factorise 15x^2-x-28
Answers
Answered by
71
15x2-x-28=0
Two solutions were found :
x = -4/3 = -1.333
x = 7/5 = 1.400
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((3•5x2) - x) - 28 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 15x2-x-28
The first term is, 15x2 its coefficient is 15 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -28
Step-1 : Multiply the coefficient of the first term by the constant 15 • -28 = -420
Step-2 : Find two factors of -420 whose sum equals the coefficient of the middle term, which is -1 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -21 and 20
15x2 - 21x + 20x - 28
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (5x-7)
Add up the last 2 terms, pulling out common factors :
4 • (5x-7)
Step-5 : Add up the four terms of step 4 :
(3x+4) • (5x-7)
Which is the desired factorization
Equation at the end of step 2 :
(5x - 7) • (3x + 4) = 0
Two solutions were found :
x = -4/3 = -1.333
x = 7/5 = 1.400
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((3•5x2) - x) - 28 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 15x2-x-28
The first term is, 15x2 its coefficient is 15 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -28
Step-1 : Multiply the coefficient of the first term by the constant 15 • -28 = -420
Step-2 : Find two factors of -420 whose sum equals the coefficient of the middle term, which is -1 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -21 and 20
15x2 - 21x + 20x - 28
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (5x-7)
Add up the last 2 terms, pulling out common factors :
4 • (5x-7)
Step-5 : Add up the four terms of step 4 :
(3x+4) • (5x-7)
Which is the desired factorization
Equation at the end of step 2 :
(5x - 7) • (3x + 4) = 0
Answered by
321
given us that
15x² - x - 28
= 15x² - ( 21 - 20 )x - 28
= 15x² - 21x + 20x - 28
= 3x ( 5x - 7 ) + 4 ( 5x - 7 )
= ( 3x + 4 ) ( 5x - 7 )
- Answered by a Useless user
______________________________
15x² - x - 28
= 15x² - ( 21 - 20 )x - 28
= 15x² - 21x + 20x - 28
= 3x ( 5x - 7 ) + 4 ( 5x - 7 )
= ( 3x + 4 ) ( 5x - 7 )
- Answered by a Useless user
______________________________
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