Question - Factoring Trinomials
Solution:
The provided trinomial is $$ 4u^2 + 5u + 7 $$, and the task is to factor it completely. Based on the image you provided, there are several options given, including:1) $$ u(4u + 5) + 7 $$2) Prime3) $$ (4u - 7)(u + 5) $$4) $$ (4u + 5)(u - 7) $$The first step in factoring is to look for a common factor. In this case, there is no common factor that divides all three terms $$4u^2$$, $$5u$$, and $$7$$.The next step would be to check if the trinomial can be factored into a product of two binomials of the form $$ (ax + b)(cx + d) $$. To do this, we would need to find two numbers that multiply to $$ac \cdot d = 4 \cdot 7 = 28$$ and add up to $$b = 5$$. However, there are no two integers that meet these criteria.Therefore, this trinomial does not factor over the integers and hence is prime. The correct choice from the options provided would be:2) Prime
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