Find the greatest common factor of the following monomial 6bc and 9b^2c

Mathematics

2 answers:

galina1969 [7]4 years ago

6 0

Both 6bc and 9b²c are multiples of the number 3bc - we can rewrite them as

3bc · 2 and 3bc · 3b

Since the two monomials share the factors 3, b and c, their greatest common factor is 3bc.

lions [1.4K]4 years ago

4 0

The greatest common factors would be the biggest number that goes into both of these monomial.

As we can see, they both have one b and one c. This is the largest number of b’s and c’s it can have, as it can’t be any bigger.

Also, the greatest common factor of 6 and 9 is 3.

So, the answer is 3bc.

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If a polynomial function f(x) has roots -8, 1, and 6i, what must also be a root of f(x)?

Naddik [55]

Answer:

it must also have the root : - 6i

Step-by-step explanation:

If a polynomial is expressed with real coefficients (which must be the case if it is a function f(x) in the Real coordinate system), then if it has a complex root "a+bi", it must also have for root the conjugate of that complex root.

This is because in order to render a polynomial with Real coefficients, the binomial factor (x - (a+bi)) originated using the complex root would be able to eliminate the imaginary unit, only when multiplied by the binomial factor generated by its conjugate: (x - (a-bi)). This is shown below:

$(x-(a+bi))*(x-(a-bi))=\\(x-a-bi)*(x-a+bi)=\\([x-a]-bi)*([x-a]+bi)=\\(x-a)^2-(bi)^2=\\(x-a)^2-b^2(-1)=\\(x-a)^2+b^2$