# Factor 10k^2-75k+125

10k2-75k+125
Factor 5 out of 10k2-75k+125.
Factor 5 out of 10k2.
5(2k2)-75k+125
Factor 5 out of -75k.
5(2k2)+5(-15k)+125
Factor 5 out of 125.
5(2k2)+5(-15k)+5(25)
Factor 5 out of 5(2k2)+5(-15k).
5(2k2-15k)+5(25)
Factor 5 out of 5(2k2-15k)+5(25).
5(2k2-15k+25)
5(2k2-15k+25)
Factor.
Factor by grouping.
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅25=50 and whose sum is b=-15.
Factor -15 out of -15k.
5(2k2-15(k)+25)
Rewrite -15 as -5 plus -10
5(2k2+(-5-10)k+25)
Apply the distributive property.
5(2k2-5k-10k+25)
5(2k2-5k-10k+25)
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
5((2k2-5k)-10k+25)
Factor out the greatest common factor (GCF) from each group.
5(k(2k-5)-5(2k-5))
5(k(2k-5)-5(2k-5))
Factor the polynomial by factoring out the greatest common factor, 2k-5.
5((2k-5)(k-5))
5((2k-5)(k-5))
Remove unnecessary parentheses.
5(2k-5)(k-5)
5(2k-5)(k-5)
Factor 10k^2-75k+125

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