Question

1) x2 + 14x + 45 = 0​

Answer 1

Step-by-step explanation:

Factoring x2-14x+45

The first term is, x2 its coefficient is 1 .

The middle term is, -14x its coefficient is -14 .

The last term, "the constant", is +45

Step-1 : Multiply the coefficient of the first term by the constant 1 • 45 = 45

Step-2 : Find two factors of 45 whose sum equals the coefficient of the middle term, which is -14 .

-45 + -1 = -46

-15 + -3 = -18

-9 + -5 = -14 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and -5

x2 - 9x - 5x - 45

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-9)

Add up the last 2 terms, pulling out common factors :

5 • (x-9)

Step-5 : Add up the four terms of step 4 :

(x-5) • (x-9)

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