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Answer :
Answer:
−(18x+19)
Step-by-step explanation:
Factor −1 out of 8⋅2−18x−35. −(18x−8⋅2+35)
Multiply −8 by 2.−(18x−16+35)
Add −16 and 35.−(18x+19)
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Final answer:
To factor the expression 8x2 - 18x - 35, one needs to find two numbers that multiply to give the product of the coefficient of x^2 and the constant term (-280) and add up to the coefficient of x (-18). These numbers are -28 and +10. This leads to factoring the expression into (4x + 5)(2x - 7).
Explanation:
The question asks to factor the expression 8x2 - 18x - 35. Factoring such an expression involves finding two binomials that when multiplied together, give back the original expression. This process can be approached through the method of splitting the middle term or using the quadratic formula.
However, in this situation, trial and error alongside the understanding of how to balance factors to achieve the original coefficients and constant term is most efficient.
Firstly, we note that the expression is a quadratic equation in the form of ax2 + bx + c. To factor it, we look for two numbers that multiply to ac (8 * -35 = -280) and add up to b (-18). Through trial and error, these numbers are found to be -28 and +10. Thus, we rewrite -18x as -28x + 10x and then factor by grouping.
The steps are as follows:
8x2 - 28x + 10x - 35
4x(2x - 7) + 5(2x - 7)
(4x + 5)(2x - 7)
Hence, the factored form of 8x2 - 18x - 35 is (4x + 5)(2x - 7).
