Consider the expression .

MATHEMATICS · Multi-part · AoPS · Mathematics · Quadratic Equations - Part 1 · Quadratic Equations - Part 1

Problem

Consider the expression x4−6x3+9x2x^4-6x^3+9x^2. (i) First factorise the quadratic polynomial x2−6x+9x^2-6x+9. (ii) Using your result from part (i), factorise x4−6x3+9x2x^4-6x^3+9x^2 completely. (iii) Verify your factorisation by expanding the factors obtained.

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