Mc Graw Hill Key To Algebra Book 4 Polynomials 1st Edition Chapter 2 Adding Polynomials

Mc Graw Hill Key To Algebra Book 4 Polynomials 1st Edition Chapter 2 Adding Polynomials

Page 2 Exercise 1 Answer

Given: (3x+5)+(4x+1)

Find: We have to find the addition of the given expression.

Given that,

(3x+5)+(4x+1)

=(3x+4x)(5x+1) [taking same power terms]

=7x+6

Hence, The answer is (3x+5)+(4x+1) = 7x + 6

Page 2 Exercise 2 Answer

Given: (2x²+3x+7) + (8x²+3x−4)

Find: We have to find the addition of the given expression.

Given that,

\(\begin{aligned}
& \left(2 x^2+3 x+7\right)+\left(8 x^2+3 x-4\right) \\
& =\left(2 x^2+8 x^2\right)+(3 x+3 x)+(7-4)
\end{aligned}\)

[taking same power terms]

= 10x²+6x+3

Hence, the answer is (2x²+3x+7) + (8x²+3x−4) = 10x² + 6x + 3.

Page 2 Exercise 3 Answer

Given: (x²+5) + (x²+4)

Find: We have to find the addition of the given expression.

Given that

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

[taking same power terms]

=2x²+9

Hence, the answer is (x²+5) + (x²+4) = 2x² + 9

Page 2 Exercise 4 Answer

Given: (5x−3) + (4x+7) + (2x−6)

Find: We have to find the addition of the given expression.

Given that,

(5x-3)+(4x+7)+(2x-6)

Hence, the answer is (5x−3) + (4x+7) + (2x−6) = 11x − 2

=(5x+4x+2x)+(-3+7-6)

[taking same power terms]

=11x+(7-9)
=11x-2

Page 2 Exercise 5 Answer

Given: (x²+6x−5) + (x²−8x−4)

Find: We have to find the addition of the given expression.

Given that,

Hence the answer is (x²+6x−5) + (x²−8x−4) = 2x² − 2x − 9

\(\begin{aligned}
& \left(x^2+6 x-5\right)+\left(x^2-8 x-4\right) \\
& =\left(x^2+x^2\right)+(6 x-8 x)+(-5-4)
\end{aligned}\)

[taking same power terms]

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

Page 2 Exercise 6 Answer

Given: (3a+4b+c) + (5a−4b+2c)

Find: We have to find the addition of the given expression.

Given that

(3a+4b+c)+(5a-4b+2c)
=(3a+5a)+4b-4b)+(c+2c)

[taking same power terms]

=(8a)+(0)+(3c)
=8a+3c

Hence, the answer is (3a+4b+c) + (5a−4b+2c) = 8a + 3c.

Page 2 Exercise 7 Answer

Given the polynomial

(3x+4) + (5x+2) + 2x

Here it is asked to add the given polynomial.

Given the polynomial

(3x+4)+(5x+2)+2x

we can add the polynomial as shown below,

⇒ \(\begin{aligned}
& (3 x+4)+(5 x+2)+2 x \\
& =3 x+4+5 x+2+2 x \\
& =3 x+5 x+2 x+4+2 \\
& =8 x+2 x+6 \\
& =10 x+6
\end{aligned}\)

Therefore, the value of (3x+4) + (5x+2) + 2x is 10x + 6.

Page 2 Exercise 8 Answer

Given the polynomial

(5x²+4x−7) + (−5x²−4x+7)

Here it is asked to add the given polynomial.

Given the polynomial

⇒ \(\left(5 x^2+4 x-7\right)+\left(-5 x^2-4 x+7\right)\)

We can add the polynomial as shown below,

⇒ \(\begin{aligned}
& \left(5 x^2+4 x-7\right)+\left(-5 x^2-4 x+7\right) \\
& =5 x^2+4 x-7-5 x^2-4 x+7 \\
& =5 x^2-5 x^2+4 x-4 x+7-7 \\
& =0+0+0 \\
& =0
\end{aligned}\)

Therefore, the value of (5x²+4x−7) + (−5x²−4x+7) is 0.

Page 2 Exercise 9 Answer

Given the polynomial

(3x²+5x+2) + (4x²+3x+2)

Here it is asked to add the given polynomial.

Given the polynomial

(3×2+5x+2)+(4×2+3x+2)

we can add the polynomials as shown below,

⇒ \(\begin{aligned}
& \left(3 x^2+5 x+2\right)+\left(4 x^2+3 x+2\right) \\
& =3 x^2+5 x+2+4 x^2+3 x+2 \\
& =3 x^2+4 x^2+5 x+3 x+2+2 \\
& =7 x^2+8 x+4
\end{aligned}\)

Therefore, the value of (3x²+5x+2) + (4x²+3x+2) is 7x² + 8x + 4.

Page 2 Exercise 10 Answer

Given the polynomial

(x²+6x+9) + (x²+4x+4)

Here it is asked to add the given polynomial.

Given polynomial

(x2+6x+9)(x2+4x+4)

we can add the polynomials as shown below,

\(\begin{aligned}
& \left(x^2+6 x+9\right)+\left(x^2+4 x+4\right) \\
& =x^2+6 x+9+x^2+4 x+4 \\
& =x^2+x^2+6 x+4 x+9+4 \\
& =2 x^2+10 x+13
\end{aligned}\)

Therefore, the value of (x²+6x+9) + (x²+4x+4) is 2x² + 10x + 13.

Page 2 Exercise 11 Answer

Given the polynomial

(5x²−4x−8) + (6x²−9x+7)

Here it is asked to add the given polynomial.

Given the polynomial,

(5x²−4x−8) + (6x²−9x+7)

we can add the polynomial as shown below

⇒ \(\begin{aligned}
& \left(5 x^2-4 x-8\right)+\left(6 x^2-9 x+7\right) \\
= & 5 x^2-4 x-8+6 x^2-9 x+7 \\
= & 11 x^2-13 x-1
\end{aligned}\)

Therefore, the value of (5x²−4x−8) + (6x²−9x+7) is 11x² − 13x − 1.

Page 2 Exercise 12 Answer

Given the polynomial

(3x−9) + (2x²+2x+2)

Here it is asked to add the given polynomial.

Given the polynomial

(3x-9)+(2x²+2x+2)
=2x²+(3x+2x)+(-9+2)
=2x²+5x-7

Therefore, the value of (3x−9) + (2x²+2x+2) is 2x² + 5x − 7.