Question

Factories the following:

(i) ax^2+ bx.
(ii) 2x^2 + 6x + 4.
(iii) x^2 + 2x + 4xy + 8y.
(iv) x^2- 6x + 9.
(v) 2y^2 + 8y + 8.
(vi) x^2 - 3x - 10.
(vii) x^2 - 25.
(viii) x^2 + 3√3x + 6.
(ix) x^2 + 1/x^2 - 2 - 3x + 3/x.
(x) a^2 x^2 + (ax^2 + 1) x + a.

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Answer 1

Answer:

I) ax² + bx

= ax² + bx

Taking 'x' common

=x(ax + b)

ii)2x² + 6x + 4

= 2x² + 6x + 4

splitting the middle term we get,

=2x² + 2x + 4x + 4

=2x(x + 1) + 4(x + 1)

=(x + 1)(2x + 4)

iii)x² + 2x + 4xy + 8y

=x² + 2x + 4xy + 8y

=x(x + 2) + 4y(x + 2)

=(x + 2)(x + 4y)

iv)x² - 6x + 9

= x² - 6x + 9

= x² - 3x - 3x + 9

=x (x - 3) - 3(x - 3)

= (x - 3)(x -3)

= (x - 3)²

v)2y² + 8y + 8

= 2y² + 8y + 8

Taking 2 as common factor, we get

= 2(y² + 4y + 4)

= 2(y² + 2y + 2y + 4)

= 2 [y(y+ 2) + 2(y + 2)]

= 2 [(y + 2)(y + 2)]

= 2(y + 2)²

vi)x² - 3x - 10

= x² - 3x - 10

Splitting the middle term we get

= x² + 5x - 2x - 10

= x(x + 5) - 2(x + 5)

= (x + 5)(x - 2)

vii)x² - 25

= x² - 25

= x² - 5²

[a² - b² = (a + b)(a - b)]

= (x + 5)(x - 5)

viii)x²+3√3x+6

=x² +3√3x + 6

Splitting the middle term, we get

=x²+2√3x+√3x+6

= x(x+2√3)+√3(x+2√3)

= (x+2√3)(x+√3)

Answer 2

I have not answered a few questions

hope at least what I have solved will help u