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Mkey [24]
2 years ago
14

5a^2-25a Select the method(s) of factoring that must be used to factor the following polynomial (select all that apply): Differe

nce of Squares, Product Sum Factoring, Greatest Common Factor (GCF), Bottoms Up Factoring, Cannot be factored.
Mathematics
1 answer:
aleksley [76]2 years ago
7 0

We are given : 5a^2-25a

Please note: We always check Greatest Common Factor (GCF) first when factoring a polynomial.

If Greatest Common Factor (GCF) exist we factor out GCF.

In the given polynomial, we can see that greatest common factor of 5a^2 and 25a is 5a.

So, we would factor out GCF 5a first.

In order to factor out GCF, we need to divide all terms of the polynomila by GCF we got.

If we factor out 5a from 5a^2 -25a, we need to divide 5a^2 and -25a by 5a.

On dividing 5a^2 by 5a we get a and

on dividing -25a by 5a we get -5.

Therefore, on factoring out 5a, we get

5a(a-5).

Therefore, we use Greatest Common Factor (GCF) method of factoring.

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The no-brain way to do it is to

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  2. divide by the coefficient of the variable.
  3. add the opposite of the constant.

Of course, at some point, you need to simplify the equation so you have something like

... ax + b = 0 . . . . . . where <em>a</em> and <em>b</em> are some constants that may be positive or negative

17) Subtract the right side.

... 10(x +3) -(-9x -4) -(x -5 +3) = 0

... 10x + 30 +9x +4 -x +5 -3 = 0 . . . . . eliminate parentheses

... x(10+9-1) +(30+4+5-3) = 0 . . . . . . . collect terms

... 18x +36 = 0 . . . . . . . . . . . . . . . . . . . simplified

... x + 2 = 0 . . . . . . . . . . . . . . . . . . . . . .divide by 18, the coefficient of x

... x = -2 . . . . . . . . . . . . . . . . . . . . . . . . add the opposite of the constant

19) Add the opposite of the left side.

... 0 = -9(1 +7x) +12(x -12)

... 0 = -9 -63x +12x -144 . . . . . . eliminate parenthses

... 0 = -51x -153 . . . . . . . . . . . . . simplify

... 0 = x +3 . . . . . . . . . . . . . . . . . divide by -51, the coefficient of x

... -3 = x . . . . . . . . . . . . . . . . . . . add the opposite of the constant

_____

If you examine the variable's coefficients you can make a choice of side to subtract that results in a positive coefficient of the variable.

This method puts variable and constant together until the end. The approach usually taught is to separate the variable terms and constant terms. (The number of steps required is the same either way.)

The reason this is "no brain" is that it always works and requires no judgment as to what you add or subtract from where. Applying a little judgment as described above can make it so you're mostly working with positive numbers, but the method works whether the numbers are positive or negative.

6 0
3 years ago
The school cafeteria has an order for 238 hot lunches. What is 238 to the nearest ten?
Alex
The answer would be 240 hope I helped
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2 years ago
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The answer is A on apex 
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At a grocery store the manager randomly selects 20 cartons of eggs, he finds 3 cartons with at least 1 broken egg. If the refrig
ivann1987 [24]

Answer:

You would expect 75 cartons with at least 1 broken egg.

There are likely to be 222 DVD players that are defective.

Step-by-step explanation:

Both examples given in this question represent a ratio of broken or defective to a sample number of cartons or DVD players.  In order to find how many would be broken or defective overall, you can set up equivalent ratios, or proportions.

Egg Cartons: \frac{broken}{#cartons}=\frac{3}{20}=\frac{x}{500}

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DVD Players:  \frac{defective}{#players}=\frac{3}{50}=\frac{x}{3700}

'x' represents the number of DVD players out of 3700 that would be expected to be defective.  To solve for 'x' you can cross-multiply and divide, or you can find what factor you would multiply the denominator by to get 3700 and then multiply the same factor by the numerator to find 'x'.  In this case 3700/50 = 74, so the factor is 74.  3 x 74 = 222, so you have 22 likely defective DVD players.

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