Question

Please answer immediately


by mid term splitting solve
${ - x}^{2} + 45x - 324 = 0$
​

Answer 1

Answer:

Factoring x2-45x+324

The first term is, x2 its coefficient is 1 .

The middle term is, -45x its coefficient is -45 .

The last term, "the constant", is +324

Step-1 : Multiply the coefficient of the first term by the constant 1 • 324 = 324

Step-2 : Find two factors of 324 whose sum equals the coefficient of the middle term, which is -45 .

-324 + -1 = -325

-162 + -2 = -164

-108 + -3 = -111

-81 + -4 = -85

-54 + -6 = -60

-36 + -9 = -45 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -36 and -9

x2 - 36x - 9x - 324

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

x • (x-36)

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

9 • (x-36)

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

(x-9) • (x-36)

Which is the desired factorization.

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