Factor the trinomial: 5x^(2)+37 x+42 Answer:

Identify structure and numbers: Identify the structure of the trinomial and look for two numbers that multiply to give the product of the coefficient of x^2 term (5) and the constant term (42), which is 5*42=210, and add up to the coefficient of the x term (37). Find numbers satisfying conditions: Find two numbers that multiply to 210 and add up to 37. After testing different combinations, we find that 14 and 15 are the numbers that satisfy both conditions because 14*15=210 and 14+15=37. Rewrite middle term: Rewrite the middle term (37x) using the two numbers found in Step 2. This gives us 5x^2 + 14x + 15x + 42. Factor by grouping: Factor by grouping. Group the first two terms and the last two terms: (5x^2 + 14x) + (15x + 42). Factor out common factors: Factor out the greatest common factor from each group. From the first group, we can factor out x, and from the second group, we can factor out 3. This gives us x(5x + 14) + 3(5x + 14). Final answer: Since both groups contain the common factor (5x + 14), factor this out to get the final answer: (x + 3)(5x + 14).

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Q. Factor the trinomial:

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5 x^{2}+37 x+42

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Answer:

Identify structure and numbers: Identify the structure of the trinomial and look for two numbers that multiply to give the product of the coefficient of $x^2$ term ( $5$ ) and the constant term ( $42$ ), which is $5\times42=210$ , and add up to the coefficient of the $x$ term ( $37$ ).
Find numbers satisfying conditions: Find two numbers that multiply to $210$ and add up to $37$ . After testing different combinations, we find that $14$ and $15$ are the numbers that satisfy both conditions because $14 \times 15 = 210$ and $14 + 15 = 37$ .
Rewrite middle term: Rewrite the middle term $37x$ using the two numbers found in Step $2$ . This gives us $5x^2 + 14x + 15x + 42$ .
Factor by grouping: Factor by grouping. Group the first two terms and the last two terms: $(5x^2 + 14x) + (15x + 42)$ .
Factor out common factors: Factor out the greatest common factor from each group. From the first group, we can factor out $x$ , and from the second group, we can factor out $3$ . This gives us $x(5x + 14) + 3(5x + 14)$ .
Final answer: Since both groups contain the common factor $(5x + 14)$ , factor this out to get the final answer: $(x + 3)(5x + 14)$ .