Which polynomial is factored completely?
121x^2+36y^2
(4x+4)(x+1)
2x(x^2-4)
3x^4-15n^3+12n^2
Answer:
Complete factored: (4x+4)(x+1) and 2x(x²-4)
Step-by-step explanation:
We have to check each option one by one
Option 1: \(121x^2+36y^2\)
It is sum of two perfect square, As we know sum of two perfect square can't be factored. It is prime equation.
False
Option 2: \((4x+4)(x+1)\)
Here we have two factor (4x+4) and (x+1). In both factor degree of x is 1. It is complete factor form.
Complete factor: \(4(x+1)(x+1)\)
True
Option 3: \(2x(x^2-4)\)
Here we have two factor 4x and x²-4. For second factor it is further factor. Because it is difference of square. Factor of x²-4 = (x+2)(x-2)
Complete Factor: 2x(x+2)(x-2)[/tex]
True
Option 4: \(3x^4-15n^3+12n^2\)
Here variable are not same. So, it can't be factor.
False
The completely factored polynomials are \(\boxed{2x\left( {{x^2} - 4} \right)}\) and \(\boxed{\left( {4x + 4} \right)\left( {x + 1} \right)}\). Option (b) and option (c) are correct.
Further Explanation:
Given:
The options are as follows,
(a). \(121{x^2} + 36{y^2}\)
(b). \(\left( {4x + 4} \right)\left( {x + 1} \right)\)
(c). \(3{x^4} - 15{n^3} + 12{n^2}\)
(d). \(3{x^4} - 15{n^3} + 12{n^2}\)
Calculation:
In option (a)
The expression \(121{x^2} + 36{y^2}\) is not in the factored form. option (a) is not correct.
In option (b)
The expression \(\left( {4x + 4} \right)\left( {x + 1} \right)\) is in the factored form.
\({\text{Factored}} = 4{\left( {x + 1} \right)^2}\)
Option (b) is correct.
In option (c)
The expression \(2x\left( {{x^2} - 4} \right)\) is in the factored form.
\(\begin{aligned}{\text{Factored}} &= 2x\left( {{x^2} - 4} \right)\\&= 2x\left( {x + 2} \right)\left( {x - 2} \right)\\\end{aligned}\)
Option (c) is correct.
In option (d)
The expression \(3{x^4} - 15{n^3} + 12{n^2}\) is not in the factored form.
Option (d) is not correct.
The completely factored polynomials are \(\boxed{2x\left( {{x^2} - 4} \right)}\) and \(\boxed{\left( {4x + 4} \right)\left( {x + 1} \right)}.\) Option (b) and option (c) are correct.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Exponents and Powers
Keywords: solution, factored, completely, polynomial, factorized form, expression, difference of cubes, exponents, power, equation, power rule, exponent rule.
