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Finding the Missing Numbers in Pairs of Equivalent Expressions

8.6.4 Finding the Missing Numbers in Pairs of Equivalent Expressions

8.6.4 • Finding the Missing Numbers in Pairs of Equivalent Expressions

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The problems below consist of pairs of equivalent expressions: one in standard form and the other in factored form. Note that the leading coefficients on the quadratic terms are all 1.

Find the missing numbers.

1.

x2+x2+ __x+x+ __ and (x+1)(x+17)(x+1)(x+17)

Compare your answer:

18 and 17, respectively. The completed expression is x2+18x+17x2+18x+17.

2.

x2+9x+14x2+9x+14 and (x+2)(x+(x+2)(x+ __))

Compare your answer:

7. The completed expression is (x+2)(x+7)(x+2)(x+7).

3.

x2−7x+10x2−7x+10 and (x−2)(x−(x−2)(x− __))

Compare your answer:

5. The completed expression is (x−2)(x−5)(x−2)(x−5).

4.

x2−9x+20x2−9x+20 and (x−(x− __)(x−(x− __))

Compare your answer:

4 and 5. The completed expression is (x−4)(x−5)(x−4)(x−5).