State the GCF and Factor 25x^3-15x^2-10x​

Accepted Solution

a) GCF; 5xb) 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]Finding GCFGCF stands for: Greatest Common FactorThe 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]Finding FactorsNow, 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 EquationLearn more about Factors of Quadratic Equation at:brainly.com/question/7361044 brainly.com/question/4460262 brainly.com/question/1332667 brainly.com/question/1357167 #learnwithBrainly