Hence Factorise The Expression 3 X 2 2 X 2 3 X 2

Hence Factorise The Expression 3 X 2 2 X 2 3 X 2 The factoring calculator transforms complex expressions into a product of simpler factors. it can factor expressions with polynomials involving any number of variables as well as more complex expressions. The process of factoring expressions with several variables is called multi variable expressions. knowing factoring and using the factoring calculator effectively can assist both professionals and students solve issues, simplify computations, and apply these concepts in many practical settings.

Solved Factorise A 2x3 3x2 17x 30 B X3 6x2 11x 6 C X3 X Algebra Using the remainder theorem, factorise each of the following completely : (i) 3x3 2x2−19x 6[2012] (ii) 2x3 x2−13x 6 (iii) 3x3 2x2−23x−30 (iv) 4x3 7x2−36x−63 (v) x3 x2−4x−4 3. using the remainder theorem, factorise the expression 3x3 10x2 x−6. hence, solve the equation 3x3 10x2 x−6=0 4. Using the factor theorem, show that (3x 2) is a factor of 3x3 2x2 – 3x – 2. hence, factorise the expression 3x3 2x2 – 3x – 2 completely. Solution (x – a) is a factor of a polynomial f (x) if the remainder, when f (x) is divided by (x – a), is 0, i.e., if f (a) = 0. f (x) = 3x 2 – x – 2 𝑓 (− 2 3) = 3 (− 2 3) 2 − (− 2 3) − 2 = 3 × 4 9 2 3 − 2 = 4 3 2 3 − 2 = 6 3 − 2 = 2 – 2 = 0 hence, 3x 2 is a factor of 3x 2 – x – 2. To solve the problem using the remainder theorem and factorize the expression 2x3 9x2 7x−6, we will follow these steps: let p(x)= 2x3 9x2 7x−6. we will check for possible rational roots using the rational root theorem. we will test some integer values for x. since p(−2) = 0, x 2 is a factor of p(x). now we will divide p(x) by x 2. 1.

Factorise I X 3 2x 2 X 2 Ii X 3 3x 2 9x 5 Iii X 3 Solution (x – a) is a factor of a polynomial f (x) if the remainder, when f (x) is divided by (x – a), is 0, i.e., if f (a) = 0. f (x) = 3x 2 – x – 2 𝑓 (− 2 3) = 3 (− 2 3) 2 − (− 2 3) − 2 = 3 × 4 9 2 3 − 2 = 4 3 2 3 − 2 = 6 3 − 2 = 2 – 2 = 0 hence, 3x 2 is a factor of 3x 2 – x – 2. To solve the problem using the remainder theorem and factorize the expression 2x3 9x2 7x−6, we will follow these steps: let p(x)= 2x3 9x2 7x−6. we will check for possible rational roots using the rational root theorem. we will test some integer values for x. since p(−2) = 0, x 2 is a factor of p(x). now we will divide p(x) by x 2. 1. The next step consists in finding when your polynomial $ (x 2) (x 3) (x 2)$ is positive. can you do that if you know the sign of each factor? now build a sign chart. Factoring quadratic expressions and simplifying rational expressions are useful in various real life situations. for example, when designing structures, engineers often need to determine the dimensions that satisfy certain area or volume constraints. Using the remainder theorem, factorise each of the following completely : (i) 3x3 2x2−19x 6 [2012] (ii) 2x3 x2−13x 6 (iii) 3x3 2x2−23x−30 (iv) 4x3 7x2−36x−63 (v) x3 x2−4x−4 3. using the remainder theorem, factorise the expression 3x3 10x2 x−6. hence, solve the equation 3x3 10x2 x−6= 0 4. In order to find the prime factors of a given polynomial we must be able to tell whether or not a polynomial is prime. one type of polynomial that is always prime is a polynomial of first degree, ax b, for which the only common factors of a and b are ± 1.