Factor the trinomialx^2 − 7x + 10What is the factored form of the trinomial, and why?A. (x−2)(x−5). The product of –2 and –5 is –10, and their sum is 7.B. (x−2)(x−5). The product of –2 and –5 is 10, and their sum is –7.C. (x+2)(x+5). The product of 2 and 5 is 10, and their sum is 7.D. (x+2)(x+5). The product of 2 and 5 is 10, and their sum is –7.
Accepted Solution
A:
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x² - 7x + 10
We are going to find something in this form: ↓ ( )( )
x² is nothing but x multiplied by itself ↓ (x )(x )
-7x + 10 follows since the sum is negative and the product is positive then the signs inside the bracket will be as follows ↓ ( x - )( x - )
-7x should be the sum and 10 should be the product multiples of 10 = 1 x 10 = 2 x 5 = -1 x -10 = -2 x -5 ↓ ↓ ↓ ↓ 1 + 10 = 11 2 + 5 = 7 -1 - 10 = -11 = -2 -5 = -7
So the sum of -2 and -5 is -7 and the product of -2 and -5 is 10 ↓ ( x - 2 )( x - 5 )