3 years ago

Use division to find all the whole number ratio equivalent to 56:24

1 answer:

4 0

56:24
reduces to 
28:12 
then to 
14:6 
then to 
7:3

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Which is the completely factored form of 12x3 – 60x2 + 4x – 20?

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Answer:

$4(x-5)(3{x}^{2}+1)$

Step-by-step explanation:

1) Find the Greatest Common Factor (GCF).

1 - What is the largest number that divides evenly into $12x^3,-60x^2,4x,$ and $-20$ ?

It is $4.$

2 - What is the highest degree of $x$ that divides evenly into $12x^3,-60x^2,4x,$ and $-20$ ?

It is 1, since $x$ is not in every term.

3 - Multiplying the results above,

The GCF is 4.

2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

$4(\frac{12{x}^{3}}{4}+\frac{-60{x}^{2}}{4}+\frac{4x}{4}-\frac{20}{4})$

3) Simplify each term in parentheses.

$4(3{x}^{3}-15{x}^{2}+x-5)$

4) Factor out common terms in the first two terms, then in the last two terms.

$4(3{x}^{2}(x-5)+(x-5))$

5) Factor out the common term $x-5$ .

$4(x-5)(3{x}^{2}+1)$

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