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Sagot :
Answer:
5 • (x - 3) • (x - 6) = 0
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
(5x2 - 45x) + 90 = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
5x2 - 45x + 90 = 5 • (x2 - 9x + 18)
Trying to factor by splitting the middle term
3.2 Factoring x2 - 9x + 18
The first term is, x2 its coefficient is 1 .
The middle term is, -9x its coefficient is -9 .
The last term, "the constant", is +18
Step-1 : Multiply the coefficient of the first term by the constant 1 • 18 = 18
Step-2 : Find two factors of 18 whose sum equals the coefficient of the middle term, which is -9 .
-18 + -1 = -19
-9 + -2 = -11
-6 + -3 = -9 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and -3
x2 - 6x - 3x - 18
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-6)
Add up the last 2 terms, pulling out common factors :
3 • (x-6)
Step-5 : Add up the four terms of step 4 :
(x-3) • (x-6)
Which is the desired factorization
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