Question 1.1 Describe the following number patterns - id1113580960, hailee232

Question

Mathematics: Question 1.1 Describe the following number patterns in your words and state the Constance difference or constant ratio.1.1.1 36. 32.28.24.201.1.2 2.6.18.54,1621.1.3 5.10.15.20.25​

hailee232 · Accepted Answer

When factored completely, m^5 + m^3 -6m is equivalent to $m(m-\sqrt2)(m+\sqrt2)(m^2+3)$

To factorize the polynomial

m^5 + m^3 -6m

notice that the GCF of each term is m. So we can factorize m out of each term as follows

m^5 + m^3 -6m=m(m^4 + m^2 -6)

the fourth-degree polynomial in the brackets an be treated as a quadratic polynomial

(m^2)^2+(m^2)-6

and factorized as such. The quadratic has the constant term . We have to look for factors of that add up to (the co-efficient of the m^2 term).

The factors that satisfy the condition are and . So we can factorize the fourth-degree polynomial as

(m^2)^2+(m^2)-6=(m^2-2)(m^2+3)

We have factorized the polynomial so far as

m^5 + m^3 -6m=m(m^2-2)(m^2+3)

But the factor (m^2-2) is a difference of two squares and can be factorized as

$m^2-2=(m-\sqrt2)(m+\sqrt2)$

Our final factored polynomial is

$m(m-\sqrt2)(m+\sqrt2)(m^2+3)$

Learn more about polynomial factorization here link

Question 1.1 Describe the following number patterns in your words and state the Constance difference or constant ratio.
1.1.1 36. 32.28.24.20
1.1.2 2.6.18.54,162
1.1.3 5.10.15.20.25

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

Question 1.1 Describe the following number patterns in your words and state the Constance difference or constant ratio.1.1.1 36. 32.28.24.201.1.2 2.6.18.54,1621.1.3 5.10.15.20.25​