Factorize 10x^2-x-24 by splitting the middle term
Answers
Explanation:
Step by step solution :
STEP
1
:
Equation at the end of step 1
((2•5x2) - x) - 24 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 10x2-x-24
The first term is, 10x2 its coefficient is 10 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -24
Step-1 : Multiply the coefficient of the first term by the constant 10 • -24 = -240
Step-2 : Find two factors of -240 whose sum equals the coefficient of the middle term, which is -1 .
-240 + 1 = -239
-120 + 2 = -118
-80 + 3 = -77
-60 + 4 = -56
-48 + 5 = -43
-40 + 6 = -34
-30 + 8 = -22
-24 + 10 = -14
-20 + 12 = -8
-16 + 15 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -16 and 15
10x2 - 16x + 15x - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (5x-8)
Add up the last 2 terms, pulling out common factors :
3 • (5x-8)
Step-5 : Add up the four terms of step 4 :
(2x+3) • (5x-8)
Which is the desired factorization
Equation at the end of step
2
:
(5x - 8) • (2x + 3) = 0
Answer:
Type I: Factorization of Quadratic polynomials of the form x2 + bx + c. (i) In order to factorize x2 + bx + c we have to find numbers p and q such that p + q = b and pq = c. (ii) After finding p and q, we split the middle term in the quadratic as px + qx and get desired factors by grouping the terms.