Answer :
Factor the following:
x^3 - 3 x^2 - 10 x
Factor x out of x^3 - 3 x^2 - 10 x:
x (x^2 - 3 x - 10)
The factors of -10 that sum to -3 are 2 and -5. So, x^2 - 3 x - 10 = (x + 2) (x - 5):
Answer: x (x + 2) (x - 5)
x^3 - 3 x^2 - 10 x
Factor x out of x^3 - 3 x^2 - 10 x:
x (x^2 - 3 x - 10)
The factors of -10 that sum to -3 are 2 and -5. So, x^2 - 3 x - 10 = (x + 2) (x - 5):
Answer: x (x + 2) (x - 5)
The factored form of a polynomial is its simplified form.
The factored form of [tex]\mathbf{f(x) = x^3 - 3x^2 - 10x}[/tex] is [tex]\mathbf{f(x) = x(x + 2)(x - 5)}[/tex]
The polynomial is given as:
[tex]\mathbf{f(x) = x^3 - 3x^2 - 10x}[/tex]
Factor out x
[tex]\mathbf{f(x) = x(x^2 - 3x - 10)}[/tex]
Expand
[tex]\mathbf{f(x) = x(x^2 - 5x + 2x - 10)}[/tex]
Factorize
[tex]\mathbf{f(x) = x(x(x - 5) + 2(x - 5))}[/tex]
Factor out x - 5
[tex]\mathbf{f(x) = x(x + 2)(x - 5)}[/tex]
Hence, the factored form of [tex]\mathbf{f(x) = x^3 - 3x^2 - 10x}[/tex] is [tex]\mathbf{f(x) = x(x + 2)(x - 5)}[/tex]
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