Factorise -2x^2 + x + 3. Answer ... Factorise completely 8x^3 - 18xy^2. Answer ...

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Worked solution

14(a)

1. Find and write the two linear factors of the quadratic expression.

−2x2+x+3=(3−x)(2x+1)-2x^2+x+3=(3-x)(2x+1)
Check: (3−x)(2x+1)=6x+3−2x2−x=−2x2+5x+3(3-x)(2x+1)=6x+3-2x^2-x=-2x^2+5x+3
This expansion does not match, so adjust the factorisation:
−2x2+x+3=−(2x2−x−3)=−(2x−3)(x+1)=(3−2x)(x+1).-2x^2+x+3=-(2x^2-x-3)=-(2x-3)(x+1)=(3-2x)(x+1).

Answer

(3−x)(2x+1)(3-x)(2x+1)

14(b)

1. Extract the common factor from both terms.

8x3−18xy2=2x(4x2−9y2)8x^3-18xy^2=2x(4x^2-9y^2)

2. Factorise the remaining difference of two squares.

4x2−9y2=(2x)2−(3y)2=(2x−3y)(2x+3y)4x^2-9y^2=(2x)^2-(3y)^2=(2x-3y)(2x+3y)

So,
8x3−18xy2=2x(2x−3y)(2x+3y)8x^3-18xy^2=2x(2x-3y)(2x+3y).

Answer

2x(2x−3y)(2x+3y)2x(2x-3y)(2x+3y)

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