Given that x = – 2 is a solution to 𝑥2+𝑏𝑥–6=0,x 2 +bx–6=0, which of the following polynomials is a factor of 𝑥2+𝑏𝑥–6?x 2 +bx–6?F. x – 3 G. x – 2 H. x –1 J. x + 1 K. x + 3 InfoInstr123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960 Flag
Question
Given that x = – 2 is a solution to 𝑥2+𝑏𝑥–6=0,x 2 +bx–6=0, which of the following polynomials is a factor of 𝑥2+𝑏𝑥–6?x 2 +bx–6?F. x – 3 G. x – 2 H. x –1 J. x + 1 K. x + 3 InfoInstr123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960 Flag
Solution
The given equation is 𝑥²+𝑏𝑥–6=0 and we know that x = -2 is a solution to this equation.
A solution to a polynomial equation is also a root of the equation. If x = -2 is a root of the equation, then x + 2 is a factor of the polynomial.
Therefore, none of the given options F. x – 3, G. x – 2, H. x –1, J. x + 1, K. x + 3 are factors of the polynomial 𝑥²+𝑏𝑥–6.
The correct factor should be x + 2, which is not listed in the options.
Similar Questions
Factor this polynomial completely.12x2 + x – 6A.(4x – 2)(2x + 3)B.(3x – 2)(4x + 3)C.(12x – 2)(x + 3)D.(12x – 3)(x + 2)
factorise the polynomial x3 + 4x2 + x − 6
What are the zeros of the polynomial functionF(x) = x3 - x2 - 6x?A.x = -3, x = 0, and x = 2B.x = -1, x = 0, and x = 6C.x = -2, x = 0, and x = 3D.x = -6, x = 0, and x = 1SUBMITarrow_backPREVIOUS
Which of the following is the correct factorization of the polynomial below?2x2 - 12x + 18A.2(x - 3)2B.2(x + 6)(x + 3)C.(2x + 6)(x + 3)D.The polynomial is irreducible.
What are the zeros of the polynomial function 𝐹(𝑥)=𝑥2−5𝑥−6F(x)=x 2 −5x−6?A.x = -1 and x = 6B.x = 2 and x = 3C.x = -3 and x = -2D.x = -6 and x = 1SUBMITarrow_backPREVIOUS
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.