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What term should go in the box to make the statement true?\newline 3x2+10x8=(3x2)(x 3x^2+10x-8=(3x-2)(x+)\square)

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Q. What term should go in the box to make the statement true?\newline 3x2+10x8=(3x2)(x 3x^2+10x-8=(3x-2)(x+)\square)
  1. Expand Factors: To find the missing term in the box, we need to expand the right side of the equation and compare it to the left side. Let's start by expanding the known factors without the box term.\newline(3x2)(x)=3x22x(3x - 2)(x) = 3x^2 - 2x
  2. Find Middle Term: Now, we need to find a term that, when multiplied by 3x3x, gives us the middle term of the left side of the equation, which is 10x10x. We already have 2x-2x from the expansion, so we need to find a number that will result in (3x×number)+(2x)=10x(3x \times \text{number}) + (-2x) = 10x.
  3. Calculate Value of 'a': Let's denote the number we are looking for as 'a'. So we have:\newline3xa2x=10x3x \cdot a - 2x = 10x\newline3ax=10x+2x3ax = 10x + 2x\newline3ax=12x3ax = 12x\newlinea=12x3xa = \frac{12x}{3x}\newlinea=4a = 4
  4. Complete the Expression: Now that we have found the value of aa, we can complete the expression: (3x2)(x+4)(3x - 2)(x + 4)

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