This question is for 17 points
I Find the factors for the given product and sum
1. Product 10 sum= 7
2. Product 18 sum =-11
3. Product -24 sum =5
4. Product -54 sum =-3
5. Product 72 sum =-17
6. Product -48 sum =-2
7. Product -56 sum =1
8. Product 36 sum 15 9. Product -45 sum =12 10.Product = -64 sum = 12
II Factorise the following 1. 2x2+5x-3
2. x2+2x-3
3. 3x²-x-10
4. x²+3x+2
5. x2-x-2
6. 2x2-13x+6
7. 2x²+x-10
8. x2+11x-26
9. 3x2-5x-2
10.x2-2x-15
Answers
Answer:
I
1. +5, +2
2. -2, -9
3. +6, -4
4. +6, -9
5. -8, -9
6. -6, +4
7. +8, -7
8. +3, +12
9. +15, -3
10. -4, +16
II
1. (x+3)(2x-1)
2. (x+3)(x-1)
3. (3x+5)(x-2)
4. (x+2)(x+1)
5. (x-2)(x+1)
6. (x-6)(2x-1)
7. (2x+5)(x-2)
8. (x+13)(x-2)
9. (3x+1)(x-2)
10. (x-5)(x+3)
Step-by-step explanation:
I
-> an easy way to do this is to find the factors of the product, which ALSO add upto the sum
for eg, 1. Product 10 sum= 7
factors of product: 1*10, 2*5
1+10=11 ..X
2+5=7 ✓
yehhh
for a harder one,
3. Product -24 sum =5
-(1*24), -(2*12), -(3*8), -(4*6) [here, either of the numbers are negative, not both]
we can see that -3+8= 5
so you get the answer!
II
-> we can do this easily with the same method as the first problem,
for eg, 1. 2x2+5x-3
I'm taking it as 2x²+5x-3
product-> product of first and last integers -> 2*-3 = -6
sum-> middle integer -> 5
if product is -6 and sum is +5
the factors are...
-(1*6), -(2*3)
since -2 + 3 or -3 +2 is not equal to 5,
-6+1 is -5, they're wrong
the correct answer is
-1+6.
so by splitting the middle term, you get
=> 2x²-x+6x-3
= x(2x-1) + 3(2x-1)
= (x+3)(2x-1)
hope it helps, you can add a comment if anything is wrong or confusing! have a good day/night byeee
I spent 20 minutes typing this down plis appreciate mi ✧◝(⁰▿⁰)◜✧
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