Question

factorise X2+27×+72​

Answer 1

The first term is, x2 its coefficient is 1 .

The middle term is, +27x its coefficient is 27 .

The last term, "the constant", is +72

Step-1 : Multiply the coefficient of the first term by the constant 1 • 72 = 72

Step-2 : Find two factors of 72 whose sum equals the coefficient of the middle term, which is 27 .

-72 + -1 = -73

-36 + -2 = -38

-24 + -3 = -27

-18 + -4 = -22

-12 + -6 = -18

-9 + -8 = -17

-8 + -9 = -17

-6 + -12 = -18

-4 + -18 = -22

-3 + -24 = -27

-2 + -36 = -38

-1 + -72 = -73

1 + 72 = 73

2 + 36 = 38

3 + 24 = 27 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 24

x2 + 3x + 24x + 72

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x+3)

Add up the last 2 terms, pulling out common factors :

24 • (x+3)

Step-5 : Add up the four terms of step 4 :

(x+24) • (x+3)

Which is the desired factorization

Final result :

(x + 24) • (x + 3).