# Class 9 Math Factorization 1. By using synthetic division method to divide the following polynomials and also find their quotient and remainder.(ix) p(x)=2 x^{4}-2 x^{3}+100 x^{2}-168 x+95 by x-2

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##### 1. By using synthetic division method to divide the following polynomials and also find their quotient and remainder.(ix) p(x)=2 x^{4}-2 x^{3}+100 x^{2}-168 x+95 by x-2

Factorize each of the following cubic polynomials by factor theorem.1. x^{3}-2 x^{2}-x+2

Tick (\checkmark) the correct answers(ii) Factors of a^{2}+2 a b+b^{2}-c^{2} is:(a) (a-b+c)(x-b-c) (b) \left(a_{+} b_{+} c\right)(a-b-c) (c) \left(a_{+} b_{+} c\right)\left(a_{+} b-c\right) (d) \left(a_{+} b_{+} c\right)(a-b-c)

1. Find the remainder by using the remainder theorem when(iii) x^{3}-x^{2}-26+40 is divided by (x-2)

2(i) If (x+2) is a factor of 3 x^{2}-4 k x-4 k^{2} then find the value(s) of k .

3. Find the factors of:(iv) (x-2)(x+2)(x-4)(x+4)-14 x^{2}

6. Find the factors of:(ii) (4 a-9 b)^{2}-(2 a+5 b)^{2}

Example 3Factorize \left(x^{2}-5 x+6\right)\left(x^{2}+5 x+6\right)-2 x^{2}

(vi) Find m so that x^{2}+4 x+m is a complete square \ldots \ldots (a) 8(b) -8 (c) 4(d) 16

1. Factorize the following:(viii) \frac{x^{6}}{27}+\frac{8}{x^{3}}

2. Completion Items. Fill in the blanks.(i) x^{2}+5 x+6=\ldots \ldots \ldots (ii) 4 a^{2}-16=\ldots \ldots \ldots (iii) 4 a^{2}+4 a b+(\ldots \ldots \ldots) is a complete square(iv) \frac{x^{2}}{y^{2}}-2+\frac{y^{2}}{x^{2}}=\ldots \ldots \ldots (v) (x+y)\left(x^{2}-x y+y^{2}\right)=\cdots \cdots \cdots (vi) Factored form of x^{4}-16 is

1. By using synthetic division method to divide the following polynomials and also find their quotient and remainder.(ii) p(x)=x^{3}-x^{2}-x-1 by x+1

1. Factorize the following:(i) b^{3}+3 b^{2} c+3 b c^{2}+c^{3}

3. Factorize the following.(i) x^{2}+8 x+16-4 y^{2}

4 . (ii) \left(x^{2}-4 x\right)\left(x^{2}-4 x-1\right)-20

3 . (ii) \frac{a^{2}}{b^{2}}-2+\frac{b^{2}}{a^{2}}

1. Use the remainder theorem to find the remainder when(ii) 4 x^{3}-4 x+3 is divided by (2 x-1)