Answer :
To find the missing factor, we need to use the relationship between the product and its factors.
Given:
- The product is [tex]\(9x^7\)[/tex].
- One of the factors is [tex]\(3x^7\)[/tex].
We can express this relationship as follows:
[tex]\[ 9x^7 = (3x^7) \times (\text{missing factor}) \][/tex]
To find the missing factor, we simply need to divide the product by the known factor:
[tex]\[ \text{missing factor} = \frac{9x^7}{3x^7} \][/tex]
When we divide [tex]\(9x^7\)[/tex] by [tex]\(3x^7\)[/tex], we follow these steps:
1. Divide the coefficients: Divide 9 by 3 to get 3.
2. Divide the powers of x: Since both factors have the same power of [tex]\(x^7\)[/tex], subtract the exponents:
[tex]\[
x^{7-7} = x^0 = 1
\][/tex]
(Recall that any number to the power of zero is 1.)
Combining these results, the missing factor simplifies to:
[tex]\[ 3 \times 1 = 3 \][/tex]
Therefore, the missing factor is 3.
Given:
- The product is [tex]\(9x^7\)[/tex].
- One of the factors is [tex]\(3x^7\)[/tex].
We can express this relationship as follows:
[tex]\[ 9x^7 = (3x^7) \times (\text{missing factor}) \][/tex]
To find the missing factor, we simply need to divide the product by the known factor:
[tex]\[ \text{missing factor} = \frac{9x^7}{3x^7} \][/tex]
When we divide [tex]\(9x^7\)[/tex] by [tex]\(3x^7\)[/tex], we follow these steps:
1. Divide the coefficients: Divide 9 by 3 to get 3.
2. Divide the powers of x: Since both factors have the same power of [tex]\(x^7\)[/tex], subtract the exponents:
[tex]\[
x^{7-7} = x^0 = 1
\][/tex]
(Recall that any number to the power of zero is 1.)
Combining these results, the missing factor simplifies to:
[tex]\[ 3 \times 1 = 3 \][/tex]
Therefore, the missing factor is 3.
