Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial.\newline6p3+9p26p^3 + 9p^2

Full solution

Q. Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial.\newline6p3+9p26p^3 + 9p^2
  1. Find GCF of Terms: We need to find the greatest common factor (GCF) of the terms 6p36p^3 and 9p29p^2. To do this, we will list the factors of the coefficients and the powers of pp to find the highest common factor.\newlineFactors of 66: 1,2,3,61, 2, 3, 6\newlineFactors of 99: 1,3,91, 3, 9\newlineCommon factors of the coefficients: 33\newlineBoth terms have at least p2p^2 in common.\newlineTherefore, the GCF is 3p23p^2.
  2. Divide by GCF: Now we will divide each term by the GCF to find the remaining factors.\newlineFor 6p36p^3, we divide by 3p23p^2 to get 2p2p.\newlineFor 9p29p^2, we divide by 3p23p^2 to get 33.
  3. Write Original Polynomial: We can now write the original polynomial as the product of the GCF and the remaining factors.\newline6p3+9p2=3p2(2p)+3p2(3)6p^3 + 9p^2 = 3p^2(2p) + 3p^2(3)\newlineCombining the terms inside the parentheses, we get:\newline6p3+9p2=3p2(2p+3)6p^3 + 9p^2 = 3p^2(2p + 3)