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Mathematics
Algebraic Expressions
Factorization: Middle Term Break-Up
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Multiple Choice
If $ac = 30$ for the polynomial $6x^2 + 11x + 5$, and we need two numbers whose product is $30$ and sum is $11$, which pair of numbers fits?
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5 and 6
10 and 3
15 and 2
1 and 30
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What is the first step in using the middle term break-up method for factoring $ax^2 + bx + c$?
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Find two numbers that multiply to $b$ and add up to $ac$.
Find two numbers that multiply to $a$ and add up to $b$.
Find two numbers that multiply to $c$ and add up to $b$.
Find two numbers that multiply to $ac$ and add up to $b$.
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Which of the following is a possible relationship for the factors of the polynomial $ax^2 + bx + c$ using the middle term break-up method?
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$a = rs$, $b = rq + sp$, $c = pq$
$a = pq$, $b = rq + sp$, $c = rs$
$a = rq + sp$, $b = rs$, $c = pq$
$a = pq$, $b = rs$, $c = rq + sp$
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After splitting the middle term of $3x^2 - x - 14$ into $-7x$ and $6x$, what is the resulting factorization?
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$(x + 3)(3x - 14)$
$(3x - 7)(x + 2)$
$(3x + 2)(x - 7)$
$(x - 2)(3x + 7)$
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For the polynomial $4x^2 + 19x + 5$, what is the value of $ac$?
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20
76
24
30
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