x^2 + 1.5 x - 10 factorise it please
Answers
Answer:
Step-by-step explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "1.5" was replaced by "(15/10)".
Step by step solution :
STEP
1
:
3
Simplify —
2
Equation at the end of step
1
:
3
((x2) - (— • x)) - 10 = 0
2
STEP
2
:
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 2 as the denominator :
x2 x2 • 2
x2 = —— = ——————
1 2
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x2 • 2 - (3x) 2x2 - 3x
————————————— = ————————
2 2
Equation at the end of step
2
:
(2x2 - 3x)
—————————— - 10 = 0
2
STEP
3
:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 2 as the denominator :
10 10 • 2
10 = —— = ——————
1 2
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
2x2 - 3x = x • (2x - 3)
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
x • (2x-3) - (10 • 2) 2x2 - 3x - 20
————————————————————— = —————————————
2 2
Trying to factor by splitting the middle term
4.3 Factoring 2x2 - 3x - 20
The first term is, 2x2 its coefficient is 2 .
The middle term is, -3x its coefficient is -3 .
The last term, "the constant", is -20
Step-1 : Multiply the coefficient of the first term by the constant 2 • -20 = -40
Step-2 : Find two factors of -40 whose sum equals the coefficient of the middle term, which is -3 .
-40 + 1 = -39
-20 + 2 = -18
-10 + 4 = -6
-8 + 5 = -3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 5
2x2 - 8x + 5x - 20
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x-4)
Add up the last 2 terms, pulling out common factors :
5 • (x-4)
Step-5 : Add up the four terms of step 4 :
(2x+5) • (x-4)
Which is the desired factorization
Equation at the end of step
4
:
(x - 4) • (2x + 5)
—————————————————— = 0
2
STEP
5
:
When a fraction equals zero
5.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
(x-4)•(2x+5)
———————————— • 2 = 0 • 2
2
Now, on the left hand side, the 2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
(x-4) • (2x+5) = 0
hope this is useful