Algebra

Example 1: Simplifying polynomials | Algebra I | Khan Academy

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Simplify 3x ^ 2 – 8x + 7 + 2x ^ 3 – x ^ 2 + 8x – 3 So when we simplify this, we’re going to collect similar phrases As a reminder to you, we can add or subtract similar phrases or simplify similar phrases As a reminder of what I mean by that, if I have x ^ 2 + x ^ 2 The two expressions are the same, both of them with the same power That is, to the same degree So if I have another x ^ 2 and x ^ 2, well, so I have 2x ^ 2 – this equals 2x ^ 2– If I have x ^ 3 – let’s suppose I have 3x ^ 3 + 4x ^ 3 Well, that means I have 7x ^ 3– I can’t take x ^ 2 and combine it with x ^ 3, I can’t simplify it this way. So this cannot be simplified You cannot simplify – these expressions are not the same because they contain x And this x is not – they’re not the same degree – So let’s look at the degree of x raised to the same degree Let’s start with the first class So the highest or highest exponent for x is here x ^ 3 But there seems to be one x raised to the third force So this cannot be added, added, or subtracted with anything else So let’s write that here So we have 2x ^ 3 And let’s look at x ^ 2. We have 3x ^ 2 here And we have -x ^ 2 here So if we want to simplify, we can combine these two phrases – we can combine – so let me write that We can combine 3x ^ 2 with x ^ 2 I am now rearranging I put similar phrases next to each other so that they are easy to simplify Now let’s take care of the x ^ 1 clause x We have the phrase -8x Let me write it here -8x Then we have an 8x positive statement here, let me write that So positive 8x Then finally let’s look at the constants We can consider them x x ^ 0 And the constants are: We have positive 7 here, so + 7 And then we have -3 here We have -3 So all I did was use the toggle feature in the plural Until I change the order – or addition and subtraction – until I change the order I follow I changed the order of things so that similar phrases are next to each other But now we can simplify So we have 2x ^ 3 – nothing to simplify with it But if we do – if we have – let me do it in the same blue color – If we have 3x ^ 2 and take it x ^ 2 Well, so we’ll still have 2x ^ 2 So this is equal to the positive of 2x ^ 2 Hence if we have -8x Add them to 8x or you can flip this over You can consider as subtracting 8x from positive 8x They will be deleted So it becomes 0 – I can write + 0 here, but this will be useless because it doesn’t change the value – And then finally we have + 7 – 3, well, that’s about 7 – 3 = 4, so I have 4 We have finished! We have simplified it 2x ^ 3 + 2x ^ 2 + 4

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