Respuesta :
Answer: The answer is [tex](x+7)(3x+1)=33x^2+22x+7.[/tex]
Step-by-step explanation: Given that
[tex](3x2 + 22x + 7) \div(x + 7) = 3x + 1,[/tex]
and we are to complete the following sentence:
[tex](x+7)(???)=???[/tex]
We have the following division algorithm for polynomials
[tex]\textup{If }a(x)\times b(x)=c(x),\\\textup{then, we have }\\\\\dfrac{c(x)}{b(x)}=a(x)~~~~~\textup{or}~~~~~~c(x)\div b(x)=a(x).[/tex]
Here, a(x) = quotient, b(x) = divisor and c(x) = dividend.
Applying this rule in the given problem, we have
[tex]\textup{since }(3x2 + 22x + 7) \div(x + 7) = 3x + 1,\\\\\textup{so, }\\\\(x+7)(3x+1)=3x^2+22x+7=0.[/tex]
Thus, the complete sentence is
[tex](x+7)(3x+1)=3x^2+22x+7=0.[/tex]
Complete sentence is; (x + 7)(3x + 1) = 3x² + 22x + 7
This question involves the concept of polynomial division.
We are told that;
(3x² + 22x + 7) ÷ (x + 7) = 3x + 1
Now, from the concept of polynomial division, we know that;
if, f(x) ÷ g(x) = h(x),
it means that we can write;
f(x) = g(x) × h(x)
Applying this same concept to our question, we can also say that;
Since (3x² + 22x + 7) ÷ (x + 7) = 3x + 1,
Then; (x + 7)(3x + 1) = 3x² + 22x + 7
Read more at; brainly.com/question/12520197
