Question

Factorise : n²-18n+72​

Answer 1

Answer:

The first term is, n2 its coefficient is 1 .

The middle term is, -18n its coefficient is -18 .

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 -18 .

-72 + -1 = -73

-36 + -2 = -38

-24 + -3 = -27

-18 + -4 = -22

-12 + -6 = -18 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -6

n2 - 12n - 6n - 72

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

n • (n-12)

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

6 • (n-12)

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

(n-6) • (n-12)

Which is the desired factorization

Answer 2

Given Equation

• n² - 18n + 72

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Solution

• We have an equation, by spiliting the middle term we will factorise the given equation.

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$\tt:\implies\: \: \: \: \: \: \: \: {n^2 - 18n + 72}$

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$\tt:\implies\: \: \: \: \: \: \: \: {n^2 - 12n - 6n + 72}$

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$\tt:\implies\: \: \: \: \: \: \: \: {n(n - 12) - 6(n - 12)}$

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$\tt:\implies\: \: \: \: \: \: \: \: {(n - 12) (n - 6)}$

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Hence,

• Value of n is 12 or 6.