Factoring <span> x2+2x-35</span>
The first term is, <span> <span>x2</span> </span> its coefficient is <span> 1 </span>.
The middle term is, <span> +2x </span> its coefficient is <span> 2 </span>.
The last term, "the constant", is <span> -35 </span>
Step-1 : Multiply the coefficient of the first term by the constant <span> <span> 1</span> • -35 = -35</span>
Step-2 : Find two factors of -35 whose sum equals the coefficient of the middle term, which is <span> 2 </span>.
<span><span> -35 + 1 = -34</span><span> -7 + 5 = -2</span><span> -5 + 7 = 2 That's it</span></span>
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 7
<span>x2 - 5x</span> + 7x - 35
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
7 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x+7) • (x-5)
Which is the desired factorization
Final result : (x + 7) • (x - 5)
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