Mc Graw Hill Key To Algebra Book 4 Polynomials 1st Edition Chapter 3 Opposites Of Polynomials
Page 3 Exercise 1 Answer
Given:
3x2 − 8x + 2
To find:
The opposite polynomial
To find the opposite polynomial:
Given the opposite polynomial
3x²-8x+2
(3x²-8x+2)×(-1).3x²-(-1).8x+(-1).2
(3x²-8x+2)×(-1)=-3x²+8x-2-4
(3x²+5x-2)-(7x²-5x+4)= 3x²-7x²+5x-2-4
(3x²+5x-2)-(7x²-5x+4)=-4x²+10x-6
The opposite polynomial: −3x2 + 8x − 2
Page 3 Exercise 2 Answer
Given:
6a + 7b + 4
To find:
The opposite polynomial
To find the opposite polynomial:
Given,
6a+7b+4
(6a+7b+4)(-1)=(-1).6a+(-1).7b+(-1).4
(6a+7b+4)x(-1)=-6a-7b-4
The opposite polynomial: −6a − 7b − 4
Page 3 Exercise 3 Answer
Given:
5x2 − 2x − 9
To find:
The opposite polynomial
To find the opposite polynomial:
Given
5x2-2x-9
(5x2-2x-9)(-1)=(-1).5x2– (-1).2x- (-1).9
(5x2-2x-9)(-1)=-5x2+2x+9
The opposite polynomial: −5x2 + 2x + 9
Page 3 Exercise 4 Answer
Given:
x2 − 16
To find:
The opposite polynomial
To find the opposite polynomial:
Given
x²-16
(x²-16)x(-1)=(-1).x²-(-1).16
(x²-16)x(-1)=-x²+16
The opposite polynomial: −x2 + 16
Page 3 Exercise 5 Answer
Given:
x5 + x4 + x3 − x2 + x − 1
To find:
The opposite polynomial
To find the opposite polynomial:
Given
⇒ \(\begin{aligned}
& x^5+x^4+x^3-x^2+x-1 \\
& \left(-x^5+x^4+x^3-x^2+x-1\right) x(-1)=(-1) x^5+(-1) \cdot x^4+(-1) \cdot x^3-(-1) \cdot x^2+(-1) \cdot x-(-1) \cdot 1 \\
& \left(x^5+x^4+x^3-x^2+x-1\right) x(-1)=-x^5-x^4-x^3+x^2-x+1
\end{aligned}\)
The opposite polynomial: −x5 − x4 − x3 + x2 − x + 1
Page 3 Exercise 6 Answer
Given:
−7x − 8
To find:
The opposite polynomial
To find the opposite polynomial:
Given
-7x-8
(-7x-8)×(-1)=-(-1).7x-)(-1).8
(_7x-8)x(-1)=7x+8
The opposite polynomial: 7x + 8
Page 3 Exercise 7 Answer
Given:
x2 + 5x − 14
To find:
The opposite polynomial
To find the opposite polynomial:
Given
x²+5x-14
⇒ \(\begin{aligned}
& \left(x^2+5 x-14\right)(-1)=(-1) \cdot x^2+(-1) \cdot 5 x-(-1) \cdot 14 \\
& \left(x^2+5 x-14\right)(-1)=-x^2-5 x+14
\end{aligned}\)
The opposite polynomial: −x2 − 5x + 14
Page 3 Exercise 8 Answer
Given:
−x2 − 5x + 14
To find:
The opposite polynomial
To find the opposite polynomial:
Given
-x2 -5x+14
\(\begin{aligned}& \left(-x^2-5 x+14\right) \times(-1)=-(-1) x^2-(-1) 5 x+(14) \cdot(-1) \\
& \left(-x^2-5 x+14\right) \times(-1)=x^2+5 x-14
\end{aligned}\)
The opposite polynomial: x2 + 5x − 14
Page 3 Exercise 9 Answer
Given:
(x2+5x−14) + (−x2−5x+14)
To find:
Addition of opposite polynomials
To find the addition of the opposite polynomial:
Given: (x2+5x−14) + (−x2−5x+14)
(x2+5x−14) + (−x2−5x+14)=(1-1)x²+(5-5)x+(-1+1)14
(x2+5x−14)+(−x2−5x+14)=0.x²+0.x+0.14
(x2+5x-14)+(-x2-5x+14)=0
The addition of opposite polynomial: (x2+5x−14) + (−x2−5x+14) = 0
Page 3 Exercise 10 Answer
Given:
(−7x−8) + (7x+8)
To find:
Addition of opposite polynomials
To find the addition of the opposite polynomial:
Given:
(-7x-8)+(7x+8)
(-7x-8)+(7x+8)=(-7+7).x+(-1+1).8
(-7x-8)+(7x+8)=0.x+0.8
(-7x-8)+7x+8)=0
The addition of opposite polynomial: (−7x−8) + (7x+8) = 0