Answered

Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Use the digits 1-20, at most one time each, to create a true statement for polynomial below.
(the _ are blanks that need to be filled in)
_x(x^2 - _x) + _x^3 = _x(_x^2 + _x) - x^2

Sagot :

MrRoyal

The complete equation of the polynomial is 2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2

How to complete the blanks?

The equation is given as:

_x(x^2 - _x) + _x^3 = _x(_x^2 + _x) - x^2

Complete the blanks using alphabets

ax(x^2 - bx) + cx^3 = dx(ex^2 + fx) - x^2

Open the brackets

ax^3 - abx^2 + cx^3 = dex^3 + dfx^2- x^2

Factorize the expression

(a + c)x^3 - abx^2 = dex^3 + (df - 1)x^2

By comparison, we have:

a + c = de

-ab = df - 1

Rewrite the second equation as:

ab + df = 1

So, we have:

a + c = de

ab + df = 1

Set a = 2 and c = 10.

So, we have:

a + c = de ⇒ de = 2 + 10 ⇒ de = 12

ab + df = 1 ⇒2b + df = 1

Express 12 as 3 * 4 in de = 12

de = 3 * 4

By comparison, we have:

d = 3 and e = 4

So, we have:

2b + df = 1

This gives

2b + 3f = 1

Set b = 11.

So, we have:

2 * 11 + 3f = 1

This gives

22 + 3f = 1

Subtract 22 from both sides

3f = -21

Divide by 3

f = -7

Hence, the complete equation is:

2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2

Read more about polynomials at:

https://brainly.com/question/4142886

#SPJ1

We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.