Question
Factor polynomial $$ 1029xy^{3}+24x^{4} $$
Answer
$$ 1029xy^{3}+24x^{4} = 3x(7y+2x)(49y^{2}-14xy+4x^{2}) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 3x } $:
$$ 1029xy^3+24x^4 = 3x ( 343y^3+8x^3 ) $$Step 2 :
To factor $ 343y^{3}+8x^{3} $ we can use sum of cubes formula:
$$ I^3 + II^3 = (I + II) (I^2 - I \cdot II + II^2)$$After putting $ I = 7y $ and $ II = 2x $ , we have:
$$ 343y^{3}+8x^{3} = ( 7y+2x ) ( 49y^{2}-14xy+4x^{2} ) $$This page was created using
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