Question

Help im in k12 9th grade

Factor

x2+7x+10
Question 2 options:

(x+1)(x+10)

(x+3)(x+4)

(x−2)(x−5)

(x+2)(x+5)

Answer 1

• (x+2)(x+5)

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)

Answer 2

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)