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Sagot :
When factoring find 2 numbers that when added together equal the middle value and when multiplied equal the last value.
min this problem the middle value is 7 and the last value is 10
5 + 2 = 7 and 5 x 2 = 10
The answer is: (x+2)(x+5)
Answer:
- (x+2)(x+5)
Step-by-step explanation:
- Factoring x^2+7x+10
- The first term is, x^2 its coefficient is 1 .
- The middle term is, +7x its coefficient is 7 .
- The last term, "the constant", is +10
- Step-1 : Multiply the coefficient of the first term by the constant 1 * 10 = 10
- Step-2 : Find two factors of 10 whose sum equals the coefficient of the middle term, which is 7 .
- -10 + -1 = -11
- -5 + -2 = -7
- -2 + -5 = -7
- -1 + -10 = -11
- 1 + 10 = 11
- 2 + 5 = 7 That's it
- Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 2 and 5
- x2 + 2x + 5x + 10
- Step-4 : Add up the first 2 terms, pulling out like factors :
- x * (x+2)
- Add up the last 2 terms, pulling out common factors :
- 5 * (x+2)
- Step-5 : Add up the four terms of step 4 :
- (x+5) * (x+2)
- Which is the desired factorization
Solution:
- (x+2) * (x+5)
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