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Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial.\newline8p3+6p8p^3 + 6p

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Q. Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial.\newline8p3+6p8p^3 + 6p
  1. Find GCF of terms: We need to find the greatest common factor (GCF) of the terms 8p38p^3 and 6p6p. To do this, we will list the prime factors of the coefficients and the common powers of pp.\newline8p3=23×p38p^3 = 2^3 \times p^3\newline6p=2×3×p6p = 2 \times 3 \times p\newlineThe common factors are 22 and pp.\newlineGCF of 8p38p^3 and 6p6p: 2p2p
  2. Express terms with GCF: Now we will express each term as the product of the GCF and the remaining factors.\newline8p38p^3 can be written as (2p)×(4p2)(2p) \times (4p^2) because 2×4×p2=8p32 \times 4 \times p^2 = 8p^3.\newline6p6p can be written as (2p)×3(2p) \times 3 because 2×3=6p2 \times 3 = 6p.
  3. Factor out GCF from polynomial: We can now factor out the GCF from the polynomial.\newline8p3+6p8p^3 + 6p\newline= (2p)(4p2)+(2p)3(2p) * (4p^2) + (2p) * 3\newline= 2p(4p2+3)2p(4p^2 + 3)\newlineThis is the factored form of the polynomial with the GCF factored out.