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Answer:

There is no strong evidence for this, and plenty of evidence that ancient and Renaissance artists used other systems — for example, ratios of integers. That is, it is not as if we have lost all writing from classical times on ideal numerical systems for art and architecture, but this idea does not appear. Therefore, it is likely that those systems were used by artists and architects, and the golden ratio was not, until its modern popularization.

Knowledge of the ratio dates back to at least Euclid (300 BC), but he just noted it as interesting in mathematics, not aesthetics. Then, it doesn't seem to really turn up in writing until about 1500, when Italian mathematician Luca Pacioli wrote about it as "the divine proportion" — and while his mystical writing touches on aesthetics, there's no evidence that anyone (even da Vinci!) took it to heart.

Step-by-step explanation:

#keep on learning

12x²y & 24x³z = 4z(3x-6x²)

12x²y - 24x³z:

Factor out common term: 12

•12x²y-24x³z

•Factor 24, 12 • 2

•Factor out 12

•12(x²y-2x³z)

Factor out common term: x²

Apply Rule: a^b+c = a^ba^c

x³ = x²x

•x²y-2x²xz

•Factor out x²

•x²(y-2xz)

Answer;

12x²(y-2xz)

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5.Collaboration and communication

I don't rlly know if this is correct hehe...

Answer:

Factoring out the greatest common factor (GCF)

To factor the GCF out of a polynomial, we do the following: Find the GCF of all the terms in the polynomial. Express each term as a product of the GCF and another factor. Use the distributive property to factor out the GCF.