Use factor theorem to determine that x - 3 is factor of x cube - 4x square + x + 6
Answers
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Answer :
(x - 3) is the factor of x³ - 4x² + x + 6.
Explanation :
Let f(x) = x³ - 4x² + x + 6
By factor theorem when f(x) / (x - a) i, f(a) = 0
Toknowtheremainderfindthezeroofx-3
Tofindzeroequatex-3to0
x - 3 = 0
x = 3
So, f(3) is the remainder
f(3) = (3)³ - 4(3)² + 3 + 6
= 27 - 4(9) + 9
= 36 - 36
f(3) = 0
So, f(3) = 0
Byfactortherem(x-3)isthefactorofx³-4x²+x+6.
Extrainfo :
Zero of a polynomial : We say that a zero of a polynomial p(x) is the value of x, which p(x) is equal to zero. this value is also called a root of the polynomial p(x).
Polynomial: An algebraic expression in which the variables involved have only non-zero negative integral powers is called a polynomial.
Cubic polynomial : A polynomial of degree 3 is called the cubic polynomial.
- If the variable in a polynomial is x, we made not the polynomial by p(x), q(x) or r(z) etc.
e.g. p(x) = 3x² + 2x + 1
q(x) = x³ - 5x² + x - 7
r(y) = y³ - 1
r(y) = y³ - 1t(z) = z² + 5z + 3
Factor theorem : If x - a is a factor of the polynomiap p(x), then p(a) = 0. Also if p(a) = 0 then (x - a) is a factor of p(x).