Question

The partial factorization of x2 – 3x – 10 is modeled with algebra tiles. An algebra tile configuration. 1 tile is in the Factor 1 spot: and is labeled x. 6 tiles are in the Factor 2 spot: 1 is labeled x and 5 are labeled negative. 18 tiles are in the Product spot: 1 is labeled x squared, 2 are labeled x, the 5 tiles below x squared are labeled negative x, and the 10 tiles below the x tiles are labeled negative. 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 1

2 positive unit tiles are needed to complete the factorization.

Given

The partial factorization of x^2 – 3x – 10 is modeled with algebra tiles.

Partial factorization;

Partial fractions are the fractions used for the decomposition of a rational expression.

When an algebraic expression is split into a sum of two or more rational expressions, then each part is called a partial fraction.

In the second line, we can see that first term 1 is labeled + x squared, second is labeled + 2x (two positive tiles above), then the 5 tiles below + x squared are labeled negative x, and the 10 tiles below the + x tiles are labeled negative.

The negative values are represented as tiles labeled below (negative tiles) while positive values are tiles labeled above (positive tiles).

Therefore,

The factorization is;

$\rm x^2-3x-10=0\\\\x^2+2x-5x-10=0\\\\x(x+2)-5(x+2)=0\\\\(x+2)(x-5)=0$

Hence, 2 positive unit tiles are needed to complete the factorization.

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