Find the interval on whitch the expression is ...

 

Find the interval on whitch the expression is defined:?x?2-7x-8 That’s the square root of the trinomial (x squared - 7x - 8)

 

I am thoroughly confused- they gave us the answers, but we need to show how we got them, so I need help.

 

The answer is (-?, -1], [8,?) That’s (negative infinity, -1], [8, infinity)

 

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Best Answer

The expression x^2-7x-8 can be factored as (x+1)(x-8).  That will be a positive quantity if x is greater than 8 (both terms positive), or less than -1 (both terms negative).  The square root of a positive quantity is a real number.  The square root of a negative quantity is not a real number, so it is not defined between -1 and +8.

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Algebraic expressions can be multiplied together. An algebraic expression may consist of a number  ( coefficient ), a letter ( variable, and/or an exponent.

When you multiply variables with exponents, you can add the exponents if the variables are the same.

Some problems require factoring algebraic expression. to factor means to

find and separate numbers that have been multiplied.   In an expression of four or more terms, you can use the method of factoring by grouping to factor the expression. 

 

In simple words: They are asking you what is the range that this function (X^2-7X-8) is possitive or zero.    Since X^2-7X-8 equals to (X+1)*(X-8)  this function is possitive or zero if X is > 8 (until infinity)   0r  X < -1  (untill minus infinity). 

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