a) GCF; 5x
b) Factors: [tex]5x(5x+2)(x-1)[/tex] and values of x are: [tex]x=0, x= -\frac{2}{5} , x= 1[/tex]
Step-by-step explanation:
We need to state the GCF and Factor of [tex]25x^3-15x^2-10x[/tex]
GCF stands for: Greatest Common Factor
The greatest number that is divisible by all the terms of the expression.
In thee given expression 5x is the GCF
i.e
[tex]5x(5x^2-3x-2)[/tex]
Now, finding factors:
[tex]25x^3-15x^2-10x[/tex]
taking 5x common:
[tex]=5x(5x^2-3x-2)[/tex]
Now, factoring the term inside the bracket:
[tex]=5x(5x^2-5x+2x-2)\\=5x(5x(x-1)+2(x-1))\\=5x(5x+2)(x-1)[/tex]
So, the factors are: [tex]5x(5x+2)(x-1)[/tex]
and values of x are:
To find values of x put the factors equal to 0
[tex]5x(5x+2)(x-1)=0\\5x=0,(5x+2)=0,(x-1)=0\\x=0, x= -\frac{2}{5} , x= 1[/tex]
Keywords: Factors of Quadratic Equation
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