Factor the expression 8x3y − 8x2y − 30xy. 8x3y − 8x2y − 30xy

Mathematics

1 answer:

Lelu [443]3 years ago

6 0

Answer:

2xy(2x +3)(2x -5)

Step-by-step explanation:

The greatest common factor of the coefficients 8 and 30 is 2. All of the variable expressions have a common factor of xy. We can factor those out to get ...

= (2xy)(4x^2 -4x -15)

Now, we want to find factors of the product (4)(-15) that have a sum of -4 (the x coefficient). Those factors are 6 and -10. Then we can rewrite the quadratic factor as ...

4x^2 +6x -10x -15

and factor by pairs:

= 2x(2x +3) -5(2x +3) = (2x -5)(2x +3)

The complete factorization is then ...

= 2xy(2x +3)(2x -5)

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3 years ago

Help with this math question

tresset_1 [31]

The given inequality is:

$|-8x+24| \leq 16$

This inequality can be divided in two parts as:

a) $-16 \leq -8x +24$
b) $-8x + 24 \leq 16$

Solving part a:

$-16 \leq -8x+24 \\ \\ 
-40 \leq -8x \\ \\ 
5 \geq x \\ 
or \\ 
x \leq 5$

Solving part b:

$-8x+24 \leq 16 \\ \\ 
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x \geq 1$

Therefore, the solution to the given inequality is $x \leq 5$ and $x \geq 1$ . Combining both the ranges we get the solution: $1 \leq x \leq 5$ .

In interval notation, this solution can be expressed as [1,5]

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3 years ago

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