SOLUTION: Hi Im stuck on this, can someone help me??
The polynomial "x^3 + 2x^2 − 29x + 42" has -7 as one zero. Find the quadratic factor.
A. x^2 - 5x - 6
B. x^2 + 5x + 6
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Polynomials-and-rational-expressions
-> SOLUTION: Hi Im stuck on this, can someone help me??
The polynomial "x^3 + 2x^2 − 29x + 42" has -7 as one zero. Find the quadratic factor.
A. x^2 - 5x - 6
B. x^2 + 5x + 6
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Question 1028779: Hi Im stuck on this, can someone help me??
The polynomial "x^3 + 2x^2 − 29x + 42" has -7 as one zero. Find the quadratic factor.
A. x^2 - 5x - 6
B. x^2 + 5x + 6
C. x^2 + 5x - 6
D. x^2 - 5x + 6 Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! looks like a problem in synthetic division, or polynomial division, if you're not familiar with synthetic division.
your equation is x^3 + 2x^2 - 29x + 42
the equation has -7 as one zero.
use synthetic division to find the remaining equation.
with synthetic division, you are dividing -7 into (1 + 2 - 29 + 42)
you bring down the 1.
you then multiply that 1 by -7 to get -7
you add -7 to 2 and you get -5
you multiply -5 by -7 to get 35
you add 35 to -29 to get 6
you multiply 6 by -7 to get -42
you add -42 to 42 to get 0.
that means that -7 is a root of the equation because the remainder is 0.
you are left with:
1 -5 + 6 + 0
that equates to x^2 - 5x + 6
that's selection D.
you would also get the same answer using polynomial division.
the following worksheet shows the results of both.
with synthetic division, you are working with the coefficients and the constants.
with polynomial division, you are working with the complete terms.
the following references should help you understand how to do the divisions.
