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Class 9 Math Factorization Example 1Factorize 3 x-3 a+x y-a y


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Example 1Factorize 3 x-3 a+x y-a y

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

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

6 . (i) 27+8 x^{3}
 6 . (i)  27+8 x^{3}

6 . (i) 27+8 x^{3}

3. Factorize the following.(iv) 1-64 z^{3}
3. Factorize the following.(iv)  1-64 z^{3}

3. Factorize the following.(iv) 1-64 z^{3}

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)
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)

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

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 .
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 .

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

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

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

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
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

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

6 . (iii) 64 x^{3}+27 y^{3}
 6 . (iii)  64 x^{3}+27 y^{3}

6 . (iii) 64 x^{3}+27 y^{3}

5 . (iv) 8 x^{3}-125 y^{3}-60 x^{2} y+150 x y^{2}
 5 . (iv)  8 x^{3}-125 y^{3}-60 x^{2} y+150 x y^{2}

5 . (iv) 8 x^{3}-125 y^{3}-60 x^{2} y+150 x y^{2}

Example 3Factorize \left(x^{2}-5 x+6\right)\left(x^{2}+5 x+6\right)-2 x^{2}
Example 3Factorize  \left(x^{2}-5 x+6\right)\left(x^{2}+5 x+6\right)-2 x^{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
(vi) Find  m  so that  x^{2}+4 x+m  is a complete square  \ldots \ldots (a) 8(b)  -8 (c) 4(d) 16

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

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

3 . (v) 4 x^{2}-17 x y+4 y^{2}
 3 . (v)  4 x^{2}-17 x y+4 y^{2}

3 . (v) 4 x^{2}-17 x y+4 y^{2}

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
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

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

4 . (ii) x(x-1)-y(y-1)
 4 . (ii)   x(x-1)-y(y-1)

4 . (ii) x(x-1)-y(y-1)

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

2. Find the factors of:(iv) a^{6}-b^{6}
2. Find the factors of:(iv)  a^{6}-b^{6}
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2. Find the factors of:(iv) a^{6}-b^{6}

3. Factorize the following.(i) x^{2}+8 x+16-4 y^{2}
3. Factorize the following.(i)  x^{2}+8 x+16-4 y^{2}
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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
 4 . (ii)  \left(x^{2}-4 x\right)\left(x^{2}-4 x-1\right)-20
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4 . (ii) \left(x^{2}-4 x\right)\left(x^{2}-4 x-1\right)-20

Example 1Factorize 3 x-3 a+x y-a y
Example 1Factorize  3 x-3 a+x y-a y
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Example 1Factorize 3 x-3 a+x y-a y

2 . (iii) x^{2}-11 x-42
 2 . (iii)  x^{2}-11 x-42
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2 . (iii) x^{2}-11 x-42

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

2 . (i) 5 a x-3 a y-5 b x+3 b y
 2 . (i)   5 a x-3 a y-5 b x+3 b y
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2 . (i) 5 a x-3 a y-5 b x+3 b y

4 . (i) 3 x^{2}-75 y^{2}
 4 . (i)  3 x^{2}-75 y^{2}
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4 . (i) 3 x^{2}-75 y^{2}

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

3. Find the factors of:(i) 4 a^{2}+12 a b+9 b^{2}
3. Find the factors of:(i)  4 a^{2}+12 a b+9 b^{2}
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3. Find the factors of:(i) 4 a^{2}+12 a b+9 b^{2}

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