36 is must be added to the expression x² + 12x to make it
perfect-square trinomial
Step-by-step explanation:
The perfect-square trinomial x² + 2ax + a² = (x + a)², then
1. The first term in the trinomial is square the 1st term in the bracket
2. The middle term in the trinomial is the product of 1st , 2nd
terms of the bracket and 2
3. The 3rd term in the trinomial is square the 2nd term in the bracket
∵ The expression is x² + 12x
∵ We must add the 3rd term which make it perfect-square trinomial
- Divide 12x by 2 to find the product of the 1st term and 2nd term
in the bracket
∵ 12x ÷ 2 = 6x
∴ The 1st term is x and the 2nd term is 6 of the bracket
∵ The 3rd term in the trinomial is square the 2nd term in the bracket
∴ The 3rd term in the trinomial is 6² = 36
∴ x² + 12x + 36 = (x + 6)²
36 is must be added to the expression x² + 12x to make it
perfect-square trinomial
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;
or p = -6