Factor theorem
If p(x) is a polynomial in x and is divided by and the remainder = f(a) is zero then (x-a) is a factor of p(x..
Factor Theorem
If p(x), a polynomial in x is divided by x-a and the remainder = f (a) is zero, then (x-a) is a factor of p(x..
Remainder Theorem
Recall the Remainder theorem and the Factor theorem. When f(x) is divided by (x-a) the remainder is (x-a) and if the remainder f(a) = 0 then x - a is a factor of the expression f (x..
Recall the Remainder theorem and the Factor theorem. When f(x) is divided by (x-a) the remainder is (x-a) and if the remainder f(a) = 0 then x - a is a factor of the expression f (x..Alternative Proof of Binomial Theorem for Positive Integral Index (Combinatorial Method)
Alternative Proof of Binomial Theorem for Positive Integral Index (Combinatorial Method). We have, (a + b) n = (a + b) (a + b) ....... n times. The terms on the RHS are obtained by taking one letter from each factor and multiplying them together. Choosing 'a' from all the..
Example 6:
Factorise using factor theorem. a) 2x 2 +x-3 b) 5x 2 +6x..
Proof:
When p(x) is divided by x-a, R = p(a) (by remainder theorem) p(x) = (x-a).q(x)+p(a) (Dividend = Divisor x quotient + Remainder Division Algorithm) But p(a) = 0 is given. Hence p(x) = (x-a).q(x) Conversely if x-a is a factor of p(x) then p(a)=0. p(x) = (x-a).q(x) + R If (x-a) ..
When p(x) is divided by x-a, R = p(a) (by remainder theorem) p(x) = (x-a).q(x)+p(a) (Dividend = Divisor x quotient + Remainder Division Algorithm) But p(a) = 0 is given. Hence p(x) = (x-a).q(x) Conversely if x-a is a factor of p(x) then p(a)=0. p(x) = (x-a).q(x) + R If (x-a) ..Algebra II
Absolute value to solve equations/inequalities Systems of linear equations/inequalities Operations on polynomials Factoring polynomials/trinomials Operations on complex numbers Operations on rational expressions Graphing quadratic equations Quadratic equations in complex number s..
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