Question

The model represents the factorization of 2x2+5x+3. An algebra tile configuration. 4 tiles are in the Factor 1 spot: 2 +x tiles, 2 + tiles. 2 tiles are in the Factor 2 spot.: 1 +x tile, 1 + tile. 10 tiles are in the Product spot in 4 columns with 2 rows. First row: 2 + x squared tiles, 3 + x tiles. Second row: 2 + x tiles, 3 + tiles. What are the factors of the polynomial? (2x+3)(x+1) (2x−3)(x−1) (3x+2)(x+1) (3x−2)(x−1)

Answer 1

The factors of the polynomial are (2x + 3) (x + 1)

Further explanation

Factoring A Quadratic Equation means finding a factor of an equation that if multiplied produces a quadratic equation

We can solve the quadratic equation with the formula or we can do it by finding the common factor as below

From the 2x² + 5x + 3 equation, we can determine a, b and c from the general quadratic equation namely ax² + bx + c:

a = 2, b = 5, c = 3

First, find two numbers that multiply to give a x c and add to give b.

From the equation above:

a x c = 6, and b = 5

we look for a factor of 6 which when added together gets the number 5

a factor of 6: 1,2,3,6

of these factors which can be added to 5 are 2 and 3

So the form of the equation becomes:

2x² + 2x + 3x + 3

(2x² + 2x) + (3x +3)

2x (x + 1) + 3 (x + 1)

(x + 1) -> common to both terms

We use the principle of distributive property of addition

ax (b + c) = axb + axc -> a = x + 1

so the factors : (2x + 3) (x + 1)

Learn more

Greatest common factor

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Keywords : factorization, polynomial, the quadratic equation

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Answer 2

Answer

A (2x+3)(x+1)

Step-by-step explanation:

i worked it out and it was right

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