HELP ME OUT PLEASE SOLVE IT.......................................................

Question

Find the Greatest common factor 

 

(1)  a^8b^3c^4,a^5bc^2,a^3b^4c^5

 

 

 

(2) 27x^5,24x^11  

 

I have solved this question which I got 3 as my GCF but am not sure of it 

 

(3) Factor the GCF out of this given expression

 

      11x^5-33x^3

 

(4) Factor the GCF out of this given expression

      15x^2-9x-3

Answer 1

 

a⁸ b³ c⁴

 

a⁵ b c²

 

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LCM --- product of common factors with highest exponent : a⁸ b³ c⁴ ( in this case is the 1st number).

 

GCF ---- Product of the common factors with lowest exponent : a⁵ b c² ( in this case is the 2nd Number).

                                                                                                         Since the 2nd number is divisible

                                                                                                          by first)

2) 27 X⁵  = 3^3. 2⁰ X⁵

                                      LCM = 2³ . 3³ X¹¹ = 216 X¹¹

  24 X¹¹ = 2³ . 3 X¹¹        

                                                 ^{GCF  =} 3 X⁵

 

 

Answer 2

1. a⁸b³c⁴  and a⁵bc²a³b⁴c⁵

                             ⇓

                      a⁸bc²(b*b³)(c*c⁴)

 

   a⁸b³c⁴ and a⁸b³c⁴(bc²)(b)(c)

 

2. 27x⁵, 24x¹¹

 

    (3)(3)(3)x⁵ and (2)(2)(3)(4)(x⁵)(x⁶)

 

3. 11x⁵-33x³ ⇒ 11(x²)(x³) - (3)(11)(x³)

 

4. 15x²-9x-3 = 3(5x² - 3x - 1)

Answer 3

1) a^3bc^2

 

2) 3x^5

 

3) 11x^3, since 11x^3(x^2 - 3)

 

4) 3, since 3(5x^2 -3x -1)