Polynomials facorization of polynomials

Polynomials and factorization of polynomials

	Polynomials Mathematics chapter 2
	What is a Polynomial?
	Type of Polynomials
	Zero of a polynomials
	Remainder Theorem
	Factor Theorem
	list of all formula of factorization
	Exercise 2.1
1	Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. (i) 4x2 – 3x + 7 (ii) y2 + √2  (iii) 3√t + t√ 2 (iv) y +2/y  (v) x10 + y3 + t50
2	Write the coefficients of x2 in each of the following: (i) 2 + x2 + x (ii) 2 – x2 + x3 (iii) (π /2)x2+ x (iv) √2x – 1
3	Give one example each of a binomial of degree 35, and of a monomial of degree 100.
4	Write the degree of each of the following polynomials: (i) 5x3 + 4x2 + 7x (ii) 4 – y2 (iii) 5t – √7 (iv) 3
5	Classify the following as linear, quadratic and cubic polynomials: (i) x2 + x (ii) x – x3 (iii) y + y2 + 4 (iv) 1 + x (v) 3t (vi) r2
	Exercise 2.2
1	Find the value of the polynomial 5x – 4x2 + 3 at (i) x = 0 (ii) x = –1   (iii) x = 2
2	Find p(0), p(1) and p(2) for each of the following polynomials: (i) p(y) = y2 – y + 1   (ii) p(t) = 2 + t + 2t2 – t3  (iii) p(x) = x3   (iv) p(x) = (x – 1) (x + 1)
3	Verify whether the following are zeroes of the polynomial, indicated against them. (i) p(x) = 3x + 1, x = - 1/3 (ii) p(x) = 5x – π, x = 4/5 (iii) p(x) = x2 – 1, x = 1, –1 (iv) p(x) = (x + 1) (x – 2), x = – 1, 2 (v) p(x) = x2, x = 0 (vi) p(x) = lx + m, x = –m/l (vii) p(x) = 3x2 – 1, x = - 1/√3 , 2/√3 (viii) p(x) = 2x + 1, x =1/2
4	Find the zero of the polynomial in each of the following cases: (i) p(x) = x + 5   (ii) p(x) = x – 5   (iii) p(x) = 2x + 5 (iv) p(x) = 3x – 2 (v) p(x) = 3x   (vi) p(x) = ax, a ≠ 0  (vii) p(x) = cx + d, c ≠ 0, c, d are real numbers.
	Exercise 3.2
1	Find the remainder when x3+3x2 + 3x + 1 is divided by (i) x + 1    (ii) x –1/2   (iii) x   (iv) x + π  (v) 5 + 2x
2	Find the remainder when x3 – ax2 + 6x – a is divided by x – a.
3	Check whether 7 + 3x is a factor of 3x3 + 7x
	Exercise 3.4
1	Determine which of the following polynomials has (x + 1) a factor : (i) x3 + x3 + x + 1 (ii) x4 + x3 + x3 + x + 1 (iii) x4 + 3x3 + 3x3 + x + 1 (iv) x3 – x3 – (2+√2)x + √2
2	Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x3 + x2 – 2x – 1, g(x) = x + 1 (ii) p(x) = x3 + 3x2 + 3x + 1, g(x) = x + 2 (iii) p(x) =
3	Find the value of k, if x – 1 is a factor of p(x) in each of the following cases:(use remainder theorem) (i) p(x) = x2 + x + k  (ii) p(x) = 2x2 + kx + √2 (iii) p(x) = kx2 – 2x + 1 (iv) p(x) = kx2 – 3x + k
4	Factorise :(quadratic equations factoring or polynomial factoring ) (i) 12x2 – 7x + 1 (ii) 2x2 + 7x + 3 (iii) 6x2 + 5x – 6 (iv) 3x2 – x – 4
5	Factorise (factoring trinomails or polynomial factoring ) : (i) x3 - 2x2 - x + 2 (ii) x3 - 3x2 - 9x - 5 (iii) x3 + 13x2 + 32x + 20 (iv) 2y3 + y2 - 2y - 1
	Additional question for factoring trinomails degrees of polynomials practice factoring polynomials polynomial factoring dividing polynomials solving polynomial equations quadratic equations polynomials comming soon ...