standard form of 2x²+3x=x+3
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Answer:
standard form
2x2+2x-3=0
Answer:
y=2x3+17x2−6x+8
Step-by-step explanation:
y=2x3+17x2−6x+8
Explanation:
To answer this question, you will have to simplify the function. Begin by using the FOIL Method to multiply the first term:
(2x+3x2)(x+3)
=2x⋅x+2x⋅3+3x2⋅x+3x2⋅3
Simplifying this yields:
3x3+11x2+6x
We now have the first term simplified. To simplify the second term, we can use the
Binomial Theorem, a useful tool when working with polynomials. One of the main points of the theorem is that the coefficients of an expanded binomial can be determined using a function called the choose function. The specifics of the choose function are more of a probability concept, so there's no need to go into it right now.
However, a simpler way to use the Binomial Theorem is
Pascal's Triangle. The numbers in Pascal's Triangle for a certain row number will correspond to the coefficients of the expanded binomial for that row number. In the case of cubing, the third row is
1,3,3,1
, so the expanded binomial would be:
(a+b)3
=1a3+3a2b+3ab2+1b3
Notice how we decrease the power of
a
and increase the power of
b
as we move down the row. Evaluating this formula with the second term,
(x−2)3
, yields:
(x−2)3
=x3+3x2(−2)+3x(−2)2+(−2)3
Simplifying gives us:x
3−6x2+12x−8
To simplify, we can subtract the second term from the first:
3x3+11x2+6x−(x3−6x2+12x−8)
=2x3+17x2−6x+8
Standard form means that the terms of the polynomial are ordered from highest degree to lowest. Because this has already been done, your final answer is:
y=2x3+17x2−6x+8
HOPE IT HELPS!!