Mc Graw Hill Key To Algebra Book 4 Polynomials 1st Edition Chapter 4 Subtracting Polynomials

Mc Graw Hill Key To Algebra Book 4 Polynomials 1st Edition Chapter 4 Subtracting Polynomials

Page 4 Exercise 1 Answer

Given:

(3x²+5x−2) − (7x²−5x+4)

To find:

The subtraction of polynomials

To find the subtraction of polynomials:

Given

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 subtraction of polynomials: (3x²+5x−2) − (7x²−5x+4) = −4x² + 10x − 6

Page 4 Exercise 2 Answer

Given:

(6x²+2x−2) − (x²+4x−1)

To find:

The subtraction of polynomials

To find the subtraction of polynomials:

Given

(6x²+2x-2)-(x²+4x-1)
(6x²+2x-2)-(x²+4x-1)=6x²+2x-2-x²4x+1
(6x²+2x-2)-(x²+4x-1)=6x²-x²+2x-4x-2+1
(6x²+2x-2)-(x²+4x-1)=5x²-2x-1

The subtraction of polynomials: (6x²+2x−2) − (x²+4x−1) = 5x² − 2x − 1

Page 4 Exercise 3 Answer

Given:

(2y²−y+3) − (3y²−y−4)

To find:

The subtraction of polynomials

To find the subtraction of polynomials:

Given

(2y²-y+3)-(3y²-y-4)
(2y²-y+3)-(3y²-y-4)=2y²-y+3y²+y+4
(2y²-y+3)-(3y²-y-4)=2y²-3y²-y+y+3+4
(2y²-y+3)-(3y²-y-4)=-y²+7

The subtraction of polynomials: (2y²−y+3) − (3y²−y−4) = −y² + 7

Page 4 Exercise 4 Answer

Given:

(y²+y−6) − (y²+5y−6)

To find:

The subtraction of polynomials

To find the subtraction of polynomials:

Given:

\(\begin{aligned}
& \left(y^2+y-6\right)-\left(y^2+5 y-6\right) \\
& \left(y^2+y-6\right)-\left(y^2+5 y-6\right)=y^2+y-6-y^2-5 y+6 \\
& \left(y^2-y-6\right)-\left(y^2+5 y-6\right)=y^2-y^2+y-5 y-6+6 \\
& \left(y^2-y-6\right)-\left(y^2+5 y-6\right)=-4 y
\end{aligned}\)

The subtraction of polynomials: (y²+y−6) − (y²+5y−6) = −4y

Page 4 Exercise 5 Answer

Given:

(4x²+3x+5) − (4x²−3x+5)

To find:

The subtraction of polynomials

To find the subtraction of polynomials:

Given: 

\(\begin{aligned}
& \left(4 x^2+3 x+5\right)-\left(4 x^2-3 x+5\right) \\
& \left(4 x^2+3 x+5\right)-\left(4 x^2-3 x+5\right)=4 x^2+3 x+5-4 x^2+3 x-5 \\
& \left(4 x^2+3 x+5\right)-\left(4 x^2-3 x+5\right)=4 x^2-4 x^2+3 x+3 x+5-5 \\
& \left(4 x^2+3 x+5\right)-\left(4 x^2-3 x+5\right)=6 x
\end{aligned}\)

The subtraction of polynomials: (4x²+3x+5) − (4x²−3x+5) = 6x

Page 4 Exercise 6 Answer

Given:

(3x²+5x−2) − (2x²−3x+7)

To find:

The subtraction of polynomials

To find the subtraction of polynomials:

Given:

\(\begin{aligned}
& \left(3 x^2+5 x-2\right)-\left(2 x^2-3 x+7\right) \\
& \left(3 x^2+5 x-2\right)-\left(2 x^2-3 x+7\right)=3 x^2+5 x-2-2 x^2+3 x-7 \\
& \left(3 x^2+5 x-2\right)-\left(2 x^2-3 x+7\right)=3 x^2-2 x^2+5 x+3 x-2-7 \\
& \left(3 x^2+5 x-2\right)-\left(2 x^2-3 x+7\right)=x^2+8 x-9
\end{aligned}\)

The subtraction of polynomials: (3x²+5x−2) − (2x²−3x+7) = x² + 8x − 9

Page 4 Exercise 8 Answer

Given:

(5a²−2a−8) − (a²−6a+3)

To find:

The subtraction of polynomials

To find the subtraction of polynomials:

Given:

\(\begin{aligned}
& \left(5 a^2-2 a-8\right)-\left(a^2-6 a+3\right) \\
& \left(5 a^2-2 a-8\right)-\left(a^2-6 a+3\right)=5 a^2-2 a-8-a^2+6 a-3 \\
& \left(5 a^2-2 a-8\right)-\left(a^2-6 a+3\right)=5 a^2-a^2-2 a+6 a-8-3 \\
& \left(5 a^2-2 a-8\right)-\left(a^2-6 a+3\right)=4 a^2+4 a-11
\end{aligned}[latex]

The subtraction of polynomials: (5a²−2a−8) − (a²−6a+3) = 4a² + 4a − 11

Page 4 Exercise 9 Answer

Given:

(8x²−8x−3) − (4x+2)

To find:

The subtraction of polynomials

To find the subtraction of polynomials:

Given: 

⇒ [latex]\begin{aligned}
& \left(8 x^2-8 x-3\right)-(4 x+2) \\
& \left(8 x^2-8 x-3\right)-(4 x+2)=8 x^2-8 x-3-4 x-2 \\
& \left(8 x^2-8 x-3\right)-(4 x+2)=8 x^2-8 x-4 x-3-2 \\
& \left(8 x^2-8 x-3\right)-(4 x+2)=8 x^2-12 x-5
\end{aligned}\)

The subtraction of polynomials: (8x²−8x−3) − (4x+2) = 8x² − 12x − 5

Page 4 Exercise 10 Answer

Given:

(3x²+5x−1) − (4x²−2x+4)

To find:

The addition and subtraction of polynomials

To find the subtraction of polynomials:

Given:

\(\begin{aligned}
& \left(3 x^2+5 x-1\right)-\left(4 x^2-2 x+4\right) \\
& \left(3 x^2+5 x-1\right)-\left(4 x^2-2 x+4\right)=3 x^2+5 x-1-4 x^2+2 x-4 \\
& \left(3 x^2+5 x-1\right)-\left(4 x^2-2 x+4\right)=3 x^2-4 x^2+5 x+2 x-1-4 \\
& \left(3 x^2+5 x-1\right)-\left(4 x^2-2 x+4\right)=-x^2+7 x-5
\end{aligned}\)

The subtraction of polynomials: (3x²+5x−1) − (4x²−2x+4) = −x² + 7x − 5

Page 5 Exercise 3 Answer

Given:

(3x+5) + (2x−3) + (4x−6)

To find:

The addition and subtraction of polynomials

To find the addition of polynomials:

Given:

\(\begin{aligned}
& (3 x+5)+(2 x-3)+(4 x-6) \\
& (3 x+5)+(2 x-3)+(4 x-6)=3 x+5+2 x-3+4 x-6 \\
& (3 x+5)+(2 x-3)+(4 x-6)=3 x+2 x+4 x+5-3-6 \\
& (3 x+5)+(2 x-3)+(4 x-6)=9 x-4
\end{aligned}\)

The addition of polynomials: (3x+5) + (2x−3) + (4x−6) = 9x − 4

Page 5 Exercise 4 Answer

Given:

(a+b−c) + (a+b+2c) − (a+b+c)

To find:

The addition and subtraction of polynomials

Given:

(a+b-c)(a+b+2c)-(a+b+c)
(a+b-c) + (a+b+2c) – (a+b+c) = a + b-c+a+b+2c-a-b-c
(a+b-c)+(a+b+2c)-(a+b+c)=a+a-a+b+b-b-c+2c-c
(a+b-c)+(a+b+2c)-(a+b+c)=a+b

(a+b-c)+(a+b+2c)-(a+b+c)= a+b

Page 5 Exercise 6 Answer

Given:

(x−y−z) + (x−y−z) − (x−y−z) + (x+y+z)

To find:

The addition and subtraction of polynomials

Given:

(x-y-z)+(x-y-z)-(x-y-z)+(x+y+z)
(x-y-z+(x-y-z)-(x-y-z)+(x+y+z)=x-y-z-x+y+z+x +y+z
(x-y-z)+(x-y-z)-(x-y-z)+(x+y+z)=x+x-x-y-y+y-7-z+7+7
(x-y-z)+(x-y-z)-(x-y-z)+x+y+z)=2x

(x-y-z) + (x-y-z) – (x – y – z) + (x + y + z) = 2x

Page 5 Exercise 7 Answer

Given:

(3a²+2b+4) − (a²+b−1) − (a²+2b−1) − (a²+b−2)

To find:

The addition and subtraction of polynomials

Given:

(x-y-z)+(x-y-z)-(x-y-z)+(x+y+z)
(x-y-z)+(x-y-z)-(x-y-z)+(x+y+z)=x-y-z+x-y-z-x+y+z+x+y+z
(x-y-z)+(x-y-z)-(x-y-z)+(x+y+z)=x-x-x+x-y-y+y-z-z+z+z
(x-y-z)+(x-y-z)-(x-y-z)+(x+y+z)=2x

(3a²+2b+4) − (a²+b−1) − (a²+2b−1) − (a²+b−2) = -2b + 8

Page 5 Exercise 8 Answer

Given:

8x − (5x−4) = 25

To find:

Solution of the equation

To solve the equation:

Given:

\(\begin{aligned}
& 8 x-(5 x-4)=25 \\
& 8 x-(5 x-4)=8 x-5 x+4 \\
& 8 x-(5 x-4)=3 x+4
\end{aligned}\)

3x+4=25
3x=21
\(x=\frac{21}{3}\)
x=7

Solution: x = 7

Page 5 Exercise 9 Answer

Given:

6x − (4x−5) = 13

To find:

Solution of the equation

To solve the equation:

Given:

6x-(4x-5)=13
6x-(4x-5)=6x-4x+5
6x-(4x-5)=2x+5
⇒ 2x+5=13
⇒ 2x=13-5
⇒ 2x=8
⇒ \(x=\frac{8}{2}\)
⇒ x=4

Solution: x = 4

Page 5 Exercise 10 Answer

Given:

10x − (3x+6) = 8

To find:

Solution of the equation

To solve the equation:

Given

10x-(3x+6)=8
10x-(3x+6)=10x-3x -6
10x-(3x+6)=7x-6
⇒ 7x-6=8
⇒ 7x=8+6
⇒7x=14
⇒x=\(\frac{14}{7}\)
⇒ x=2

Solution: x = 2

Page 5 Exercise 11 Answer

Given:

(6x+9) − (2x−5) = 38

To find:

Solution of the equation

To solve the equation:

Given:

(6x+9)-(2x-5)=38
(6x+9)-(2x-5)=6x+9-2x+5?
(6x+9)-(2x-5)=4x+14
⇒ 4x+14=38
⇒4x=38-14
⇒4x=24
⇒x=\(\frac{24}{4}\)
⇒ x=6

Solution: x = 6

Page 5 Exercise 12 Answer

Given:

(9x+10) − (3x+2) = 74

To find:

Solution of the equation

To solve the equation:

Given:

(9x+10)-(3x+2)=74
(9x+10)-3x+2)=9x+10-3x-2
(9x+10)-(3x+2)=6x+8
⇒6x+8=74
⇒6x=74-8
⇒6x=66
⇒ \(x=\frac{66}{6}\)
⇒ x=11

Solution: x = 11

Page 5 Exercise 13 Answer

Given:

The sides: (3k+4),(2k−1),(3k+4),(2k−1)

To find:

The perimeter

To find the perimeter add the following polynomials:

Given:

The sides: (3k+4),(2k-1),(3k+4),(2k-1)

The perimeter

(3k+4)(2k-1)+(3k+4)+(2k-1)=3k+4+2k-1+3k+4+2k-1
(3k+4)+(2k-1)+(3k+4)+(2k-1)=3k+2k+3k+2k+4-1+4-1
(3k+4)(2k-1)+(3k+4)+(2k-1)=10k+6

The perimeter: 10k + 6

Page 6 Exercise 14 Answer

Given:

The sides: (4m+7),(2m),(5m+7),(2m+1)

To find:

The perimeter

To find the perimeter add the following polynomials:

Given:

The sides: (4m+7,(2m),(5m+7),(2m+1)

The perimeter

(4m+7)(2m)+(5m+7)+(2m+1)=4m+7+2m+5m+7+2m+1
(4m+7)+(2m)+(5m+7)+(2m+1)=4m+2m+5m+2m+7+7+1
(4m+7)+(2m)+(5m+7)+(2m+1)=13m+15

The perimeter: 13m + 15

Page 6 Exercise 15 Answer

Given:

The sides: (4x−3),(4x−3),(4x−3),(4x−3)

To find:

The perimeter

To find the perimeter add the following polynomials:

Given:

The sides: (4x-3),(4x-3),(4x-3),(4x-3)

The perimeter

(4x-3)+(4x-3)+(4x-3)+(4x-3)=4x-3+4x-3+4x-3+4x-3+4x-3
(4x-3)+(4x-3)+(4x-3)+(4x-3)=4x+4x+4x+4x-3-3-3-3
(4x-3)+(4x-3)+(4x-3)+(4x-3)=16x-12

The perimeter: 16x − 12

Page 6 Exercise 16 Answer

Given:

The sides: (2x+1),(2x+1),(2x+1),(2x+1),(2x+1),(2x+1)

To find: the perimeter of the given figure

To find the perimeter add the following polynomials:

Given:

The sides: (2x+1),(2x+1),(2x+1),(2x+1),(2x+1)
The perimeter

(2x+1)+(2x+1)+(2x+1)(2x+1)=2x+x+2x+12x+x+2x+1+2x+1
(2x+1+(2x+1)(2x+1)+(2x+1)=2x+2x+2x+2x+2x+1+1+1+1+1+1+
(2x+1)+(2x+1)+(2x+1)+2x+1)+(2x+1)=12x+6

The perimeter: 12x + 6