Factorise 6x² – x-35
Answers
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
((2•3x2) + x) - 35
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 6x2+x-35
The first term is, 6x2 its coefficient is 6 .
The middle term is, +x its coefficient is 1 .
The last term, "the constant", is -35
Step-1 : Multiply the coefficient of the first term by the constant 6 • -35 = -210
Step-2 : Find two factors of -210 whose sum equals the coefficient of the middle term, which is 1 .
-210 + 1 = -209
-105 + 2 = -103
-70 + 3 = -67
-42 + 5 = -37
-35 + 6 = -29
-30 + 7 = -23
-21 + 10 = -11
-15 + 14 = -1
-14 + 15 = 1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -14 and 15
6x2 - 14x + 15x - 35
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (3x-7)
Add up the last 2 terms, pulling out common factors :
5 • (3x-7)
Step-5 : Add up the four terms of step 4 :
(2x+5) • (3x-7)
Which is the desired factorization
Final result :
(3x - 7) • (2x + 5)