# DAV Class 8 Maths Chapter 8 Worksheet 1 Solutions

The DAV Class 8 Maths Solutions and DAV Class 8 Maths Chapter 8 Worksheet 1 Solutions of Polynomials offer comprehensive answers to textbook questions.

## DAV Class 8 Maths Ch 8 WS 1 Solutions

Question 1.
Find out whether the given expression is a polynomial or not. If not, give reasons.

(i) 5x3 – 4x2 + $$\frac{1}{2}$$
Solution:
Yes, it is polynomial of degree 3.

(ii) √3z2 – 5√z + 6
Solution:
Not, it is not a polynomial as the power of z is $$\frac{1}{2}$$.

(iii) 6x4 + $$\frac{2}{3}$$ x3 – $$\frac{3}{4}$$ x2 – 1
Solution:
Yes, it is a polynomial of degree 4.

(iv) 7x$$\frac{2}{3}$$ – 8x$$\frac{3}{2}$$ + x2
Solution:
Not, it is not a polynomial as it contains variables with rational powers.

(v) 5x – $$\frac{1}{x}+\frac{1}{x^2}$$ – 2
Solution:
Not, it is not a polynomial as power of x is an negative integer.

(vi) p4 – 3p3 – p + 1
Solution:
Yes, it is a polynomial of degree 4. Question 2.
Write each of the following polynomials in standard form and also write down their degree:

(i) p6 – 8p9 + p7 + 5
Solution:
Standard form of the given polynomial is – 8p9 + p7 + p6 + 5
degree = 9

(ii) 4z3 – 3z5 + 2z4 + z + 1
Solution:
The standard form of the given polynomial is – 3z5 + 2z4 + 4z3 + z + 1
degree = 5

(iii) (x + $$\frac{2}{3}$$) (x + $$\frac{3}{4}$$)
Solution:
(x + $$\frac{2}{3}$$) (x + $$\frac{3}{4}$$) = (x2)2 + $$\left(\frac{2}{3}+\frac{3}{4}\right)$$ x + $$\frac{2}{3} \times \frac{3}{4}$$
= x2 + $$\frac{17}{12}$$ x + $$\frac{1}{2}$$, which is in standard form
degree = 2 (iv) (x2 – $$\frac{2}{3}$$) (x2 + $$\frac{4}{3}$$)
Solution:
(x2 – $$\frac{2}{3}$$) (x2 + $$\frac{4}{3}$$) = (x2)2 + $$\left(-\frac{2}{3}+\frac{4}{3}\right)$$ x2 + $$\left(-\frac{2}{3}\right)\left(\frac{4}{3}\right)$$
= x4 + $$\frac{2}{3}$$ x2 – $$\frac{8}{9}$$ which is in standard form.
degree = 4

(v) (z2 + 5) (z2 – 6)
Solution:
(z2 + 5) (z2 – 6) = (z2)2 + (5 – 6) z2 + 5 (- 6)
= z4 – z2 – 30 which is in standard form.
degree = 4

(vi) (y3 – 4) (y3 – 5)
Solution:
(y3 – 4) (y3 – 5) = (y3)2 + (- 4 – 5) y3 + (- 4) (- 5)
= y6 – 9y3 + 20, which is in standard form
degree = 6

(vii) (p2 + 2) (p2 + 7)
Solution:
(p2 + 2) (p2 + 7) = (p2)2 + (2 + 7) p2 + 2 × 7
= p4 + 9p2 + 14, which is in standard form
degree = 4

(viii) ($$\frac{5}{6}$$z – $$\frac{3}{4}$$z2 – $$\frac{2}{3}$$z3 + 1)
Solution:
Standard form of ($$\frac{5}{6}$$z – $$\frac{3}{4}$$z2 – $$\frac{2}{3}$$ z3 + 1) is – $$\frac{2}{3}$$ z3 – $$\frac{3}{4}$$ z2 + $$\frac{5}{6}$$ z + 1
degree = 3

(ix) 4p + 15p6 – p5 + 4p2 + 3
Solution:
Standard form of 4p + 15p6 – p5 + 4p2 + 3 is 15p6 – p5 + 4p2 + 4p + 3
degree = 6.

(x) q10 + q6 – q4 + q8
Solution:
Standard form of q10 + q6 – q4 + q8 is q10 + q8 + q6 – q4
degree = 10. ### DAV Class 8 Maths Chapter 8 Worksheet 1 Notes

1. Monomials: The expression that contains only one term is called a monomial.
e.g. 4x2, – 9, 32mp, etc.

2. Binomials: The expression that contains two terms is called a binomial.
e.g. a + b, a + 4, lm + ms, 5 – 2xy, z2 – x2, etc.

3. Trinomial: The expression that contains three terms is called a trinomial.
e.g. a + b + c, 2mn + 5m + n, 2a + 3x + 5z, etc.

4. Polynomial: The expression that contains many number of terms is called a polynomial.
e.g. 3x + y + 4z + 3t – 5w, 2n + 5y – 3, 4a – 5b – c – d, etc.

Example of polynomial in one variable:
P(x) = a0 + a1x + a2x2 + a3x3 + a4x4 + ……………….. + anxn
where x is a variable and a0, a1, a2, a3, a4, …………., an are the coefficients.

Degree of a polynomial:

The highest power of the variable in a polynomial of one variable is called its degree.

• If degree is 1, then it is called as linear polynomial.
e.g. P(x) = ax + b
• If degree is 2, then it is called as quadratic polynomial.
e.g. P(x) = ax2 + bx + e
• If degree is 3, then it is called as cubic polynomial.
e.g. P(x) = ax3 + bx2 + cx + d.
• If degree is 4, then it is called as biquadratic polynomial.
e.g. P(x) = ax4 + bx3 + cx2 + dx + e Example 1.
Classify the following polynomials as monomials, binomials and trinomials:
(i) x + y
(ii) 100
(iii) x2 + x3 + 1
(iv) 2y – 3y2 + 4y3
(v) ab + bc + cd
(vi) 3x
Solution:
(i) binomial
(ii) monomial
(iii) trinomial
(iv) trinomial
(v) trinomial
(vi) monomial

Example 2.
Write the following polynomials in standard form:
(i) – √3x + 5 – 2√2x3 + 5x2 – x4
(ii) 5 + 3x – 4x2 + 7x3 + x6
(iii) – 6 + x9 – 3x8 – 2x3
(iv) 3x – 5x2 + 7x3 + 8x5.
(v) x5 – x4 + 3x3 + x + 2.
Solution:
(i) – √3x + 5 – 2√2x3 + 5x2 – x4
Standard form is: – x4 – 2√2x3 + 5x2 – √3x + 5

(ii) 5 + 3x – 4x2 + 7x3 + x6
Standard form is: x6 + 7x3 – 4x2 + 3x + 5

(iii) – 6 + x9 – 3x8 – 2x3
Standard form is: x9 – 3x8 – 2x3 – 6

(iv) 3x – 5x2 + 7x3 + 8x5
Standard form is: 8x5 + 7x3 – 5x2 + 3x

(v) x5 – x4 + 3x3 + x + 2
Standard form is: x5 – x4 + 3x3 + x + 2 Example 3:
Divide 8x3 – 4x2 – 2x by 4x.
Solution:
8x3 – 4x2 – 2x ÷ 4x
= $$\frac{8 x^3-4 x^2-2 x}{4 x}$$
= $$\frac{8 x^3}{4 x}-\frac{4 x^2}{4 x}-\frac{2 x}{4 x}$$
= 2x2 – x – $$\frac{1}{2}$$

Example 4.
Divide 8y3 + 10y – 6y2 + 3 by 1 + 4y by long division method and verify the 