Verify whether the following are zeros of the polynomial, indicated against them. (iii)p( x) =x2 –1,x = 1, –1 (iv)p( x) = ( x + 1) ( x –2),x =–1, 2 Using Factor theorem, show that (x + 2) is a factor of––12. Factorize the following: (i) 6–18 xy (ii) + 7–x –7 (iii) 16–81(iv) + 5 x –24 (v) 9–22 x + 8 Using Remainder Theorem, find the remainder when : (i) 4–7+ 3 x –2 is divided byx –1 (ii) –7+ 6 x + 4 is divided byx –3 (iii) + 2–x + 3 is divided byx + 3 (iv) 4–4+x –2 is divided by 2 x + 1 (v) –a+ 5 x + a is divided byx –a (vi) + a–6 x + 2a is divided byx + a 9. If 35 is the remainder when 2+ ax + 7 is divided byx –4, find the value ofa. 10. Without actual division, prove that 2+ 13+x –70 is exactly divisible byx –2. Without actual division, prove that 2 + 13+x –70 is exactly divisible byx –2. 11. Show that x –1 is a factor of–2–5 x + 6. 12. Find the value ofp for which the polynomialx4 –2+p+ 2 x + 8 is exactly divisible byx + 2. The polynomials a+ 4–3 and 4+ 4 x –a when divided byx –3, leaves the remainderR1 andR2 respectively. Find the value of a ifR1 = 3 R2. 16. Find the integral zeros of–3–x + 3.
