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POLYNOMIALS - Coggle Diagram
POLYNOMIALS
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Sum of the coefficients of a polynomial is found by In order to find the sum of the coefficients of a
polynomial we substitute 1 for each variable.
- Sum of the coefficients P(x+3) is p(4)
- Sum of the coefficients of Q(x^2+5x-1) is Q(1+5-1) = Q(5)
- Sum of the coefficients of P(x) is p(1)
Sum of the coefficients of (x^2+3).R(x-1) is 4, R(0)
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The constant term of a polynomial is found by In order to find the constant term of a polynomial
we substitute zero for each variable.
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Zero Polynomial: If P(x) = 0, it is called zero polynomial. Degree of zero polynomial is undetermined. All elements of each polynomial must be zero.
Example: If Q(x)=(2m-8).X^3 + (n+6).x^2+k.x+ m+ t - 10 is a zero polynomial, find m.n-k.t.
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Constant Polynomial: For a0 ∈ R and a0 ≠ 0 and a0 ≠ 0, if P(x) = a0 then p(x)is said to be a constant polynomial. The degree of a constant polynomial is zero.
Examples: P(x) 7, Q(x) = -√¯3, R(x)=2a^2+a, T(x)=y^2-3y
An algebraic expression is a collection of variables and real numbers. The most common type of
algebraic expression is the polynomial.
The "poly" in "polynomial" means "many". The term "polynomial" refers to sums of many terms, but the
term is used to refer to anything from one term to the sum of a zillion terms.
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