Factorising-Quadratics Aqa Foundation

Factorising simple quadratics

What is a quadratic expression?

• A quadratic expression is in the form:

  • ax² + bx + c (where a ≠ 0)

• If there are any higher powers of x (like x³ say) then it is not a quadratic

How do I factorise quadratics by inspection?

• This is shown most easily through an example: factorising 

• We need a pair of numbers that for 

  • multiply to give c

    • which in this case is -8

  • and add to give b

    • which in this case is -2

  • +2 and -4 satisfy these conditions

    • 2 × (-4) = -8 and 2 + (-4) = -2

  • Write these numbers in a pair of brackets like this: 

    • 

How do I factorise quadratics by grouping?

• This is shown most easily through an example: factorising 

• We need a pair of numbers that for <img alt=”x squared plus b x plus c” data-mathml='<math ><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ height=”23″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2223%22%20width%3D%2280%22%20wrs%3Abaseline%3D%2217%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Eb%3C%2Fmi%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmi%3Ec%3C%2Fmi%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math117e62166fc8586dfa4d1bc0e17’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADRjdnQgDVUNBwAAAVAAAAA6Z2x5ZoPi2VsAAAGMAAAAoWhlYWQQC2qxAAACMAAAADZoaGVhCGsXSAAAAmgAAAAkaG10eE2rRkcAAAKMAAAACGxvY2EAHTwYAAAClAAAAAxtYXhwBT0FPgAAAqAAAAAgbmFtZaBxlY4AAALAAAABn3Bvc3QB9wD6AAAEYAAAACBwcmVwa1uragAABIAAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACAAAAAEAAQAAQAAACv%2F%2FwAAACv%2F%2F%2F%2FWAAEAAAAAAAABVAMsAIABAABWACoCWAIeAQ4BLAIsAFoBgAKAAKAA1ACAAAAAAAAAACsAVQCAAKsA1QEAASsABwAAAAIAVQAAAwADqwADAAcAADMRIRElIREhVQKr%2FasCAP4AA6v8VVUDAAABAIAAVQLVAqsACwBJARiyDAEBFBMQsQAD9rEBBPWwCjyxAwX1sAg8sQUE9bAGPLENA%2BYAsQAAExCxAQbksQEBExCwBTyxAwTlsQsF9bAHPLEJBOUxMBMhETMRIRUhESMRIYABAFUBAP8AVf8AAasBAP8AVv8AAQAAAAAAAQAAAAEAANV4zkFfDzz1AAMEAP%2F%2F%2F%2F%2FWOhNz%2F%2F%2F%2F%2F9Y6E3MAAP8gBIADqwAAAAoAAgABAAAAAAABAAAD6P9qAAAXcAAA%2F7YEgAABAAAAAAAAAAAAAAAAAAAAAgNSAFUDVgCAAAAAAAAAACgAAAChAAEAAAACAF4ABQAAAAAAAgCABAAAAAAABAAA3gAAAAAAAAAVAQIAAAAAAAAAAQASAAAAAAAAAAAAAgAOABIAAAAAAAAAAwAwACAAAAAAAAAABAASAFAAAAAAAAAABQAWAGIAAAAAAAAABgAJAHgAAAAAAAAACA