Use synthetic division to find the quotient if polynomial P(x) = x3 – 7x + 6 is divided by x – 2.
Question 17 options:

A)

x2 – 2x + 3

B)

x2 – 2x – 3

C)

x2 + 2x – 3

D)

x2 + 2x + 3

Answer:

C.) [tex]x^2+2x-3[/tex]

Step-by-step explanation:

They give us the function; [tex]P(x)=x^3-7x+6[/tex], which is then divided by the binomial, [tex](x-2)[/tex].

We can use polynomial synthetic division to solve this! First, let's understand how we must use it properly.

As we can tell from the function [tex]P(x)=x^3-7x+6[/tex] , there is an exponent value of 3, and an "invisible" exponent of one on -7x. When doing the synthetic division, we must put in a zero before we introduce the term '-7x' in our process of division.

The binomial [tex](x-2)[/tex] tells us that we are dividing the function by that, but we have to take the opposite value of the integer value, and here's why.

[tex](x-2)=0[/tex]

If we are trying to solve for 'x' here, we have to add plus sides by two, and we get x=2. That is what we have to put on the left side of the synthetic division we will use, we are essentially stating that one of the root/solution(s) to the function is 2, and we get verification of that when the synthetic division results in zero towards the end.  

Then when the synthetic division has been done, since we are dividing by that binomial, we take out the values that we know already, which are '1', '2', and '-3', and take away one power of exponent to each of them (if applicable)

Thus, leaving us with our answer, [tex]x^2+2x-3[/tex].

The required quetient of the given expression is x² - 2x -3. Options C is correct.

It is a method for performing division of polynomials, with little writing and lesser calculations than complex division.

here,
synthetic division is given as,
put divisor equal zero,
x - 2 = 0 so x = 2

Now,
Arranging the division with zero and coefficients and constant of the expressions,

2    |   1  0   -7    6
     +      2   4   -6
----------------------------
          1  2  -3   0

So, the question, by synthetic division is given as x² + 2x -3.

Thus, the required quetient of the given expression is x² - 2x -3. Options C is correct.

Learn more about synthetic divisions here:

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