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12345 [234]
3 years ago
9

Select all that apply. Which of the following are linear factors of p(x) = x 3 - 2x 2 - 5x + 6 ?1.x+1

Mathematics
2 answers:
Mrac [35]3 years ago
7 0
We can know the answer to this by letting p(x) be equal to zero and by substituting the values of x to the function.

p(x)= x^{3} -2 x^{2} -5x+6=0

To know what to substitute, we equate all factors to zero since even if only one of these factors is zero, the product of all factors would immediately be zero. 

1. x+1=0; x=-1
2. x+2=0; x=-2
3. x-1=0; x=1
4. x-3=0; x=3

We then try to substitute each value of x to the original polynomial and see if it will equal to zero.

1. (-1)^{3} -2(-1)^{2} -5(-1)+6=8\neq0
2. (-2)^{3} -2(-2)^{2} -5(-2)+6=0
3. (1)^{3} -2(1)^{2} -5(1)+6=0
4. (3)^{3} -2(3)^{2} -5(3)+6=0

As we can see, all but number 1 equated to zero therefore numbers 2, 3, and 4 are all linear factors of p(x).

ANSWER: Numbers 2, 3, and 4.
Virty [35]3 years ago
7 0
To be a linear factor, the value of x must make the value of the polinomial equal to zero:
1. x+1=0→x+1-1=0-1→x=-1
p(-1)=(-1)^3-2(-1)^2-5(-1)+6
p(-1)=-1-2(1)+5+6
p(-1)=-1-2+5+6
p(-1)=8 different to zero, then x+1 is not a linear factor of p(x)

2. x+2=0→x+2-2=0-2→x=-2
p(-2)=(-2)^3-2(-2)^2-5(-2)+6
p(-2)=-8-2(4)+10+6
p(-2)=-8-8+10+6
p(-2)=0, then x+2 is a linear factor of p(x)

3. x-1=0→x-1+1=0+1→x=1
p(1)=(1)^3-2(1)^2-5(1)+6
p(1)=1-2(1)-5+6
p(1)=1-2-5+6
p(1)=0, then x-1 is a linear factor of p(x)

4. x-3=0→x-3+3=0+3→x=3
p(3)=(3)^3-2(3)^2-5(3)+6
p(3)=27-2(9)-15+6
p(3)=27-18-15+6
p(3)=0, then x-3 is a linear factor of p(x)

Answer: The factor of p(x) are options 2, 3, and 4
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3 years ago
How many ways can a person select 3 coins from a box consisting of a penny, a nickel, a dime, a quarter, a half dollar, and a on
tekilochka [14]

Answer:

A person can select 3 coins from a box containing 6 different coins in 120 different ways.

Step-by-step explanation:

Total choices = n = 6

no. of selections to be made = r = 3

The order of selection of coins matter so we will use permutation here.

Using the formula of Permutation:

                  nPr = \frac{n!}{(n-r)!}

We can find all possible ways arranging 'r' number of objects from a given 'n' number of choices.

Order of coin is important means that if we select 3 coins in these two orders:

--> nickel - dime - quarter

--> dime - quarter - nickel

They will count as two different cases.

Calculating the no. of ways 3 coins can be selected from 6 coins.

nPr = \frac{n!}{(n-r)!} = \frac{6!}{(6-3)!}

nPr = 120

6 0
3 years ago
What’s the answer of the equation:<br><br> 104mn + (-84mn) =36
inn [45]

Answer:

1\frac{4}{5}mn

Step-by-step explanation:

104mn - 84mn = 36 \\  \\ 20mn = 36 \\  \\ 1\frac{4}{5}mn

This what you can do unless you are solving for either variable.

I am joyous to assist you anytime.

8 0
3 years ago
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