(5y3-17y2+14y)÷(y-2)
Answers
Answer:
Draw a line XY, locate point p outside AB. Construct a line passing through P and perpendicular to XY
Step-by-step explanation:
Step by Step Solution
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Reformatting the input :
Changes made to your input should not affect the solution:
(1): "y2" was replaced by "y^2". 1 more similar replacement(s).
Step by step solution :
STEP
1
:
Equation at the end of step 1
((5 • (y3)) - (2•7y2)) - 3y = 0
STEP
2
:
Equation at the end of step
2
:
(5y3 - (2•7y2)) - 3y = 0
STEP
3
:
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
5y3 - 14y2 - 3y = y • (5y2 - 14y - 3)
Trying to factor by splitting the middle term
4.2 Factoring 5y2 - 14y - 3
The first term is, 5y2 its coefficient is 5 .
The middle term is, -14y its coefficient is -14 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 5 • -3 = -15
Step-2 : Find two factors of -15 whose sum equals the coefficient of the middle term, which is -14 .
-15 + 1 = -14 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 1
5y2 - 15y + 1y - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
5y • (y-3)
Add up the last 2 terms, pulling out common factors :
1 • (y-3)
Step-5 : Add up the four terms of step 4 :
(5y+1) • (y-3)
Which is the desired factorization
Equation at the end of step
4
:
y • (y - 3) • (5y + 1) = 0
STEP
5
:
Theory - Roots of a product
5.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.