FACTORISE:
a) 15x2 + x-6
b) 3√2 x2 – 5x +√2
c) 2x3 + 9x2 +10x +3
Answers
Step-by-step explanation:
): "x2" was replaced by "x^2".
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((3•5x2) - x) - 6
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 15x2-x-6
The first term is, 15x2 its coefficient is 15 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 15 • -6 = -90
Step-2 : Find two factors of -90 whose sum equals the coefficient of the middle term, which is -1 .
-90 + 1 = -89
-45 + 2 = -43
-30 + 3 = -27
-18 + 5 = -13
-15 + 6 = -9
-10 + 9 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 9
15x2 - 10x + 9x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (3x-2)
Add up the last 2 terms, pulling out common factors :
3 • (3x-2)
Step-5 : Add up the four terms of step 4 :
(5x+3) • (3x-2)
Which is the desired factorization
Final result :
(3x - 2) • (5x + 3)