Answer :
The Greatest Common Factor (GCF) of the terms in the polynomial [tex]10x^(^5^)+35x^(^4^)+15x^(^3^)[/tex] is [tex]5x^(^3^)[/tex]because it is the largest factor that can divide into all the terms of the polynomial.
The subject here is Mathematics specifically dealing with polynomials. To find the greatest common factor (GCF) of the terms in the polynomial [tex]10x^(5)+35x^(4)+15x^(3)[/tex], we first observe each term. You will see each term include a factor of 5 and a power of x. We have to find the smallest exponent and the highest common numerical factor.[tex]10x^(5)[/tex], [tex]35x^(4)[/tex] and[tex]15x^(3)[/tex]have 5 as their common numerical factor and the smallest power of x in all three terms is[tex]x^(3)[/tex].
So, the Greatest Common Factor for these three terms is 5x^(3) because it's the largest factor that can divide into all the terms of the polynomial. To further understand this, we can divide each term by the GCF: [tex]10x^(5)[/tex] divide [tex]5x^(3)[/tex] gives us [tex]2x^(2)[/tex]. Similarly,[tex]35x^(4)[/tex] divide by[tex]5x^(3)[/tex]gives us 7x, and[tex]15x^(3)[/tex] divide by[tex]5x^(3)[/tex]gives us 3. This shows that we can factor out the GCF from each term in the polynomial.
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