=
3) (x
choose your answer...
choose your answer...
く
choose your answer...
く
choose your answer...

Answer 1

Let's fill in the blanks according to the rules for factoring quadratics.

1. **Rule:** If b and c are both positive, then p and q are **both positive.**

2. **Rule:** If b and c are both negative, then p and q are **both negative.**

3. **Rule:** If b is positive and c is negative, then p and q have **opposite signs.**

4. **Rule:** If b is negative and c is positive, then p and q are **both negative.**

Now, let's look at the examples and complete them:

1. Example: \( x^2 + 6x + 9 = (x + 3)(x + 3) \) or \( (x + 3)^2 \)

2. Example: \( x^2 - 4x - 12 = (x - 6)(x + 2) \)

3. Example: \( x^2 + 4x - 12 = (x + 6)(x - 2) \)

4. Example: \( x^2 - 6x + 9 = (x - 3)(x - 3) \) or \( (x - 3)^2 \)

So completed, the blanks are:

1. If b and c are both positive, then p and q are **both positive.**

2. If b and c are both negative, then p and q are **both negative.**

3. If b is positive and c is negative, then p and q have **opposite signs.**

4. If b is negative and c is positive, then p and q are **both negative.**