Factorise 54x2+42x3-30x4
Answers
Answer:
STEP
1
:
Equation at the end of step 1
((54•(x2))+(42•(x3)))-(2•3•5x4)
STEP
2
:
Equation at the end of step
2
:
((54 • (x2)) + (2•3•7x3)) - (2•3•5x4)
STEP
3
:
Equation at the end of step
3
:
((2•33x2) + (2•3•7x3)) - (2•3•5x4)
STEP
4
:
STEP
5
:
Pulling out like terms
5.1 Pull out like factors :
-30x4 + 42x3 + 54x2 = -6x2 • (5x2 - 7x - 9)
Trying to factor by splitting the middle term
5.2 Factoring 5x2 - 7x - 9
The first term is, 5x2 its coefficient is 5 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is -9
Step-1 : Multiply the coefficient of the first term by the constant 5 • -9 = -45
Step-2 : Find two factors of -45 whose sum equals the coefficient of the middle term, which is -7 .
-45 + 1 = -44
-15 + 3 = -12
-9 + 5 = -4
-5 + 9 = 4
-3 + 15 = 12
-1 + 45 = 44
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
-6x2 • (5x2 - 7x - 9)
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
((54•(x2))+(42•(x3)))-(2•3•5x4)
STEP
2
:
Equation at the end of step
2
:
((54 • (x2)) + (2•3•7x3)) - (2•3•5x4)
STEP
3
:
Equation at the end of step
3
:
((2•33x2) + (2•3•7x3)) - (2•3•5x4)
STEP
4
:
STEP
5
:
Pulling out like terms
5.1 Pull out like factors :
-30x4 + 42x3 + 54x2 = -6x2 • (5x2 - 7x - 9)
Trying to factor by splitting the middle term
5.2 Factoring 5x2 - 7x - 9
The first term is, 5x2 its coefficient is 5 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is -9
Step-1 : Multiply the coefficient of the first term by the constant 5 • -9 = -45
Step-2 : Find two factors of -45 whose sum equals the coefficient of the middle term, which is -7 .
-45 + 1 = -44
-15 + 3 = -12
-9 + 5 = -4
-5 + 9 = 4
-3 + 15 = 12
-1 + 45 = 44
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
-6x2 • (5x2 - 7x - 9)