Question

1. Factorise: 54x2 + 42x3 – 30x4
2. Factorise: 2x2yz + 2xy2z + 4xyz.
Please give me answer ​

Answer 1

Step-by-step explanation:

1.

Given Equation is 54x^2 + 42x^3 - 30x^4.

It can be written as -30x^4 + 42x^3 + 54x^2.

                              = -6x^2(5x^2 - 7x -9).

2.

Equation is 2x^2yz + 2xy^2z + 4xyz

=> 2xyz(x + y + 2)

Hope my answer helped you!

Answer 2

$6x^{2}((9-5x)(1+x)+3x)$.

$2x^{2} yz+2xy^{2} z+4xyz$.

• The positive integers that can divide a number evenly are known as factors in mathematics. Let's say we multiply two numbers to produce a result. The product's factors are the number that is multiplied. Each number has a self-referential element.
• There are several examples of factors in everyday life, such putting candies in a box, arranging numbers in a certain pattern, giving chocolates to kids, etc. We must apply the multiplication or division method in order to determine a number's factors.
• The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are  called factors. A factor is therefore another number's divisor.

Here, the expression is given as,

• $54x^{2} +42x^{3} -30x^{4}$

Now, we have,

$6x^{2} (9+7x-5x^{2} )\\=6x^{2}(9+4x-5x^{2} +3x)\\=6x^{2} (9+9x-5x-5x^{2} +3x)\\=6x^{2}((9(1+x)-5x(1+x)+3x)\\=6x^{2}((9-5x)(1+x)+3x)$

Hence, $6x^{2}((9-5x)(1+x)+3x)$ is the factorization for $6x^{2}((9-5x)(1+x)+3x)$.

• $2x^{2} yz+2xy^{2} z+4xyz$

Now, we have,

$=2xyz(x+y+2)$

Hence, $2xyz(x+y+2)$ is the factorization for $2x^{2} yz+2xy^{2} z+4xyz$.

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