When written in factored form, which two polynomials have a factor of x + 12? a. x2 + 10x – 24 b. x2 – 8x – 48 c. x2 – 12x + 27 d. x2 + 15x + 36 e. x2 + 8x + 12

You should write x squared as x^2

both a and d have x + 12 as a factor  Let me know if anything here doesn't make sense.  

Step-by-step explanation:

You should write x squared as x^2 Let's factor each though.  I am going to use the method of finding d and e where d + e = b and d * e = a * c where a, b and c are ax^2 + bx + c in a quadratic polynomial.  To do this first find all factors of a*c and try adding them all.  

a) x^2 + 10x - 24, a = 1, b = 10 and d = -24

a*c = -24 = d*e so let's try out all factors and see what happens when we add them because d + e = 10

-1 and 24 don't work

1 and -24 don't work

2 and -12 don't work

-2 and 12 does work so there's the answer.

x^2 - 2x + 12x - 24

x(x - 2) + 12(x - 2)

(x + 12)(x-2)  And hey, x + 12!

b) x^2 - 8x - 48 a*c = -48 = d*e and d+e = -8

-1 and 48 doens't work

1 and -48 doesn't work

2 and -24 doesn't work

-2 and 24 doesn't work

3 and -16 doesn't work

-3 and 16 doesn't work

4 and -12 DOES work

x^2 + 4x - 12x - 48

x(x + 4) - 12(x + 4)

(x - 12)(x + 4)

No x + 12 so this is not a correct answer

c) x^2 - 12x + 27 a*c = 27 = d*e and d+e = -12

1 and 27 doesn't work

-1 and -27 doesn't work

3 and 9 doesn't work

-3 and -9 does work

x^2 - 12x + 27

x^2 - 3x - 9x + 27

x(x - 3) - 9(x - 3)

(x-9)(x-3) No x+12 so not a right answer.

d) x^2 + 15x + 36 where a*c = 36 = d*e and d+e = 15

1 and 36 doesn't work

-1 and -36 doesn't work

2 and 18 doesn't work

-2 and -18 doesn't work

3 and 12 DOES work

x^2 + 15x + 36

x^2 + 3x + 12x + 36

x(x + 3) + 12(x + 3)

(x+12)(x+3)  And here is x + 12 again so it is one of the right answers.

e) x^2 + 8x + 12 where a*c = 12 = d*e and d+e = 8

1 and 2 doesn't work

-1 and -2 doesn't work

2 and 6 DOES work

x^2 + 8x + 12

x^2 + 2x + 6x + 12

x(x + 2) + 6(x + 2)

(x+6)(x+2) No x+12 so not  an answer.

this means a and d are the right answer for this question.

answer: c

step-by-step explanation: because you don't have to draw a point of intersection. couldyou give me brainliest?

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introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.