Question

Consider this polynomial, where a is an unknown real number.
p(t) = x^4 +5x^3 + ax^2 - 3x + 11
The remainder of the quotient of P(x), and (x+ 1) is 17.
Braulio uses synthetic division to find the value of a, and Zahra uses the remainder theorem to find the value of a.

Answer 1

Answer:

Brauilo is wrong because he divided by (x+1) instead of (x-1)

Step-by-step explanation:

The remainder Theorem states that

if polynomial f(x) is divided by binomial x-a, the remainder will equal f(a). The factor is positive so the binomial is the same as

which is why we divide by -1, or subsitue -1 into the equation p(x).

Answer 2

The remainder of a polynomial division can be gotten using remainder theorem or synthetic division.

The true statement is: Brauilo did not find the value of a, because he divided by (x+1) instead of (x-1)

From the question, we have the following parameters:

$\mathbf{p(x) = x^4 +5x^3 + ax^2 - 3x + 11}$

$\mathbf{Divisor =x+ 1}$

$\mathbf{Remainder = 17}$

First, we set the divisor to 0.

$\mathbf{Divisor =x+ 1 = 0}$

So, we have:

$\mathbf{x+ 1 = 0}$

Solve for x

$\mathbf{x= -1}$

The above equation means that, the value of x that will be used to test the polynomial is -1

From the question,

• Zahra used $\mathbf{x= -1}$; this is represented as: P(-1)
• Braulio used $\mathbf{x= 1}$; this is represented in the synthetic division

Hence, Braulio is incorrect, because he used the wrong value of x

Read more about polynomial division at:

https://brainly.com/question/12011809