Problem 27
Question
Factor each trinomial, or state that the trinomial is prime. $$6 x^{2}-11 x+4$$
Step-by-Step Solution
Verified Answer
The factored form of the trinomial \( 6x^2 - 11x + 4 \) is \( (2x - 1) (3x - 4) \).
1Step 1: Calculate product and find factors
First, calculate the product of the coefficient of \( x^2 \) and the constant term, i.e., \( ac = 6*4 = 24 \). Find two numbers that multiply to 24 and add up to -11, which are -8 and -3.
2Step 2: Rewrite the trinomial
Next, rewrite the middle term (\( -11x \)) of the trinomial as the sum of the terms -8x and -3x. This gives us \( 6x^2 - 8x - 3x + 4 \).
3Step 3: Factor by grouping
Factor by grouping, by factoring out the common factors in each group: \( 2x (3x - 4) -1 (3x - 4) \).
4Step 4: Combine common factors
Now it's possible to factor out the common binomial factor, \( 3x - 4 \), to get the final answer: \( (2x - 1) (3x - 4) \).
Other exercises in this chapter
Problem 26
Find the intersection of the sets. $$\\{0,1,3,5\\} \cap\\{-5,-3,-1\\}$$
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Use the quotient rule to simplify the expressions Assume that \(x>0\). $$ \frac{\sqrt{48 x^{3}}}{\sqrt{3 x}} $$
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