factorise 25 a square minus 35 A + 12
Answers
Answer:
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(52a2 - 35a) + 12
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 25a2-35a+12
The first term is, 25a2 its coefficient is 25 .
The middle term is, -35a its coefficient is -35 .
The last term, "the constant", is +12
Step-1 : Multiply the coefficient of the first term by the constant 25 • 12 = 300
Step-2 : Find two factors of 300 whose sum equals the coefficient of the middle term, which is -35 .
-300 + -1 = -301
-150 + -2 = -152
-100 + -3 = -103
-75 + -4 = -79
-60 + -5 = -65
-50 + -6 = -56
-30 + -10 = -40
-25 + -12 = -37
-20 + -15 = -35 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and -15
25a2 - 20a - 15a - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
5a • (5a-4)
Add up the last 2 terms, pulling out common factors :
3 • (5a-4)
Step-5 : Add up the four terms of step 4 :
(5a-3) • (5a-4)
Which is the desired factorization
Final result :
(5a - 4) • (5a - 3)