Help to factor an expression

Question

Please help me solve this expression to factor completely.

 

          35g^2 + 6g -9

 

 

 

 

 

thank you

Answer 1

 35 g^2 + 6g - 9

                                                       35 * -9 = - 315

 

                                                        315 = 3 * 105 = 9 * 35= 45 * 7 = 15 * 21

                                                          

                                                        See that +21 - 15 = 6

 

Break up the 6g = 21g - 15g 

 

  35 g^2 + 21 g - 15g - 9 =

 

   7g ( 5g + 3 ) - 3 (5 g + 3) =

    

    ( 5g + 3 ) ( 7g - 3 )

 

 

 

Answer 2

35g^2 + 6g -9 = (ag+b)(cg+d) = (ac)g^2 + (ad+bc)g + (bd)

 

ac = 35 = 5*7, ad+bc = 6, bd = -9 = -3 * 3

 

a ..... c ...... b ..... d ..... ad ..... bc ..... ad+bc

5 ..... 7 ..... -3 ..... 3 .... 15 ..... -21 ... -6

5 ..... 7 ..... 3 ..... -3 .... -15 ..... 21 ... 6 <== this set

 

35g^2 + 6g -9 = (5g+3)(7g-3)

Answer 3

quadratic expressions follow the form ax² + bx + c, where is this situation a > 1.

 

35g² + 6g - 9

 

Step 1: To make it easily factorable , take "a" and multiply it with "c".

a= 35 and c= -9

 

so the expression becomes g² + 6g - 315.

 

Step 2:Now factor this expression ,the factors must add to 6 and multiply to -315: ( g + 21) ( g - 15)

 

 

Step 3: Bring the "a" back into each binomial in front of g: (35g + 21) ( 35g - 15)

 

Step 4: Simplify each binomial by dividing by the GCF( greatest common factor):

 

(35g+ 21) has a GCF of 7, so this will become (5g + 3).

 

(35g - 15) has a GCF of 5, so this will become (7g - 3)

 

So the completely factored solution is (5g + 3) (7g - 3)