Question

set 1. write a polynomial for the shaded area, then factor the polynomial. l i t

Explanation:

Step1: Find polynomial for L

Count terms: $x^2 + 4x + 4x + 16 = x^2 + 8x + 16$

Step2: Factor polynomial for L

Recognize perfect square: $(x+4)^2$

Step3: Find polynomial for I

Count terms: $4x^2 + 6x + 6x + 9 = 4x^2 + 12x + 9$

Step4: Factor polynomial for I

Recognize perfect square: $(2x+3)^2$

Step5: Find polynomial for T

Area of square minus square: $(2x)^2 - 3^2 = 4x^2 - 9$

Step6: Factor polynomial for T

Difference of squares: $(2x-3)(2x+3)$

Answer:

• L: Polynomial: $x^2 + 8x + 16$, Factored form: $(x+4)^2$
• I: Polynomial: $4x^2 + 12x + 9$, Factored form: $(2x+3)^2$
• T: Polynomial: $4x^2 - 9$, Factored form: $(2x-3)(2x+3)$