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patriot [66]
3 years ago
9

PLEASE ANSWER + BRAINLIEST !! (show work)

Mathematics
1 answer:
e-lub [12.9K]3 years ago
8 0
The missing value could be 16 or 19; if it is 16, the binomials would be
4(x+3)(x+1).  If it is 19, the binomials would be (x+4)(4x+3).

To factor these, we want factors of a*c that sum to b; in this trinomial, a*c is 4(12)=48.  If we use 12 and 4 to make 48, this would give a b value of 16:
4x²+16x+12

These two factors will be how we "split up" bx:
4x²+12x+4x+12

Now we group together the first two and last two:
(4x²+12x)+(4x+12)

Factor out the GCF of each group:
4x(x+3)+4(x+3)

Factor out the GCF of this new expression:
(x+3)(4x+4)

In the last binomial, they are both divisible by 4, so factor this out:
4(x+1)(x+3)

If we use 16*3 to make 48, this would give us a b value of 19; we would "split up" bx as follows:
4x²+16x+3x+12

Group:
(4x²+16x)+(3x+12)

Factor out the GCF:
4x(x+4)+3(x+4)

Factor out the GCF again:
(x+4)(4x+3)
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<h3>Fraction addition:</h3>
  • If the denominators are not same, find the LCM of the denominators.

          LCM of 3 and 9 is 9.

  • Now, find equivalent fractions with denominator as 9.

          \sf \dfrac{1}{3}=\dfrac{1*3}{3*3}\\\\

              \sf =\dfrac{3}{9}

  • Now add.

      \sf \dfrac{4}{9}+\dfrac{1}{3}=\dfrac{4}{9}+\dfrac{3}{9}\\\\

                 \sf =\dfrac{7}{9}

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