Question - Factoring Trinomials
Solution:
The question is asking to factor the trinomial $$2x^2 + 11x + 14$$.To factor it, one of the methods is to look for two numbers that both add up to the coefficient of the $$x$$ term (which is 11 in this case) and multiply to the product of the coefficient of $$x^2$$ term and the constant term (which is $$2 \times 14 = 28$$).So, we need two numbers that add up to 11 and multiply to 28. These two numbers are 4 and 7, because:\[4 + 7 = 11\]\[4 \times 7 = 28\]Now we can rewrite the middle term (11x) using 4 and 7:\[2x^2 + 4x + 7x + 14\]Next, let's factor by grouping:\[2x(x + 2) + 7(x + 2)\]Now, we can take out the common factor $$(x + 2)$$:\[(2x + 7)(x + 2)\]Therefore, the factored form of $$2x^2 + 11x + 14$$ is $$(2x + 7)(x + 2)$$.
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