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3 years ago

Factor the following polynomial written in standard form. B^2-14B+49

Mathematics

1 answer:

Vladimir79 [104]3 years ago

8 0

After factoring $B^2-14B+49$ we get $(B-7)(B-7)$

Step-by-step explanation:

We need to factorize the polynomial:

$B^2-14B+49$

Factorization is done by breaking the middle term such that the sum is equal to the middle value of polynomial and product is equal to product of first and last term in the polynomial.

So, Factorizing:

$B^2-14B+49\\=B^2-7B-7B+49\\=B(B-7)-7(B-7)\\=(B-7)(B-7)$

So, After factoring $B^2-14B+49$ we get $(B-7)(B-7)$

Keywords: Factorization, Factors

Learn more about factors at:

#learnwithBrainly

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Question 2 of 5

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Given:

The different recursive formulae.

To find:

The explicit formulae for the given recursive formulae.

Solution:

The recursive formula of an arithmetic sequence is $f(n)=f(n-1)+d, f(1)=a,n\geq 2$ and the explicit formula is $f(n)=a+(n-1)d$ , where a is the first term and d is the common difference.

The recursive formula of a geometric sequence is $f(n)=rf(n-1), f(1)=a,n\geq 2$ and the explicit formula is $f(n)=ar^{n-1}$ , where a is the first term and r is the common ratio.

The first recursive formula is:

$f(1)=5$

$f(n)=f(n-1)+5$ for $n\geq 2$ .

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 5. So, the explicit formula for this recursive formula is:

$f(n)=5+(n-1)(5)$

$f(n)=5+5(n-1)$

Therefore, the correct option is A, i.e., $f(n)=5+5(n-1)$ .

The second recursive formula is:

$f(1)=5$

$f(n)=3f(n-1)$ for $n\geq 2$ .

It is the recursive formula of a geometric sequence with first term 5 and common ratio 3. So, the explicit formula for this recursive formula is:

$f(n)=5(3)^{n-1}$

Therefore, the correct option is F, i.e., $f(n)=5(3)^{n-1}$ .

The third recursive formula is:

$f(1)=5$

$f(n)=f(n-1)+3$ for $n\geq 2$ .

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 3. So, the explicit formula for this recursive formula is:

$f(n)=5+(n-1)(3)$

$f(n)=5+3(n-1)$

Therefore, the correct option is D, i.e., $f(n)=5+3(n-1)$ .

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