Question

Claire Judice

Mixed Multistep Factoring (Equation)
Dec 01, 6:42:28 PM
Solve algebraically for all values of x:
5x5 + 6x4 + 80x3 + 96x² = 0
Answer:
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Answer 1

The values of 'x' are -1.2, 0, 0,
`-4i` or
`4i`.

Explanation:

Given:

The equation to solve is given as:

`5x^5+6x^4+80x^3+96x^2=0`

Factoring
`x^2` from all the terms, we get:

`x^2(5x^3+6x^2+80x+96)=0`

Now, rearranging the terms, we get:

`x^2(5x^3+80x+6x^2+96)=0`

Now, factoring
`5x` from the first two terms and 6 from the last two terms, we get:

`x^2(5x(x^2+16)+6(x^2+16))=0\\x^2(x^2+16)(5x+6)=0`

Now, equating each factor to 0 and solving for 'x', we get:

`x^2=0\\x=0\ and\ 0\\\\5x+6=0\\x=(-6)/(5)=1.2\\\\x^2+16=0\\x^2=-16\\x=√(-16)=\pm 4i`

There are 3 real values and 2 imaginary values. The value of 'x' as 0 is repeated twice.

Therefore, the values of 'x' are -1.2, 0, 0,
`-4i` or
`4i`.