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Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial.\newline6r3+9r6r^3 + 9r

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Q. Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial.\newline6r3+9r6r^3 + 9r
  1. Find GCF Factors: We need to find the greatest common factor (GCF) of the terms 6r36r^3 and 9r9r. To do this, we will list the factors of the coefficients and the powers of rr to find the common factors.\newlineFactors of 66: 1,2,3,61, 2, 3, 6\newlineFactors of 99: 1,3,91, 3, 9\newlineCommon factors of the coefficients: 33\newlinePowers of rr: r3r^3 and rr\newlineThe smallest power of rr that is common to both terms is rr.\newlineTherefore, the GCF of 6r36r^3 and 9r9r is 9r9r55.
  2. Divide by GCF: Now we will divide each term by the GCF to find the remaining factors.\newlineFor 6r36r^3, we divide by 3r3r to get 2r22r^2.\newlineFor 9r9r, we divide by 3r3r to get 33.
  3. Write Original Polynomial: We can now write the original polynomial as the product of the GCF and the remaining factors. \newline6r3+9r=3r(2r2+3)6r^3 + 9r = 3r(2r^2 + 3)