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Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial. \newline2f3+4f22f^3 + 4f^2

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Q. Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial. \newline2f3+4f22f^3 + 4f^2
  1. Find GCF and Common Power: We need to find the greatest common factor (GCF) of the terms 2f32f^3 and 4f24f^2. To do this, we look for the highest power of ff that is common to both terms and the largest number that divides both coefficients.\newlineThe coefficients are 22 and 44, and the GCF of these numbers is 22.\newlineBoth terms have at least an f2f^2 in them, so we can factor out f2f^2 as well.\newlineTherefore, the GCF of 2f32f^3 and 4f24f^2 is 4f24f^200.
  2. Factor Out GCF: Now we will express each term as a product of the GCF and the remaining factors.\newlineFor the first term, 2f32f^3, we divide it by the GCF, 2f22f^2, to get the remaining factor:\newline2f3÷2f2=f2f^3 \div 2f^2 = f.\newlineFor the second term, 4f24f^2, we divide it by the GCF, 2f22f^2, to get the remaining factor:\newline4f2÷2f2=24f^2 \div 2f^2 = 2.
  3. Express Terms as Product: We can now write the original polynomial as a product of the GCF and the sum of the remaining factors: \newline2f3+4f2=2f2(f+2)2f^3 + 4f^2 = 2f^2(f + 2).\newlineThis is the factored form of the polynomial using the greatest common factor.