Question

Thomasina is asked to factorise y^2 - 2y + 35.

She gives the answer (y + 7)(y - 5).

Thomasina is wrong. Explain why

Answer 1

Explanation:

hello :

(y + 7)(y - 5) = y² -5y+7y-35=y²+2y-35 no y²-2y-35

Answer 2

there is no factorization of y^2 -2y +35 in real numbers

Explanation:

Thomasina correctly determined two factors of 35 that differ by 2, but that is not what is needed here. For this problem, she needs two factors of 35 that have a sum of 2.* (There aren't any real-number factors that meet that condition.)

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The factorization in complex numbers would be ...

= (y -1 -i√34)(y -1 +i√34)

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* Technically, she needs two factors of 35 with a sum of -2. Both factors would have to be negative.