Answer:
Let's go through the questions:
1. **Classify the following as linear, quadratic, and cubic polynomials:**
- (i) \(4x+5\) → Linear
- (ii) \(5x^3+6x^2\) → Cubic
- (iii) \(u^2-\frac{5}{2}u\) → Quadratic
- (iv) \(t+\sqrt{3}\) → Not a polynomial
- (v) \(5-y^2+y^3\) → Cubic
- (vi) \(2r^3+4r^2+5t+7\) → Not a polynomial
- (vii) \(5y^2+3y+\pi\) → Quadratic
- (viii) \(4x^3 (x) 4\) → Not a polynomial
Four examples of a linear polynomial: \(2x+3\), \(4y-7\), \(9z+1\), \(6t-2\).
2. **Give four examples of a binomial of degree 15:**
- \(3x^{15} - 5y^{15}\)
- \(2a^{15} - 7b^{15}\)
- \(x^{15} + y^{15}\)
- \(4m^{15} - 6n^{15}\)
3. **Write monomials of degree 150:**
- \(5x^{150}\)
- \(2y^{150}\)
- \(9z^{150}\)
- \(3t^{150}\)
4. **Which expressions are polynomials in one variable:**
- (i) \(x^{15}+x^{10}+y^{2}\) → Not a polynomial (contains \(y\))
- (ii) \(4-x^{2}+5y^{3}\) → Not a polynomial (contains \(y\))
- (iii) \(2x^{5}+3y^{6}+7t^{10}\) → Not a polynomial (contains \(y\) and \(t\))
- (iv) \(\sqrt{3}y^{10}+5x^{11}-z^{16}\) → Not a polynomial (contains \(\sqrt{3}\), \(y\), and \(z\))
5. **Write the coefficients of \(x^2\) in each of the following:**
- (i) \(\frac{\pi}{4}x^2+5x^0\) → Coefficient of \(x^2\): \(\frac{\pi}{4}\)
- (ii) \(9x^3-5x^2+4x-6\) → Coefficient of \(x^2\): \(-5\)
- (iii) \(-x^3+6x^2-5x+3\) → Coefficient of \(x^2\): \(6\)
- (iv) \(4\sqrt{2}x^2+5\) → Coefficient of \(x^2\): \(4\sqrt{2}\)
- (v) \(3-v3x+4\) → Coefficient of \(x^2\): \(0\)
- (vi) \(3+7x^2-x\) → Coefficient of \(x^2\): \(7\)
6. **Write the degree of each of the following polynomials:**
- (i) \(u+\sqrt{2}\) → Degree: \(1\)
- (ii) \(x^{10}+x^{15}+4\) → Degree: \(15\)
- (iii) \(2-u-u^{3}+5u^{10}\) → Degree: \(10\)
- (iv) \(5x^{2}-6x^{2}\) → Degree: \(2\) (It's a constant term, so degree is \(0\))
- (v) \(x^{150}\) → Degree: \(150\)
7. **\(2\) is a polynomial of degree:**
- (b) \(0\)
8. **Degree of a cubic polynomial is:**
- (a) \(3\)
9. **A trinomial can have at most three terms:**
- (a) True
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Answers & Comments
Answer:
Let's go through the questions:
1. **Classify the following as linear, quadratic, and cubic polynomials:**
- (i) \(4x+5\) → Linear
- (ii) \(5x^3+6x^2\) → Cubic
- (iii) \(u^2-\frac{5}{2}u\) → Quadratic
- (iv) \(t+\sqrt{3}\) → Not a polynomial
- (v) \(5-y^2+y^3\) → Cubic
- (vi) \(2r^3+4r^2+5t+7\) → Not a polynomial
- (vii) \(5y^2+3y+\pi\) → Quadratic
- (viii) \(4x^3 (x) 4\) → Not a polynomial
Four examples of a linear polynomial: \(2x+3\), \(4y-7\), \(9z+1\), \(6t-2\).
2. **Give four examples of a binomial of degree 15:**
- \(3x^{15} - 5y^{15}\)
- \(2a^{15} - 7b^{15}\)
- \(x^{15} + y^{15}\)
- \(4m^{15} - 6n^{15}\)
3. **Write monomials of degree 150:**
- \(5x^{150}\)
- \(2y^{150}\)
- \(9z^{150}\)
- \(3t^{150}\)
4. **Which expressions are polynomials in one variable:**
- (i) \(x^{15}+x^{10}+y^{2}\) → Not a polynomial (contains \(y\))
- (ii) \(4-x^{2}+5y^{3}\) → Not a polynomial (contains \(y\))
- (iii) \(2x^{5}+3y^{6}+7t^{10}\) → Not a polynomial (contains \(y\) and \(t\))
- (iv) \(\sqrt{3}y^{10}+5x^{11}-z^{16}\) → Not a polynomial (contains \(\sqrt{3}\), \(y\), and \(z\))
5. **Write the coefficients of \(x^2\) in each of the following:**
- (i) \(\frac{\pi}{4}x^2+5x^0\) → Coefficient of \(x^2\): \(\frac{\pi}{4}\)
- (ii) \(9x^3-5x^2+4x-6\) → Coefficient of \(x^2\): \(-5\)
- (iii) \(-x^3+6x^2-5x+3\) → Coefficient of \(x^2\): \(6\)
- (iv) \(4\sqrt{2}x^2+5\) → Coefficient of \(x^2\): \(4\sqrt{2}\)
- (v) \(3-v3x+4\) → Coefficient of \(x^2\): \(0\)
- (vi) \(3+7x^2-x\) → Coefficient of \(x^2\): \(7\)
6. **Write the degree of each of the following polynomials:**
- (i) \(u+\sqrt{2}\) → Degree: \(1\)
- (ii) \(x^{10}+x^{15}+4\) → Degree: \(15\)
- (iii) \(2-u-u^{3}+5u^{10}\) → Degree: \(10\)
- (iv) \(5x^{2}-6x^{2}\) → Degree: \(2\) (It's a constant term, so degree is \(0\))
- (v) \(x^{150}\) → Degree: \(150\)
7. **\(2\) is a polynomial of degree:**
- (b) \(0\)
8. **Degree of a cubic polynomial is:**
- (a) \(3\)
9. **A trinomial can have at most three terms:**
- (a) True