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.\newline9p26p9p^2 - 6p

Full solution

Q. Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial.\newline9p26p9p^2 - 6p
  1. Find GCF of Terms: We need to find the greatest common factor (GCF) of the terms 9p29p^2 and 6p6p. To do this, we will list the factors of the coefficients and the powers of pp to find the common factors.\newlineFactors of 99: 11, 33, 99\newlineFactors of 66: 11, 22, 33, 66\newlineThe common factors of the coefficients are 11 and 33.\newlineFor the variable pp, since the smallest power of pp is 11 (in the term 6p6p), the GCF will include pp to the first power.\newlineThe GCF of 9p29p^2 and 6p6p is pp11.
  2. Divide by GCF: Now we will divide each term by the GCF to factor it out.\newlineFor the term 9p29p^2, we divide by 3p3p to get 3p3p.\newline9p2÷3p=3p9p^2 \div 3p = 3p\newlineFor the term 6p6p, we divide by 3p3p to get 22.\newline6p÷3p=26p \div 3p = 2
  3. Write Factored Form: We can now write the original polynomial as the product of the GCF and the remaining factors.\newline9p26p=3p(3p2)9p^2 - 6p = 3p(3p - 2)\newlineThis is the factored form of the polynomial.