.variable {
font-style:italic;
font-size: 125%;
}
.exponent {
font-size: 75%;
vertical-align: super;
}
.equation {
background: #ccffcc;
padding: 10px;
box-shadow: 10px 10px 5px #888888;
display: inline-block;
}
.bracket:before {
content:”(“;
}
.bracket:after {
content:”)”;
}
.wrong {
color: #ff0000;
}
.right {
color: #00ff00;
}
// Create HTML to display polynomial
// Assumes: 1) All coefficients in array
// 2) Lowest power of x first i.e. zero
// 3) No leading-zero coefficients
function showPolynomial(c,anchorID){
poly=’
‘
for(i=c.length-1;i>=0;i–){
// Suppress 1 multiplier and last coefficient=0 cases
if((c[i]==1) && (i>0)){
// Not c[0] and is 1 multiplier
coeff=””
}else{
if((c[i]==0) && (i==0)){
// c[0] and 0 is multiplier
coeff=””
}else{
// Normal case
coeff=c[i]
}
}
// Print term if non-zero coefficient
if(c[i]!=”0″){
switch(i){
case 0:
term=’‘+coeff+’‘
break
case 1:
term=’‘+coeff+’x‘
break
default:
term=’‘+coeff+’x‘+i+’‘
}
// Figure out if we want a + before term
if((c[i]<0)||(i==c.length-1)){
plusTerm=""
}else{
plusTerm='+‘
}
poly+=plusTerm+term
}
}
poly=poly+’‘
anchor=document.getElementById(anchorID)
anchor.innerHTML=poly
}
function multiplyPoly(p1,p2){
order=(p1.length-1)+(p2.length-1)
var result=Array()
for(p=0;p<=order;p++)
{
result[p]=0
}
for(i1=0;i1<p1.length;i1++){
for(i2=0;i2<p2.length;i2++){
result[i1+i2]+=p1[i1]*p2[i2]
}
}
return result
}
function polysEqual(p1,p2){
// Polynomials need to be of the same order
if(p1.length!=p2.length) return false
for(i=0;i-1){
poly[0]=parseInt(factorString.substring(plusPos+1))
return poly
}
// check for mx-n case
minusPos=factorString.indexOf(“-“)
if(minusPos>-1){
poly[0]=-parseInt(factorString.substring(minusPos+1))
return poly
}
// check for mx case
if (factorString.substring(xpos+2)==””){
poly[0]=0
return poly
}
// Broken case
return null
}
function checkIt(){
// Check first factor user might’ve typed in
f1=parseFactor(“f1”)
if(f1==null){
alert(“Type in the first factor – such as 2x+1 or 3x or x-1.”)
}
// Check second factor user might’ve typed in
f2=parseFactor(“f2”)
if(f2==null){
alert(“Type in the second factor – such as 2x+1 or 3x or x-1.”)
}
// If both factors are non-null proceed
if((f1!=null) && (f2!=null)){
guessMultiplied=multiplyPoly(f1,f2)
showPolynomial(guessMultiplied,”product”)
yesno=document.getElementById(“yesno”)
if(polysEqual(p12,guessMultiplied)){
yesno.innerHTML=”correct!”
yesno.setAttribute(“class”,”right”)
}else{
yesno.innerHTML=”wrong.”
yesno.setAttribute(“class”,”wrong”)
}
document.getElementById(“prodDiv”).style.display=”block”
}
}
Factorising Polynomials
Factorising Polynomials
Factorising polynomials is a basic but satisfying exercise in algebra. Try it here, with some random machine-generated examples.
Factorising is the process of turning a polynomial such as:
x2+3x+2
Into simpler factors. In this case they would be
x+1 and x+2.
If you multiply the two factors together you get the original polynomial.
Notice how the 3 in the polynomial is the sum of the 1 and the 2 in the pair of factors.
Also how the 2 in the polynomial is the product of the 1 and the 2 in the two factors.
This actually wouldn’t be the case if the coefficient of the x2 term weren’t 1.
But it’s not difficult to extend the thinking to cope with these cases.
And now it’s your turn.
Factorise:
3x2+8x+4
Write the two factors in the form 2x+1 or x or x-3.
Factor 1:
Factor 2:
Check
Product of your factors:
Your factors were
Try another
Like this:
Like Loading...
Mainframe, Performance, Topics 
One thought on “Factorise”