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2. Sydney Harbour Bridge is unusually wide. The area of the bridge can be represented by the trinomial 10x2 - 7x - 3. a) Factor the trinomial to determine the binomial factors that represent the length and width of the bridge.

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sqdancefan

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Answer:

  • length: (10x +3)
  • width: (x -1)

Step-by-step explanation:

To factor the quadratic expression Ax² +Bx +C, you look for factors of the product AC that have a sum of B.

  AC = 10(-3) = -30 = 1(-30) = 2(-15) = 3(-10) = 5(-6)

These factor pairs have sums of -29, -13, -7, -1. The pair we want is (3)(-10), which has a sum of -7.

Using this pair of factors, we can rewrite the "B" term as a sum.

  10x² -7x -3 = 10x² +3x -10x -3

This can be factored by grouping pairs of terms together:

  = (10x² +3x) +(-10x -3)

  = x(10x +3) -1(10x +3)

  = (x -1)(10x +3)

If we consider the length to be greater than the width, then these binomial factors might represent ...

  length: (10x +3)

  width: (x -1)

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