Question
order the steps to solve (x^2 + 6x + 9) ÷ (x + 3) by recognizing it as a perfect square trinomial from top to bottom
1. recognize x^2 + 6x + 9 as a perfect square trinomial (x + 3)^2
2. set up the division problem with x^2 + 6x + 9 as the dividend
3. divide the first term x^2 by x to get x
4. multiply x by x + 3 to get x^2 + 3x
5. check that the remainder is 0
6. divide 3x by x to get 3
7. subtract x^2 + 3x from x^2 + 6x to get 3x
1. recognize x^2 + 6x + 9 as a perfect square trinomial (x + 3)^2
2. set up the division problem with x^2 + 6x + 9 as the dividend
3. divide the first term x^2 by x to get x
4. multiply x by x + 3 to get x^2 + 3x
5. check that the remainder is 0
6. divide 3x by x to get 3
7. subtract x^2 + 3x from x^2 + 6x to get 3x
Answers
Answered by
GPT-4o mini
To solve \((x^2 + 6x + 9) ÷ (x + 3)\) by recognizing it as a perfect square trinomial, the steps should be ordered as follows:
1. **Set up the division problem with \(x^2 + 6x + 9\) as the dividend.**
2. **Recognize \(x^2 + 6x + 9\) as a perfect square trinomial \((x + 3)^2\).**
3. **Divide the first term \(x^2\) by \(x\) to get \(x\).**
4. **Multiply \(x\) by \(x + 3\) to get \(x^2 + 3x\).**
5. **Subtract \(x^2 + 3x\) from \(x^2 + 6x\) to get \(3x\).**
6. **Divide \(3x\) by \(x\) to get \(3\).**
7. **Check that the remainder is \(0\).**
So the ordered steps are: **2, 1, 3, 4, 7, 6, 5.**
1. **Set up the division problem with \(x^2 + 6x + 9\) as the dividend.**
2. **Recognize \(x^2 + 6x + 9\) as a perfect square trinomial \((x + 3)^2\).**
3. **Divide the first term \(x^2\) by \(x\) to get \(x\).**
4. **Multiply \(x\) by \(x + 3\) to get \(x^2 + 3x\).**
5. **Subtract \(x^2 + 3x\) from \(x^2 + 6x\) to get \(3x\).**
6. **Divide \(3x\) by \(x\) to get \(3\).**
7. **Check that the remainder is \(0\).**
So the ordered steps are: **2, 1, 3, 4, 7, 6, 5.**