Question

factorise 25 a square minus 35 A + 12 ​

Answer 1

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)