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Analyze the expression and then choose the sentences describing whether the binomial theorem can be used to factor it. Check all that apply.

x^3 – 24x^2 + 192x – 512

A.) The value of n is 3, and the first and last terms are perfect cubes.

B.) The middle terms do not take into account the coefficients from Pascal’s triangle.

C.) The exponents on each term follow the pattern for a binomial expansion.

D.) The sign of the constant must be positive in the binomial expansion. The signs are all reversed.

E.) The expression can be factored using the binomial theorem.

F.) The expression cannot be factored using the binomial theorem.

Respuesta :

Answer:

-The middle terms do not take into account the coefficients from Pascal’s triangle.

-The exponents on each term follow the pattern for a binomial expansion.

-The expression cannot be factored using the binomial theorem.

The statements that apply for the expression are A , D and E

What is Binomial Theorem ?

Binomial theorem explains how to expand the algebraic statement (x + y)ⁿ  to a sum of terms using individual exponents of variables x and y.

The expression given is

x³ – 24x² + 192x – 512

as the first and the last term is a  perfect cube

In general (a-b)³ = a³ - 3a²b +3ab²-b³

here a = x and b = 8

(x-8)³ = x³ +3 *x*8² -3 *8*x² -8³

(x-8)³ = x³ – 24x² + 192x – 512

Therefore it can be factorized using Binomial Theorem , n = 3 and the factors follow the rule for binomial expansion so the statements that are correct are A , C and E

To know more about Binomial Theorem

https://brainly.com/question/27813780

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