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Algebra 1 - Leaving Cert Higher Level Maths

Algebra 1 - Leaving cert Higher Level MathsAdam KellyNovember 27, ,andIhavemo di epro ofsprovidedforsomestatementsandtheorems, theydonotneedtob elearnedforthepurp ofsarejusttoincreasetheunderstandingofth estatementsb Polynomial :axxn+an 1xn 1+ +a2x2+a1x+a0 Whereai R;i= 0,1,2, .. , n;n ,withnon-zerocoe eci ctyp esofp olynomialswhichyouneedtoknow. Alinearp olynomialisofdegree1(ax+b) Aquadraticp olynomialisofdegree2(ax2+bx+c) Acubicp olynomialisofdegree3(ax3+bx2+cx+d)Therea realsonamesforp olynomialsbasedonhowmanytermstheyhave. Amonomialisap olynomialcontainingasingleterm. Abinomialisap olynomialcontainingtwoterms. Atrinomialisap (forexample4in4x3).definitionConstant Addition and Subtraction of Polynomial ExpressionsAddingandsubtractingp olynomialsinvolvesthecombinationoflikete rmsbyaddingtheirco e the following expression:(6x2 7x+ 4) + (7x2 9x+ 8)Solution(6x2 7x+ 4) + (7x2 9x+ 8)= (6x2+ 7x2) + ( 7x 9x) + (4 + 8)= 13x2 16x2+ 12example Multiplying Polynomial ExpressionsPolynomialsaremultipliedusing thedistributiveprop ertyofaddition:a(b+c) =ab+acSimplify the following

Factor. An algebraic factor is an expression that divides a olynomialp leaving no e-r mainder. definition acFtorising is a very important part of the LC maths course, not to mention algebra in general. It is very important that you get good at this skill and become familiar with the common techniques and patterns that come up. A few factoring ...

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