Factorise 2/3x2 - 17/3x - 28
Answers
Answer:
(x - 12) • (2x + 7)
—————————
3
Step-by-step explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step by step solution :
Step 1 :
17
Simplify ——
3
Equation at the end of step 1 :
2 17
((—•(x2))-(——•x))-28
3 3
Step 2 :
2
Simplify —
3
Equation at the end of step 2 :
2 17x
((— • x2) - ———) - 28
3 3
Step 3 :
Equation at the end of step 3 :
2x2 17x
(——— - ———) - 28
3 3
Step 4 :
Adding fractions which have a common denominator :
4.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2x2 - (17x) 2x2 - 17x
——————————— = —————————
3 3
Equation at the end of step 4 :
(2x2 - 17x)
——————————— - 28
3
Step 5 :
Rewriting the whole as an Equivalent Fraction :
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 3 as the denominator :
28 28 • 3
28 = —— = ——————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
2x2 - 17x = x • (2x - 17)
Adding fractions that have a common denominator :
6.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x • (2x-17) - (28 • 3) 2x2 - 17x - 84
—————————————————————— = ——————————————
3 3
Trying to factor by splitting the middle term
6.3 Factoring 2x2 - 17x - 84
The first term is, 2x2 its coefficient is 2 .
The middle term is, -17x its coefficient is -17 .
The last term, "the constant", is -84
Step-1 : Multiply the coefficient of the first term by the constant 2 • -84 = -168
Step-2 : Find two factors of -168 whose sum equals the coefficient of the middle term, which is -17 .
-168 + 1 = -167
-84 + 2 = -82
-56 + 3 = -53
-42 + 4 = -38
-28 + 6 = -22
-24 + 7 = -17 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -24 and 7
2x2 - 24x + 7x - 84
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x-12)
Add up the last 2 terms, pulling out common factors :
7 • (x-12)
Step-5 : Add up the four terms of step 4 :
(2x+7) • (x-12)
Which is the desired factorization
Final result :
(x - 12) • (2x + 7)
———————————————————
3
hope it helps you this answer
