Factorise : 3x^3-33x^2+84x
Answers
Step-by-step explanation:
3x3-33x2+84x
Final result :
3x • (x - 4) • (x - 7)
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((3 • (x3)) - (3•11x2)) + 84x
Step 2 :
Equation at the end of step 2 :
(3x3 - (3•11x2)) + 84x
Step 3 :
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
3x3 - 33x2 + 84x = 3x • (x2 - 11x + 28)
Trying to factor by splitting the middle term
4.2 Factoring x2 - 11x + 28
The first term is, x2 its coefficient is 1 .
The middle term is, -11x its coefficient is -11 .
The last term, "the constant", is +28
Step-1 : Multiply the coefficient of the first term by the constant 1 • 28 = 28
Step-2 : Find two factors of 28 whose sum equals the coefficient of the middle term, which is -11 .
-28 + -1 = -29
-14 + -2 = -16
-7 + -4 = -11 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -4
x2 - 7x - 4x - 28
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-7)
Add up the last 2 terms, pulling out common factors :
4 • (x-7)
Step-5 : Add up the four terms of step 4 :
(x-4) • (x-7)
Which is the desired factorization
Final result :
3x • (x - 4) • (x - 7)
Answer:
3x-(x-4)(x-7)
Step-by-step explanation:
regard the attachnent
