factorise and then divide :-( 49a^2-56a) by ( 21a -24)
Answers
Answer:
(-7a - 3) • (7a + 5)
Step-by-step explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "a2" was replaced by "a^2".
STEP
1
:
Equation at the end of step 1
((0 - 72a2) - 56a) - 15
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
-49a2 - 56a - 15 = -1 • (49a2 + 56a + 15)
Trying to factor by splitting the middle term
3.2 Factoring 49a2 + 56a + 15
The first term is, 49a2 its coefficient is 49 .
The middle term is, +56a its coefficient is 56 .
The last term, "the constant", is +15
Step-1 : Multiply the coefficient of the first term by the constant 49 • 15 = 735
Step-2 : Find two factors of 735 whose sum equals the coefficient of the middle term, which is 56 .
-735 + -1 = -736
-245 + -3 = -248
-147 + -5 = -152
-105 + -7 = -112
-49 + -15 = -64
-35 + -21 = -56
-21 + -35 = -56
-15 + -49 = -64
-7 + -105 = -112
-5 + -147 = -152
-3 + -245 = -248
-1 + -735 = -736
1 + 735 = 736
3 + 245 = 248
5 + 147 = 152
7 + 105 = 112
15 + 49 = 64
21 + 35 = 56 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 21 and 35
49a2 + 21a + 35a + 15
Step-4 : Add up the first 2 terms, pulling out like factors :
7a • (7a+3)
Add up the last 2 terms, pulling out common factors :
5 • (7a+3)
Step-5 : Add up the four terms of step 4 :
(7a+5) • (7a+3)
Which is the desired factorization
Final result :
(-7a - 3) • (7a + 5)