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Hagrid
Factoring the first polynomial expression completely will give us (b+4)(b+8). Try to check it for yourself by multiplying the factors and you will get b2+12b+32. For the second polynomial expression, the factors are (a-5)(a+4). To check, just do the FOIL method and you will get a2-a-20.
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Answer:

b² + 12b + 32 = (b + 8)(b + 4)

a² - a - 20 = (a - 5)(a + 4)

Step-by-step explanation:

b² + 12b + 32

To factor, let's find two numbers that multiply to 32, and add to 12.

I find the two numbers as 4 and 8.

We can expand 12b as 4b + 8b, and factor the pairs.

Factor:

  • b² + 12b + 32
  • b² + 4b + 8b + 32
  • (b² + 4b) + (8b + 32)
  • b(b + 4) + 8(b + 4)
  • (b + 8)(b + 4)

The factored form is (b + 8)(b + 4)

a² - a - 20

Using the same process, find two numbers that multiply to -20 and add to -1

The numbers are 4 and -5

Factor:

  • a² - a - 20
  • a² + 4a - 5a - 20
  • (a² + 4a) + (-5a - 20)
  • a(a + 4) -5(a + 4)
  • (a - 5)(a + 4)

The factored form is (a - 5)(a + 4)

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