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1 year ago

Factor completely 12x4 6x3 18x2. Prime 6(2x4 x3 3x2) 6x2(2x2 x 3) 6x(2x3 x2 3x).

Mathematics

1 answer:

Katena32 [7]1 year ago

3 0

The factors of the above equation are 6,x,x & 2x²+x+3.

We have the expression: 12x⁴+6x³+18x²

<h3>what is the factor?</h3>

a factor is a number that divides the other number leaving no remainder.

we can take 6x² as common and rewrite the expression as,

6x²(2x²+x+3)

6. x.x(2x²+x+3)

further, we cannot make factors since the quadratic equation 2x²+x+3 does not have real roots.

therefore, the factors of the above equation are 6,x,x & 2x²+x+3

to get more about factors refer to the link,

brainly.com/question/25829061

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<u>Solution: </u>

The number of combinations of n things such that m things taken together are given by:-

$C_{(\boldsymbol{n}, \boldsymbol{m})}=\frac{n !}{m !(\boldsymbol{n}-\boldsymbol{m}) !}$

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A committee consisting of 4 faculty members and 5 students is to be formed. There are 12 faculty members and 13 students eligible to serve on the committee.

Then, the number of ways to form the committee is formed given by :-

$\begin{array}{l}{12 C_{4} \times 13 C_{5}} \\\\ {=\frac{12 !}{4 !(12-4) !} \times \frac{13 !}{5 !(13-5) !}} \\\\ {=\frac{12 !}{4 ! 8 !} \times \frac{13 !}{5 ! 8 !}} \\\\ {\frac{12 \times 11 \times 10 \times 9 \times 8 !}{27 \times 8 !} \times \frac{13 \times 12 \times 11 \times 10 \times 9 \times 8}{120 \times 8 !}} \\\\ {=637065}\end{array}$

Hence, the number of ways to form the committee is formed = 637065

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