the partial factorization of $x^{2}-3x - 10$ is modeled with algebra tiles. which unit tiles are needed to…

the partial factorization of $x^{2}-3x - 10$ is modeled with algebra tiles. which unit tiles are needed to complete the factorization? 2 negative unit tiles 2 positive unit tiles 5 negative unit tiles 5 positive unit tiles

the partial factorization of $x^{2}-3x - 10$ is modeled with algebra tiles. which unit tiles are needed to complete the factorization? 2 negative unit tiles 2 positive unit tiles 5 negative unit tiles 5 positive unit tiles

Answer

Explanation:

Step1: Factor the quadratic expression

We factor (x^{2}-3x - 10) using the formula (x^{2}+bx + c=(x + m)(x + n)) where (m + n=b) and (mn=c). For (x^{2}-3x - 10), we need two numbers (m) and (n) such that (m + n=-3) and (mn=-10). The numbers are (m = 2) and (n=-5) since (2+( - 5)=-3) and (2\times(-5)=-10), so (x^{2}-3x - 10=(x + 2)(x-5)).

Step2: Analyze the unit - tiles

The constant term in the factored form ((x + 2)(x - 5)=x^{2}-5x+2x - 10=x^{2}-3x - 10). The constant term (-10) means we need 10 negative unit - tiles. From the given partial factorization, we already have some negative unit - tiles. We know that (-10=(- 5)\times2). We need 5 negative unit tiles to complete the factorization.

Answer:

5 negative unit tiles