Question

Ques 3 - factorize:
(i) 12x^2 + 8x+1
(ii) 4x² + 4x+1
(iii)6x2+17x + 5
(iv) 3x2-x-2​

Answer 1

Solution:

1.

12x²+8x+1

=12x²+(6+2)x+1

=12x²+6x+2x+1

=6x(2x+1)+1(2x+1)

=(6x+1)(2x+1)

2.

4x²+4x+1

=4x²+(2+2)x+1

=4x²+2x+2x+1

=2x(2x+1)+1(2x+1)

=(2x+1)(2x+1)

3.

6x²+17x+5

=6x²+(15+2)x+5

=6x²+15x+2x+5

=3x(2x+5)+1(2x+5)

=(3x+1)(2x+15)

4.

3x²-x-2

=3x²-(6-1)x-2

=3x²-6x+x-2

=3x(x-2)+1(x-2)

=(3x+1)(x-2)

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Answer 2

Answer:

12$x^{2}$+8x+1=0

12$x^{2}$+6x+2x+1=0

6x(2x+1)+1(2x+1)=0

(6x+1)(2x+1)=0

∴x= -¹/₆ or -¹/₂

4$x^{2}$+4x+1=0

a=2x

b=1

$a^{2} +b^{2} +2ab=(a+b)^{2}$

∴$(2x+1)^{2}$=4x²+4x+1=0

∴x= -¹/₂

6$x^{2}$+17x+5=0

6$x^{2}$+2x+15x+5=0

2x(3x+1)+5(3x+1)=0

(2x+5)(3x+1)=0

x=-⁵/₂ or -¹/₃

3$x^{2}$-x-2=0

3$x^{2}$-3x+2x-2=0

3x(x-1)+2(x-1)=0

(3x+2)(x-1)=0

x=1 or -²/₃

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