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3 years ago

Show work by factoring completely30x^3 + 22x^2 + 4x

Mathematics

1 answer:

xz_007 [3.2K]3 years ago

5 0

Given:

The expression is

$30x^3+22x^2+4$

To find:

Factorized form of given expression.

Solution:

We have,

$30x^3+22x^2+4$

$=2x(15x^2+11x+2)$

Splitting the middle term, we get

$=2x(15x^2+6x+5x+2)$

$=2x(3x(5x+2)+1(5x+2))$

$=2x(3x+1)(5x+2)$

Therefore, the complete factorized form of given expression is $2x(3x+1)(5x+2)$ .

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Basically when a variable with a negative exponent, such as $a^{-2}$ , you just take the reciprocal of it and then change the exponent sign, or in simple terms flip it. The reciprocal of a^{-2} and changing the exponent sign is is $\frac{1}{a^{2} }$ .

To demonstrate let’s solve the first problem:

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