CBSE Class 9 Mathematics Polynomials Worksheet Set D

Very Short Answer Type Questions

Question. How many terms are there in the polynomial 5 – 3t + 2t⁶ ?
Answer : Number of terms = 3

Question. If, p (− 1/4) = 0, where p(x) = 8x³ – ax² – x + 2, then find the value of a.
Answer : ∵ p(−1/4) = 0 
⇒ 8(-1/4)³ - a (- 1/4)² - (- 1/4) + 2 = 0 
⇒ -8/64 - a/16 + 1/4 + 2 = 0
⇒ -1/8 + 1/4 + 2 = a/16 ⇒ -1+2+16/8 = a/16
⇒ a = 17 × 2
∴ a = 34

Question. Find the product of (lx +my) and (lx – my).
Answer : Product of (lx + my) and (lx – my) = (lx + my) (lx – my)
= (lx)² – (my)² = l²x² – m²y²

Question. Find the value of p(x) = √2x² + √2x + 6 at x = √2
Answer : p (√2) = √2(√2)² + √2 (√2) + 6
=2√2 + 2 + 6
=2√2 + 8

Question. Find the factors of x² + 2x – 15.
Answer : We have, x² + 2x – 15 = x² + 5x – 3x – 15
= x(x + 5) – 3(x + 5) = (x + 5) (x – 3)
∴ Factors of x² + 2x – 15 are (x + 5) and (x – 3).

Question. Find the zeroes of the polynomial 3x + p.
Answer : 3x + π = 0 ⇒ 3x = – π ⇒ x = − π/3
∴ x = − π/3 is the zero of the polynomial 3x + p.

Question. Factorise : a3 – b3 + 3ba² – 3ab²
Answer : We have, a³ – b3 + 3a²b – 3ab²
= (a – b) (a² + b² + ab) + 3ab (a – b)
= (a – b) [a² + b² + 4ab]

Question. Factorise : 14a2b – 7ab²
Answer : We have, 14a²b – 7ab² = 7ab(2a – b)

Question. Find the zero of the polynomial q(x) = 3x + 2.
Answer : We have, q(x) = 3x + 2
Put q(x) = 0 ⇒ 3x + 2 = 0 ⇒ x = −2/3
∴ −2/3 is the zero of the polynomial q(x) = 3x + 2.

Question. Is x + 2 a zero of p(x) = 2x³ – x² + 3?
Answer : (x + 2) will be a zero of p(x), if p (–2) = 0
∴ p(–2) = 2(–2)³ – (–2)² + 3 = –16 – 4 + 3 = –17 ≠ 0
∴ x + 2 is not a zero of p(x).

Please click the below link to access CBSE Class 9 Mathematics Worksheet - Polynomials (3)