what is the greatest common factor of 35b^2 15b^3 and 5b; what is the greatest common factor of 44c^5 22c^3 and 11c^4; what is the greatest common factor of 3x^4 15x^3 and 21x^2; what is the greatest common factor of 6a6a6, a, 8a^{2}8a 2 8, a, squared, and 141414?; khan academy; binomial factor; factor polynomials; factorization

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QWLIGHTGO QWLIGHTGO · Answer 1

a. The greatest common factor of 35[tex]b^2[/tex], 15[tex]b^3[/tex] , and 5b is 5b.

b. The greatest common factor of 44[tex]c^5[/tex], 22[tex]c^3[/tex] , and 11[tex]c^4[/tex] is 11[tex]c^3[/tex].

c. The greatest common factor of 3[tex]x^4[/tex], 15[tex]x^3[/tex] , and 21[tex]x^2[/tex] is 3[tex]x^2[/tex] .

d. The greatest common factor of 6a, 8[tex]a^{2}[/tex], and 14 is 2.

let's find the GCF for the given expressions as follows -

a. 35[tex]b^2[/tex], 15[tex]b^3[/tex] , and 5b

factors of 35[tex]b^{2}[/tex] = 5, 7, b, b

factors of 15[tex]b^{3}[/tex] = 5, 3, b, b, b

factors of 5b = 5, b

here, the common factors are = 5,b

Hence, the GCF is = 5 x b = 5b

b. 44[tex]c^5[/tex], 22[tex]c^3[/tex] , and 11[tex]c^4[/tex]

factors of 44[tex]c^5[/tex] = 4, 11, c, c, c, c, c.

factors of 22[tex]c^3[/tex] = 2, 11, c, c, c.

factors of 11[tex]c^4[/tex] = 11, c, c, c, c.

here, the common factors are = 11, c, c, c.

Hence, the GCF is = 11 x c x c x c = 11[tex]c^3[/tex]

c. 3[tex]x^4[/tex], 15[tex]x^3[/tex] , and 21[tex]x^2[/tex]

factors of 3[tex]x^4[/tex] = 3, x, x, x, x

factors of 15[tex]x^3[/tex] = 3, 5, x, x, x.

factors of 21[tex]x^2[/tex] = 3, 7, x, x.

here, the common factors are = 3, x, x.

Hence, the GCF is = 3 x [tex]x[/tex] x [tex]x[/tex] = 3[tex]x^2[/tex] .

d. 6a, 8[tex]a^{2}[/tex], and 14

factors of 6a = 3, 2, a

factors of 8[tex]a^{2}[/tex] = 2, 4, a, a

factors of 14 = 2, 7

here, the common factors are = 2

Hence, the GCF is = 2