**3 - 30*x**2 - 116*x - 91. Let n(k) = -7*k**4 + k**3 + 28*k**2 + 116*k + 90. Let i(p) = -5*n(p) - 6*v(p). Factor i(t).
-(t - 8)*(t + 2)**2*(t + 3)
Let h(m) = -2*m + 217. Let v be h(21). Let i be ((-225)/v)/((-15)/14). Factor 3/5*z**4 + i*z - 9/5*z**2 + 0*z**3 + 0.
3*z*(z - 1)**2*(z + 2)/5
Let j = 0 - -2. Let -80*w + 0*w**2 - 4*w**j + 144*w - 112 = 0. Calculate w.
2, 14
Let q(n) = 2*n**2 - n + 1. Let v be q(1). Let u = -69/20980 + 42719/230780. Factor -u*h**v + 18/11*h + 20/11.
-2*(h - 10)*(h + 1)/11
Let p(w) be the second derivative of 20*w + 46*w**2 - 5/6*w**4 + 113/3*w**3 + 1. Factor p(d).
-2*(d - 23)*(5*d + 2)
Let m(j) = -14*j**3 + 485*j**2 - 11715*j + 4611. Let v(s) = 59*s**3 - 1941*s**2 + 46861*s - 18445. Let l(q) = 26*m(q) + 6*v(q). Factor l(b).
-2*(b - 48)**2*(5*b - 2)
Let a(i) be the second derivative of 3*i**5/20 - 1303*i**4/4 + 425103*i**3/2 - 1271403*i**2/2 + 12211*i. Suppose a(p) = 0. Calculate p.
1, 651
Let w(l) = -l**3 - 9*l**2 + l + 14. Let h be w(-9). Suppose h*m = 106 + 44. Factor 2*z - 20*z**4 + 7*z**2 + 19*z**5 - 14*z**5 + 3*z + m*z**3 - 27*z**2.
5*z*(z - 1)**4
Let p(i) be the second derivative of -17*i**7/252 - 37*i**6/12 - 461*i**5/40 - 989*i**4/72 + i**3 + 15*i**2 + 3*i + 1131. Solve p(h) = 0 for h.
-30, -1, 6/17
Suppose 295*o**2 + 2*o**4 + 270*o - 430*o**2 + 266*o**3 - 482*o**2 + 79*o**2 = 0. What is o?
-135, 0, 1
Let l(d) be the third derivative of d**5/300 + 71*d**4/40 - 107*d**3/15 - 56*d**2 - 6. Suppose l(o) = 0. Calculate o.
-214, 1
Let c be 2085/54*5/(-100)*3. Let v = c - -57/8. Let -v - 4/3*x - 1/3*x**2 = 0. Calculate x.
-2
Let t be (-2 - -1)/(6/(-18)). What is f in 34*f + 4*f**2 + 7*f - 4*f**t + 7*f = 0?
-3, 0, 4
Let q(p) be the second derivative of 99*p + 0 + 2*p**2 - p**4 - 4/3*p**3. Factor q(k).
-4*(k + 1)*(3*k - 1)
Let t(c) = c**3 - 66*c**2 - 188*c + 8110. Let f be t(67). Determine d, given that -4/7*d + 2/7*d**f - 6/7*d**4 + 6/7*d**2 + 2/7*d**5 + 0 = 0.
-1, 0, 1, 2
Let c(n) = -3*n + 30. Let i be c(9). Let t(b) = -b**2 - 36*b - 324. Let h be t(-18). Factor 8/7*u**i - 5/7*u**4 + 6/7*u + 19/7*u**2 + h.
-u*(u - 3)*(u + 1)*(5*u + 2)/7
Let i(l) = -l**2 + 3*l - 1. Let d(h) = -2*h**3 - 340*h**2 - 13758*h + 14106. Let v(f) = d(f) - 6*i(f). Factor v(k).
-2*(k - 1)*(k + 84)**2
Let b(t) = -162*t + 147. Let k(n) = -270*n + 246. Let d(m) = -13*b(m) + 8*k(m). Let a be d(1). Factor 12/5*h**a + 0*h - 6/5*h**4 + 0 - 8/5*h**2 + 1/5*h**5.
h**2*(h - 2)**3/5
Let d(g) = -4*g**2 + 7*g - 1. Let s be d(1). Factor 25*u**s - 5*u - 30 + 17*u**3 + 5 - 12*u**3.
5*(u - 1)*(u + 1)*(u + 5)
Let n = 142/239 - 45/478. Factor n*b**2 + 3/2 + 2*b.
(b + 1)*(b + 3)/2
Let r(w) = 23*w**4 + 333*w**3 - 53*w**2 - 306*w - 24. Let d(f) = f**4 + f**3 + f**2 - 2*f + 8. Let j(y) = 3*d(y) + r(y). Find i, given that j(i) = 0.
-13, -12/13, 0, 1
Let c(t) be the second derivative of 7*t**6/6 - 2479*t**5/2 + 487930*t**4 - 230859920*t**3/3 + 65721280*t**2 - 858*t. Let c(z) = 0. Calculate z.
2/7, 236
Let l(t) be the first derivative of -2/3*t**3 - 16 - 1/12*t**4 + 0*t + 1/30*t**5 - t**2. Let k(x) be the second derivative of l(x). Factor k(c).
2*(c - 2)*(c + 1)
Suppose -32292 = 60*k - 8*k. Let i be (14 - (-8502)/k) + (-4)/46. Factor 2/9*v + 4/9 - i*v**2.
-2*(v - 2)*(v + 1)/9
Let r be 0 - (-3 + 4 + -4). Suppose r*d + 2*a = -2*a + 46, a = 1. Find s such that 147*s**2 + 13 - 126*s + 6 - 6 + d = 0.
3/7
Let w(r) = -2*r**3 - 694*r**2 + 3. Let v be w(-347). Let -3*g**2 + 64/5 + 48/5*g + 1/5*g**v = 0. What is g?
-1, 8
Suppose -4*p + 3*r + 13 = -1, 14 = 2*p - 5*r. Suppose -z + 1 = -k, 0 = p*k - 4*k - 2*z + 2. Find f such that k + 3/7*f + 3/7*f**2 = 0.
-1, 0
What is z in -15*z + 284/5 + 1/5*z**2 = 0?
4, 71
Let d = -45209/39 + 3515/3. Let k = 143 - 141. Find s such that -d - 2/13*s**k - 36/13*s = 0.
-9
Let r(t) be the second derivative of -t**5/4 - 95*t**4/12 - 175*t**3/6 - 85*t**2/2 - 75*t + 6. Factor r(k).
-5*(k + 1)**2*(k + 17)
Factor -1215*b - 20780*b**2 + 10393*b**2 + 10392*b**2 - 1330 - 1120.
5*(b - 245)*(b + 2)
Let d(t) = t**2 - 3*t + 1. Let f(c) = 3*c**2 - 4343*c + 4335. Let p(u) = -5*d(u) + f(u). Factor p(a).
-2*(a - 1)*(a + 2165)
Let s(h) be the third derivative of 135/2*h**3 - 2 + 0*h + 3/4*h**4 + 20*h**2 + 1/300*h**5. Factor s(q).
(q + 45)**2/5
Suppose -p = 2*r - 97, 5*p - 52*r - 445 = -54*r. Let n be (p/174)/((-1)/(-4)). Find u such that 38/3*u + 40/3*u**n - 25/6*u**3 + 8/3 = 0.
-2/5, 4
Let r(o) be the first derivative of 3*o**5/80 - 7*o**4/16 + 15*o**3/8 - 27*o**2/8 - 76*o - 31. Let a(t) be the first derivative of r(t). Factor a(f).
3*(f - 3)**2*(f - 1)/4
Let 2*o**5 + 7*o**4 - 63*o**3 - 42*o**4 + 111*o**3 + 576*o**2 + 136*o**3 - 13*o**4 = 0. What is o?
-2, 0, 8, 18
Suppose 4*b - 3*p + 13 = 2*p, 3*p = -4*b + 27. Suppose 4*i = -2*c - 2, 6*i + b*c + 3 = i. Factor 0*f**3 + i*f + 0*f**2 - 2/5*f**4 + 0.
-2*f**4/5
Let b(h) be the third derivative of h**8/28 - 38*h**7/105 - h**6/15 + 44*h**5/15 + 4*h**4 + 1258*h**2. Let b(t) = 0. Calculate t.
-1, -2/3, 0, 2, 6
Let d(o) be the third derivative of o**5/30 + 85*o**4/12 - 182*o**3 - 2*o**2 + 4*o - 8. Factor d(a).
2*(a - 6)*(a + 91)
Let u be (-22660)/(-274186)*(21 - -1). Factor 0 + u*m**4 + 24/11*m**3 + 2/11*m + 6/11*m**5 + 12/11*m**2.
2*m*(m + 1)**3*(3*m + 1)/11
Let g(m) be the third derivative of 2*m**7/63 + 4*m**6/45 + 13*m**5/180 + m**4/72 - 214*m**2 + 1. Find k, given that g(k) = 0.
-1, -1/2, -1/10, 0
Factor 432 - 15*v + 222*v**2 - 691*v**2 + 3*v + 239*v**2 + 226*v**2.
-4*(v - 9)*(v + 12)
Suppose 4*x - 4*w + 4 = x, 0 = 5*x + 2*w - 28. Suppose 0*k = x*l - 3*k, 2*l = -5*k. Factor 2/7*o**5 - 4/7*o**2 + 0*o + l + 0*o**4 - 6/7*o**3.
2*o**2*(o - 2)*(o + 1)**2/7
Let o = -1307 + 1310. Suppose p - o*v - 10 = -16, 4*p + v - 15 = 0. Factor 0 + 0*z + z**p - 1/5*z**5 + 1/5*z**4 + 3/5*z**2.
-z**2*(z - 3)*(z + 1)**2/5
Let q(d) = 1. Let c(a) = 3*a**2 + 1644*a + 1633. Let f(y) = c(y) + 8*q(y). Factor f(k).
3*(k + 1)*(k + 547)
Suppose 10*w - 45 = -5*w. Let k be -8*2/w*-3. Determine g, given that 6*g**2 + 2*g**5 + 8*g + 2*g**4 + 10*g**4 + 2*g**2 - 6*g**3 - k*g**4 = 0.
-1, 0, 2
Let w(l) be the second derivative of 89*l - 5/4*l**3 + 3/8*l**4 + 7/4*l**2 + 0 - 1/40*l**5. Factor w(p).
-(p - 7)*(p - 1)**2/2
Let a(o) be the second derivative of o**5/70 + 13*o**4/2 + 1183*o**3 + 107653*o**2 + 2*o - 929. Factor a(p).
2*(p + 91)**3/7
Suppose 0 = -3*r + 57, 5*r + 144 - 227 = 4*l. Solve -14/9*u**2 - 2/9*u**4 - 10/9*u**l - 2/3*u + 0 = 0 for u.
-3, -1, 0
Let s(p) = -7*p**2 - 237*p - 7933. Let d be (-10)/15*(4 + 2). Let z(v) = 6*v**2 + 240*v + 7934. Let i(m) = d*s(m) - 5*z(m). Determine o, given that i(o) = 0.
-63
Let p(t) be the first derivative of -13/2*t - 11/6*t**3 - 53 + 1/8*t**4 - 25/4*t**2. Suppose p(x) = 0. What is x?
-1, 13
Let p(z) be the first derivative of -z**6/720 + z**5/60 - z**4/16 + 2*z**3/3 - 57*z - 66. Let d(l) be the third derivative of p(l). Find j such that d(j) = 0.
1, 3
Let q be -9*(1 - (3 - 0)) + 1. Let -q*l**3 + 51*l**3 - 51*l**2 + 50*l + 4*l**4 - 10*l - 25*l**2 = 0. What is l?
-10, 0, 1
Find n such that -683*n**2 - 124*n**3 - 5*n**4 - 121*n**3 + 2214 - 595*n - 4 - 622*n**2 - 60 = 0.
-43, -5, -2, 1
Suppose 0 - 1/3*j**2 + 205/3*j = 0. Calculate j.
0, 205
Let k be 8 + ((-32)/128 - ((-2391)/(-276) - 1)). Let k*c**3 - 8/23*c - 8/23 + 2/23*c**2 = 0. Calculate c.
-2, -1, 2
Determine q so that 0 - 7/3*q - 1/3*q**2 = 0.
-7, 0
Let k(u) be the second derivative of u**4/6 + 67*u**3 - 202*u**2 + 30*u - 5. Let k(i) = 0. What is i?
-202, 1
Let g(w) be the third derivative of -w**6/840 + 3*w**5/70 - 5*w**4/8 + 100*w**3/21 + 2*w**2 + 121*w + 2. Let g(b) = 0. Calculate b.
5, 8
Let o be 17/(-2)*-23*528/12903. Solve 32/11 - o*s**3 - 222/11*s**2 - 10/11*s**4 - 112/11*s = 0.
-4, -1, 1/5
Let a(c) be the first derivative of c**3/6 + 69*c**2/4 + 2259. What is t in a(t) = 0?
-69, 0
Let g(p) be the third derivative of p**7/420 + 19*p**6/60 + 73*p**5/30 + 6*p**4 - 2*p**2 + 52*p. Factor g(c).
c*(c + 2)**2*(c + 72)/2
Let o(m) be the second derivative of m**6/1980 - 3*m**4/44 + 29*m**3/6 - 172*m. Let r(w) be the second derivative of o(w). Suppose r(y) = 0. What is y?
-3, 3
Let r(n) = 2*n**3 - 28*n**2 - 3*n + 43. Let j be r(14). Let k be j/(8/(32/34)). Let -18/17*w**4 + k*w**5 + 42/17*w**3 + 0 - 38/17*w**2 + 12/17*w = 0. What is w?
0, 1, 6
Suppose -51*d +