Question

Here are pairs of equivalent expressions, one in standard form and the other in factored form. Find

the missing numbers.
1. x2 +
+
and (x – 9) (x - 3)
2. 22 – 9x + 20 and (x – 4) (x +

Answer 1

The missing terms for the quadratic expressions are found by expanding the given factored forms using the FOIL method. For (x - 9)(x - 3), the missing terms in the standard form x^2 + ___ + ___ are -12 and 27. For (x - 4)(x + ___), the missing term is 5, making the factored expression (x - 4)(x + 5).

Step-by-step explanation:

The student's question appears to be related to polynomials, specifically identifying missing terms in quadratic expressions given in both standard form and factored form. Let's find the missing numbers.

For the first expression x2 + ___ + ___ and the factored form (x - 9)(x - 3), we use the FOIL method (First, Outer, Inner, Last) to expand the factored form:

• x * x = x2
• x * -3 = -3x
• -9 * x = -9x
• -9 * -3 = 27

Combining like terms, we get x2 - 12x + 27. Therefore, the missing numbers for the first expression are -12 and 27.

For the second expression 22 - 9x + ___ and the factored form (x - 4)(x + ___), we already have a part of the expression in the factored form. Knowing that the constant term in the standard form is 20 and the factored form when multiplied out should result in the standard form, we can deduce that the factor missing in the second part of the factored expression is 5. Thus, the missing number for the second expression is 5.