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Maths core one someone help me please!!

Can someone please explain (without confusing me) how to show something as a product of three linear factors and showing real roots, out of the whole syllabus these are the only things that are confusing me, and are the only things that I am losing marks on, please someone help me urgently!!!
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Original post by em_willi30
Can someone please explain (without confusing me) how to show something as a product of three linear factors and showing real roots, out of the whole syllabus these are the only things that are confusing me, and are the only things that I am losing marks on, please someone help me urgently!!!
I'll give rep! Thank You!


In core 1, the question of showing something as 3 linear factors will usually come up after a question like: "Prove (x+3) is a factor".
Then you already know one of the 3 factors is (x+3) so then you open another bracket and put in a quadratic where, when multiplied by (x+3) gives you the original equation. Then you can factorise the quadratic to get 2 factors and together with the (x+3) you have 3 linear factors.

As for real roots, just use the discriminant of b^2-4ac, if answer is > 0 it has 2 real roots, <0 it has no real roots and =0 means it has a repeated solution.
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em_willi30
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Thank you! You're an absolute star! ⭐️⭐️⭐️


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Just a quick tip to remember discriminants if you get confused because I do. b^2-4ac <0 has no roots. As a child that is not even zero yet, has no roots. b^2-4ac >0 has two real roots as a child that is larger/older than zero has two real roots (its parents) and b^2-4ac = 0 has one repeated root. As a child that is exactly zero has only one root, its mother.

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