Question

Of chapter factorisation of polynomials- factorise:(40-18m-m^2)

Answer 1

40-18m+2m2

Final result :

2 • (m - 4) • (m - 5)

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(40 - 18m) + 2m2

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

2m2 - 18m + 40 = 2 • (m2 - 9m + 20)

Trying to factor by splitting the middle term

3.2 Factoring m2 - 9m + 20

The first term is, m2 its coefficient is 1 .

The middle term is, -9m its coefficient is -9 .

The last term, "the constant", is +20

Step-1 : Multiply the coefficient of the first term by the constant 1 • 20 = 20

Step-2 : Find two factors of 20 whose sum equals the coefficient of the middle term, which is -9 .

-20 + -1 = -21

-10 + -2 = -12

-5 + -4 = -9 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -4

m2 - 5m - 4m - 20

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

m • (m-5)

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

4 • (m-5)

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

(m-4) • (m-5)

Which is the desired factorization

Final result :

2 • (m - 4) • (m - 5)