MATH SOLVE

4 months ago

Q:
# 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)

Accepted Solution

A:

The factors of the polynomial are (2x + 3) (x + 1)Further explanationFactoring 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 moreGreatest common factor : factorization, polynomial, the quadratic equation#LearnwithBrainly