Question

4.2 practice with calcchat™ and calcview™
in exercises 1–6, find the sum. (see example 1.)

1. $(3x^2 + 4x - 1) + (-2x^3 - 3x + 2)$
2. $(-5x^2 + 4x - 2) + (-8x^2 + 2x + 1)$
3. $(12x^5 - 3x^4 + 2x - 5) + (8x^4 - 3x^3 + 4x + 1)$
4. $left(8x^4 - \frac{1}{3}x^2 - 1\

ight) + \left(3x^3 + \frac{1}{3}x^2 + 7x + 1\
ight)$

1. $(2x^5 + 7x^6 - 3x^2 + 9x) + (5x^5 + 8x^3 - 6x^2 + 2x - 5)$
2. $left(9x^4 - 3x^3 + 4x^2 + \frac{7}{6}x + 7\

ight) + \left(11x^4 - 9 - 4x^2 - \frac{5}{6}x\
ight)$

in exercises 7–12, find the difference. (see example 2.)

1. $(3x^3 - 2x^2 + 4x - 8) - (5x^3 + 12x^2 - 3x - 4)$
2. $(7x^4 - 9x^3 - 4x^2 + 5x + 6) - (2x^4 + 3x^3 - x^2 + x - 4)$
3. $(5x^6 - 2x^4 + 9x^3 + 2x - 4) - (7x^5 - 8x^4 + 2x - 11)$
4. $(4x^5 - 7x^3 - 9x^2 + 18) - (14x^5 - 8x^4 + 11x^2 + x)$
5. $(8x^5 + 1.6x^3 - 2x^2 + 10x) - (4 + 9x^5 - x^3 - 13x^2)$
6. $(3.2x - 9x^2 + 11x^4 - 8.5) - (2.4x^4 + 6x^3 + 2x - 9)$

in exercises 13–20, find the product. (see example 3.)

1. $7x^3(5x^2 + 3x + 1)$
2. $-4x^5(11x^3 + 2x^2 + 9x + 1)$
3. $(5x^2 - 4x + 6)(-2x + 3.5)$
4. $\left(-x - \frac{1}{2}\

ight)(2x^2 + 5x + 8)$

1. $(x^2 - 2x - 4)(x^2 - 3x - 5)$
2. $(3x^2 + x - 2)(-4x^2 - 2x - 1)$
3. $(3x^3 - 9x + 7)(x^2 - 2x + 1)$
4. $(4x^2 - 8x - 2)(x^4 + 3x^2 + 4x)$

Explanation:

Step1: Identify the operation (sum)

We need to add the two polynomials: \((12x^{5}-3x^{4}+2x - 5)+(8x^{4}-3x^{3}+4x + 1)\)

Step2: Combine like terms

• For \(x^{5}\) term: \(12x^{5}\) (only one term)
• For \(x^{4}\) term: \(-3x^{4}+8x^{4}=5x^{4}\)
• For \(x^{3}\) term: \(-3x^{3}\) (only one term)
• For \(x\) term: \(2x + 4x=6x\)
• For constant term: \(-5 + 1=-4\)

Step3: Write the result

Combine all the terms: \(12x^{5}+5x^{4}-3x^{3}+6x - 4\)

Answer:

\(12x^{5}+5x^{4}-3x^{3}+6x - 4\)