2. 3x^2 + 12x + 9 (3x+3)(x+3) 3. 2y^2 + 15y + 7...

2. 3x^2 + 12x + 9 (3x+3)(x+3) 3. 2y^2 + 15y + 7 (y+1)(y+14) X. Factoring: Putting It All Together 5x^2 + 20x - 60 = 5(x^2 + 4x - 12) = 5(x + 6)(x - 2) 1. 2x^2 - 8 2. 2x^2 + 8x + 6 3. 3n^2 + 9n - 30 XII. Extra: Factoring by Grouping 6ax - 2b - 3a + 4bx = 6ax - 3a + 4bx - 2b = 3a(2x - 1) + 2b(2x - 1) = (2x - 1)(3a + 2b) 1. x^2 + 2x + xy + 2y 2. 3a^2 - 2b - 6a + ab 3. t^3 - t^2 + t - 1 Hint: t - 1 = 1(t - 1) 4. 10 + 2t - 5s - st

Transcript

00:01 Hi, we need to perform factorization.

00:04 First question here, third one, 2y square, 2y square plus 15 y plus 7.

00:18 The question we have, so what we do, just take here this is a, this will be b is 15, this is c.

00:25 So we require two numbers, that is some of two numbers, is equal to 15, right? and the product is equal to a into c, that is 2 into 7, that is 14, right? think about two numbers, the numbers are given as, so some is 15 and product is 14, two numbers are 14 and 1.

00:45 So we just back price now, so we'll get 2y square plus 14y plus 1y plus 1y plus 7.

00:58 That's how we get.

00:59 So from here factorize the first pair, so 2y, y plus 7 plus 1 here, y plus 7, right? we solve this, it's going to add to be 2y plus 1, then y plus 7.

01:17 2y plus 1, y plus 7.

01:19 Even if you multiply this, you will get 2y square plus 15y plus 7.

01:25 So this is a factoration of this one, 2y plus 1, y plus 7.

01:32 On to the next one, so the next one is given as, for example, the first one is 2x square minus 8, 2 x squared minus 8, 2 x squared minus 8.

01:42 What we can do now in first factor out two from here, 2 n times x square minus 4.

01:47 Now we know the formula being a square minus b squared is equal to a plus p times a minus b.

01:59 This we have right.

02:00 So we solve this now, it's going to be 2 times x squared minus 2 square.

02:05 This is going to be 2 times it's going to be x plus 2 times we have x minus 2.

02:12 So the factorization of the first one.

02:18 Now, second one, we have 2x square plus 8x.

02:26 2x square plus 8x we have plus x.

02:34 Now, how to factorize this? so factorize this, what we can do? the method which is given, we can just first factor out 2 from here.

02:46 So vector 2, it will be x square plus 4x plus 3.

02:51 Right, now we factorize here x square.

02:55 Plus 4x plus 3.

02:56 So we require two numbers whose sum is equal to 4 and product is equal to 3.

03:03 Two numbers are given as 3 and 1.

03:05 So if i twice this, x square plus 3x plus 1x plus 3.

03:12 So factor out here, x plus 3 plus 1 x plus 3.

03:18 So we get plus 1, x plus 3.

03:23 We want to put the value here, so we get 2 times x plus 1, x plus 3 that is the required factorization.

03:33 For third part, it has given as 3 n squared 3 n squared plus 9 n minus 30 plus 9 n we have minus 30...

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