Subject: Mathematics
Book: Maths Mastery
The Remainder Theorem states that the remainder when a polynomial f(x) is divided by (x – a) is simply f(a). For example, if you want the remainder when x² – 5x + 6 is divided by (x – 3), evaluate f(3) = 3² – 5×3 + 6 = 9 – 15 + 6 = 0. The Factor Theorem extends this, indicating if f(a) = 0, then (x – a) is a factor of the polynomial. These shortcuts alleviate long division and facilitate polynomial factoring, essential in solving polynomial equations, analyzing algebraic structures, and simplifying advanced math problems with speed and precision.
If 3x = 81, what is the value of x?
View QuestionIf a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?
View QuestionWhat is the value of x if log(x) + log(4) = log(32)?
View QuestionIf the radius of a circle is 7 cm, what is its circumference?
View QuestionIf a + b = 10 and ab = 21, what is the value of a^2 + b^2?
View QuestionThe sum of the squares of two consecutive integers is 145. What are the integers?
View QuestionWhat is the sum of all even numbers between 1 and 100?
View QuestionWhat is the remainder when 5^100 is divided by 3?
View QuestionIf 2x - 3 = 7, what is the value of x?
View QuestionWhat is the probability of drawing an ace from a standard deck of 52 cards?
View Question