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4 years ago

Complete the sentence below. If (3x2 + 22x + 7) ÷(x + 7) = 3x + 1, then (x + 7)(???????) =???? .

Mathematics

2 answers:

g100num [7]4 years ago

7 0

Answer: The answer is $(x+7)(3x+1)=33x^2+22x+7.$

Step-by-step explanation: Given that

$(3x2 + 22x + 7) \div(x + 7) = 3x + 1,$

and we are to complete the following sentence:

$(x+7)(???)=???$

We have the following division algorithm for polynomials

$\textup{If }a(x)\times b(x)=c(x),\\\textup{then, we have }\\\\\dfrac{c(x)}{b(x)}=a(x)~~~~~\textup{or}~~~~~~c(x)\div b(x)=a(x).$

Here, a(x) = quotient, b(x) = divisor and c(x) = dividend.

Applying this rule in the given problem, we have

$\textup{since }(3x2 + 22x + 7) \div(x + 7) = 3x + 1,\\\\\textup{so, }\\\\(x+7)(3x+1)=3x^2+22x+7=0.$

Thus, the complete sentence is

$(x+7)(3x+1)=3x^2+22x+7=0.$

svetoff [14.1K]4 years ago

3 0

Answer:

3x+1, 3x^2+22x+7, and closure

Step-by-step explanation:

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