Which are factors of x2 – 4x – 5?

Mathematics

1 answer:

Kitty [74]4 years ago

7 0

Answer:

(x-5)(x+1)

Step-by-step explanation:

Since the highest power of x is 2, u can assume the equation to be (x +/- A) (x +/- B), whereby A and B are unknowns.

Since the coefficient of X^2 is 1, and the number in the equation is - 5, the only possible values for A and B to get - 5 is either - 5 and 1 or 1 and - 5.

Since coefficient of x is - 4 and number in equation is - 5, imagine inserting those numbers in the equation and cross multiplying back. You would realise that the answer should be as listed above.

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Simplify -6i(8-6i)(-8-8i)

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Answer:

-96 + 672\,i

Step-by-step explanation:

This is a product of complex numbers, so we have in mind not only the general rules for multiplying binomials, but also the properties associated with the powers of the imaginary unit "i", in particular $i^2=-1$

We start by making the first product indicated which is that of a pure imaginary number (-6i) times the complex number (8-6i). We use distributive property and obtain the new complex number that results from this product:

$-6\,i\,(8-6\,i)= (-6\,i)\,* 8 \, -\,6\,i\,(-6\,i)=-48\,i+36\,i^2=-48\,i+36\,(-1)=-36-48\,i$

Now we make the second multiplication indicated (using distributive property as one does with the product of binomials), and combine like terms at the end:

$(-36-48\,i)\,(-8-8\.i)=(-36)\.(-8)+(-36)(-8\,i)+(-48\,i)\,(-8)+(-48\,i)(-8\,i)=\\=288+288\,i+384\,i+384\,i^2=288+288\,i+384\,i+384\,(-1)=\\=288-384+288\,i+384\,i=-96+672\,i$