E-Math — Algebra
MOE/SEAB Elementary Mathematics (4052 / SEC K310) Number and Algebra strand: algebraic manipulation, linear and fractional equations, simultaneous linear equations, quadratic factorisation and equations, indices, standard form and graphs of functions.
Solve the equation 2x² − 7x + 3 = 0 by factorisation.
Before splitting the middle term, look at the leading coefficient 2 and the constant term +3: what two integers multiply to give 2 × 3 = 6 and add to give −7?
−6 and −1 multiply to +6 and add up to −7.
Spot on. Rewrite −7x using −6x and −x, then factorise by grouping to find the two linear brackets and the two roots.
Key takeaway: Factorise ax² + bx + c by finding factors of ac that sum to b, then set each linear factor to zero.
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