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= Noe. a ee | O20}, Si Bs {fi Ai " s Werk shoot HF REMAINDER & FACTOR THEOREM (9709/3) 1 7 @) The polynomial x + ax? — x? + bx +2, where @ and b are constants. is denoted by p(x). It is given that (x— 1) and (x + 2) are factors of p(x). Find the values of a and b. . (5) (ii) When a and b have these values, find the quotient when p(x) is divided by +x-2. GB) -* 2 Ams: (1) @= 3, b=-S cy M421 erooraseonuiti X2_ The polynomial p (2) is defined by oe . - p(z) = 23 + mz? 4+ 242 + 32, here 1 is a constant, It is given that (z + 2) is a factor of p(z). i (i) Find the value of m. . i (21 1 (Gi) Hence, showing all your working, find (a) the three roots of the equation p(z) =0,-- -, < ‘ GI (b)_ the six roots of the equation’p(z?} = 0. wee {6} . we [2s me Aus tylypNWeC =-2! Zach 1. s7OsRBOMNIOrO wy Uy %=783 UWzeday 5 ¥0eP cag, 3 The polynomial x3 + 4x2 + ax +2, where a is a constant, is denoted by p(x). It is given that the remainder when p(x) is divided by (x+ 1) is equal to the remainder when p(x) is divided by (x- 2). * (i) Find the value of a. . G) (ii) When a has this value, show that (x — 1) is a factor of p(x) and find the quotient when p(x) is divided by (x — 1). (31 2 AWS. Qe cll, CHOKD- srarsowrn 4 The polynomial 233 + ac + bx —4, where a and b are constants, is denoted by p(x). The result of Be differentiating p(x) with respect to x is denoted by p'(x). It is given that (x +2) is a factor of p(x) and of p(x). (i) Find the values ofaandb. = @ =F» b=Y {s] (ii) When a and b have these values, factorise p(x) completely. B) 9709/320INOSIS LADKADO-V 5 The polynomial 4x2 — 4? + 3x +a, where’a is a constant, is denoted by p(x). It is given that p(x) is Bd divisible by 2x? - 3x +3." (i) Find the value ofa. (3] bg (Go) When ahas this value, solve the inequality p(x) < 0, justifying your answer. B] _ oy bp L_ 3A 43 2 stossonvees Q=3 , LK -L thet abet LA oe ee XR | Hew Wane cae FELL. FR 6 The polynomial x4 + 3x? +a, where a is a constant, is denoted by p(x). It is'given thatx” +x+2isa factor of p(x). Find the value of a and the other quadratic factor of p(x). [4} fo MG frctee f STOS03I0INIO7/2 Ae | , Py 2 xt x42 —_—_ Scanned with CamScanner S re EY 
