What is the the degree of polynomial P defined by : P(x) = -5(x - 2)(x^3 + 5) + x^5?
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calendarEducator since 2008
write3,662 answers
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The degree of a polynomial is the highest power of x.
For example:
f(x) = x^3 -4x^2 +1 ==> f(x) is a third degree polynomial.
To determine the degree of the given polynomila, we will need to open the brackets and rewrite into terms.
Let us open the brackets.
==> P(x) = -5(x-2)(x^3 + 5) + x^5
==> P(x) = -5 (x^4 + 5x^2 -2x^3 -10) + x^5
==> P(x) = x^5 - 5x^4 -+10x^3 -25x^2 -10
We notice that the highest power is x^5
Then the polynomial is a fifth degree.
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calendarEducator since 2010
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We have P(x) = -5(x - 2)(x^3 + 5) + x^5
P(x) = -5(x - 2)(x^3 + 5) + x^5
=> P(x) = (-5x + 10)(x^3 + 5) + x^5
=> P(x) = -5x^4 - 25x + 10x^3 + 50 + x^5
=> P(x) = x^5 - 5x^4 + 10x^3 - 25x + 50
The degree of a polynomial is the highest power of x in the expression.
Here the degree is 5
calendarEducator since 2009
write278 answers
starTop subjects are Math, Science, and Social Sciences
The degree of a polynomial is the largest exponent when the polynomial is written in standard form. So, expand this polynomial into standard form:
5(x - 2)(x3 + 5) + x5 =
x^5+5 x^4-10 x^3+25 x-50
So this polynomial is of degree 5.
To find the degree of the polynomial P(x) = -5(x - 2)(x^3 + 5) + x^5.
The degree of the polynomial is the degree of the highest term.
So we expand the right side:
P(x) = -5(x-2)(x^3+5) +x^5
P(x) = -5(x^4 +5x-2x^3-10)+x^5.
P(x) = -5(x^4-2x^3+5x-10) +x^5.
P(x) = -5x^4+10x^3-25x+50+x^5.
We arrange the terms on the right side.
P(x) = x^5 -5x^4 +10x^3-25x+50
The highest term is x^5 with degree 5.
So the degree of the polynomial is 5.
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