ind h such that s(h) = 0.
321
Let f(j) = -41*j**4 + 5*j**3 + 8*j**2 - 3*j - 5. Let u(k) = -33*k**4 + 4*k**3 + 7*k**2 - 2*k - 4. Let n(p) = 4*f(p) - 5*u(p). Suppose n(r) = 0. What is r?
-1, 0, 2
Let h(x) be the second derivative of x**6/45 + 2*x**5/15 - 19*x**4/18 + 14*x**3/9 - 465*x. Factor h(o).
2*o*(o - 2)*(o - 1)*(o + 7)/3
Let b = 38 + -40. Let h be (1/b)/(6/(-24)). Factor -s**2 - 21 - 18*s - s**h + 5.
-2*(s + 1)*(s + 8)
Solve 62500 - 14625*w + 106660*w**3 - 213323*w**3 + 106662*w**3 - 246*w**2 = 0.
-125, 4
Let i(m) be the third derivative of m**5/60 - m**4/2 - 13*m**3/6 + m**2 + 195. Factor i(z).
(z - 13)*(z + 1)
Let c = -22 + 74. Let d = c - 50. Let 0*g**3 - d*g**4 - 10*g**5 + g**3 - 3*g**5 + 14*g**5 = 0. What is g?
0, 1
Let m = -107 - -7063/66. Let a(r) be the second derivative of -1/231*r**7 - 4*r + 0*r**2 - 3/110*r**5 - m*r**4 + 0 + 0*r**3 - 1/55*r**6. Factor a(g).
-2*g**2*(g + 1)**3/11
Let q(m) be the first derivative of m**3/3 + 47*m**2 + 765*m + 3051. Factor q(x).
(x + 9)*(x + 85)
Suppose 0 = -213*v - 435*v + 59325 - 4893. Determine m, given that v*m + 1/2*m**3 + 25/2*m**2 + 72 = 0.
-12, -1
Solve -1/3*g**5 + 35*g**4 + 107/3*g**2 + 0 + 71*g**3 + 0*g = 0 for g.
-1, 0, 107
Let t(k) = -3*k**2 + 17*k + 18. Let p(u) = 10*u**2 - 50*u - 53. Suppose 5*a + 54 = -4*x, -25 = 4*a + x + 27. Let g(s) = a*t(s) - 4*p(s). Solve g(q) = 0 for q.
-1, 20
Let g be (-12)/(-14)*77/33. Let a be 4 - 1/((-77)/(-264)). Factor -a*k**g + 0*k - 2/7*k**3 + 0.
-2*k**2*(k + 2)/7
Let u(h) be the third derivative of h**6/24 + h**5/12 - 295*h**4/8 + 825*h**3/2 - 9066*h**2. What is b in u(b) = 0?
-15, 3, 11
Let f(c) = 2*c**2 - 4*c + 6. Let b(h) = 1. Let w(q) = 6*b(q) - f(q). Let z = -319 - -321. Let t(p) = p**2 - 4*p. Let k(v) = z*t(v) + 3*w(v). Factor k(s).
-4*s*(s - 1)
Let p be 207/(-4071) + 33507/1062. Factor -3/2*a**2 + p + 6*a.
-3*(a - 7)*(a + 3)/2
Let a be ((-4)/88)/(-12*18/1188). Let k(z) be the first derivative of -3/4*z + 1/2*z**2 - 22 - a*z**4 + 1/6*z**3 + 1/20*z**5. Solve k(l) = 0.
-1, 1, 3
Let u(x) be the first derivative of -5*x**3/12 + 2879*x**2/8 + 144*x + 9908. Factor u(q).
-(q - 576)*(5*q + 1)/4
Let x be (14777/(-8444))/(98/(-16)). Factor 0 + 2*n**2 - x*n**4 + 12/7*n**3 + 0*n.
-2*n**2*(n - 7)*(n + 1)/7
Let i = 103 - 73. Let v = 34 - i. Determine c so that -7 + 4*c + 6 - 6*c**2 - 2*c**v - 2*c**4 + 3*c**4 + 4*c**3 = 0.
1
Let d(g) be the third derivative of 1/84*g**8 + g**2 + 0*g**3 + 4/5*g**5 - 1/15*g**6 - 2/35*g**7 + 9*g + 0 - 4/3*g**4. Factor d(w).
4*w*(w - 2)**2*(w - 1)*(w + 2)
Solve -63*d - 18*d**2 - 260 - 19*d**2 + 35*d**2 - 76*d - 123*d = 0 for d.
-130, -1
Solve 0*f**2 - 190 + 93 - f**3 - 4*f**4 + 95 - 5*f + 21*f**2 - 9*f**2 = 0.
-2, -1/4, 1
Suppose -136 = -16*b + 8*b. Suppose b*d - 29 = 5. Let -2*x**2 + 559*x**4 - 2*x**d - 557*x**4 + 2*x**3 = 0. What is x?
-2, 0, 1
Let t(z) = -100*z**3 - 230*z**2 - 440*z - 175. Let h be (76 - 25) + -7 + 1. Let q(c) = -9*c**3 - 21*c**2 - 40*c - 16. Let w(s) = h*q(s) - 4*t(s). Factor w(i).
-5*(i + 1)*(i + 2)**2
Let f be ((-12)/10)/((-18)/60). Suppose -3*r = -o + f - 14, 50 = 5*r + 5*o. Solve 6*d**5 - 2*d**r - 2*d**5 + 2*d**3 + 4*d**4 = 0.
-1, 0
Suppose 0 = 7*a + 28*a - 11 - 59. Let h(b) be the first derivative of 0*b - 4/5*b**5 + 0*b**2 - a + 4*b**4 - 16/3*b**3. Factor h(q).
-4*q**2*(q - 2)**2
Let b(t) be the first derivative of t**7/21 + 2*t**6/5 + 13*t**5/10 + 2*t**4 + 4*t**3/3 - 56*t + 57. Let i(l) be the first derivative of b(l). Factor i(a).
2*a*(a + 1)**2*(a + 2)**2
Let p be (-1 + (-112)/40 + 3)*475/(-228). Factor -35/3*z + 50/3*z**2 - p*z**3 - 30.
-5*(z - 9)*(z - 2)*(z + 1)/3
Let w(z) = -2*z**3 + 4*z**2 - 6*z**2 - 21*z**2 - z**2 + 4*z**4 + 18*z - 44*z. Let t(v) = v**4 - v**3 + 3*v. Let g(b) = 2*t(b) - w(b). Factor g(i).
-2*i*(i - 4)*(i + 2)**2
Let v = 479 - 533. Let z be 2*v/(-24)*(-15)/(-18). Factor -9/2 + 3/4*n**2 + z*n.
3*(n - 1)*(n + 6)/4
Suppose 0 = 5*z - 5*g + 1 - 76, -2*g = z. Let 15*h**2 + z*h - 95*h**2 + 20*h**3 + 25*h**2 + 30*h**2 - 5*h**4 = 0. Calculate h.
0, 1, 2
Let i(r) be the third derivative of r**8/560 - 18*r**7/175 + 11*r**6/25 + 183*r**5/50 - 89*r**4/40 - 33*r**3 + 1316*r**2. Suppose i(k) = 0. Calculate k.
-2, -1, 1, 5, 33
Suppose -165*z = -171*z + 12. Suppose 4*n - 20 = -4*u, 0 = -5*n + 3*u + u - z. Factor 14/13*b**n - 24/13*b - 8/13.
2*(b - 2)*(7*b + 2)/13
Let c = 58 + -289/5. Let h = -1435 + 1435. Factor -3/5*k**2 - 2/5*k + h - c*k**3.
-k*(k + 1)*(k + 2)/5
Factor 853*z**4 - 1600*z**2 - 4*z**5 + 512*z**3 + 2240*z - 1386 + 234 - 32*z**3 - 893*z**4.
-4*(z - 2)**4*(z + 18)
Let g(d) = -d**2 - 9*d + 4. Let t be g(-9). Suppose 0 = -3*y + 4*l + 17, -5*l - 5 = -y - t*l. What is n in 6/11*n**y + 0 - 2*n**2 + 12/11*n = 0?
0, 2/3, 3
Suppose -6 = -3*y + 3. Determine a, given that 28*a**2 - 2116*a**3 - 40 + 12 + 2114*a**y + 2*a = 0.
-1, 1, 14
What is f in 175780*f - 3745/4*f**2 - 174845 + 5/4*f**3 = 0?
1, 374
Suppose -90*z + 63480 = 2*z. Let g = -4828/7 + z. Factor -52/7*m + 338/7 + g*m**2.
2*(m - 13)**2/7
Suppose -8*s + 183 - 1607 = 0. Let d = -175 - s. Find z, given that -15/4*z**2 - 6*z - 3 - 3/4*z**d = 0.
-2, -1
Let w be (-56)/(-6) + 3/(-9). Let k be (-8)/(-3) + (-6)/w. Factor -10 - 14*v**k + 5*v + 29*v**2 - 5*v**2 - 5*v**3.
-5*(v - 2)*(v - 1)*(v + 1)
Let o(d) be the first derivative of -28/15*d**3 + 18/5*d**2 - 8/5*d - 106. Factor o(w).
-4*(w - 1)*(7*w - 2)/5
Let b(h) be the second derivative of h**5/4 - 1115*h**4/12 + 20905*h**3/2 - 61605*h**2/2 + 3088*h. Factor b(y).
5*(y - 111)**2*(y - 1)
Let l(y) = y**2 - 1. Let s(z) = -8*z**2 + 2112*z - 278780. Let o(t) = -4*l(t) - s(t). Suppose o(x) = 0. What is x?
264
Suppose -1/3*i**3 - 65*i + 29/3*i**2 - 75 = 0. Calculate i.
-1, 15
Let r(q) be the third derivative of 2*q**7/105 - 3*q**6/10 + 14*q**5/15 - q**2 + 4084*q. Factor r(u).
4*u**2*(u - 7)*(u - 2)
Suppose -2/7*t**2 + 464/7 - 228/7*t = 0. Calculate t.
-116, 2
Let n be (-1)/(-417)*(-12)/26*-1. Let w = 3632/16263 - n. Determine p so that -w*p**4 + 4/9*p**3 + 0*p + 0 + 2/3*p**2 = 0.
-1, 0, 3
Suppose -149*r = -144*r + 3025. Let d = r - -609. Let -21/8*m**2 - 15/8*m**d - 3/4*m + 0 - 27/8*m**3 - 3/8*m**5 = 0. What is m?
-2, -1, 0
Let g be (-8)/2 - 342/(-6585)*77. Let w = 6593/8780 + g. Solve 0 - 1/2*r**2 - w*r + 1/4*r**3 = 0 for r.
-1, 0, 3
Let n(s) be the second derivative of -2/15*s**6 + 23/5*s**5 + 0 + 318*s**3 - 648*s**2 + 109*s - 175/3*s**4. What is h in n(h) = 0?
1, 4, 9
Let t be 6 + (-4 - 14) + -2. Let f(i) = 11*i + 156. Let u be f(t). Determine n so that -3/5*n**u + 0 + 2/5*n + 1/5*n**3 = 0.
0, 1, 2
Let v = -130 - -132. Suppose -470 = v*y - 12*y. Factor 52*k**4 - 31*k**2 - 27*k**4 + 70*k**3 - 12 - 5*k - y*k.
(k - 1)*(k + 3)*(5*k + 2)**2
Let w(g) = -87*g**2 + 795*g - 1320. Let z(b) = 9*b**2 - 80*b + 132. Let p(v) = -4*w(v) - 39*z(v). Factor p(d).
-3*(d - 2)*(d + 22)
Suppose -d + 2 = 2*o, o - 2*d - 6 + 0 = 0. Solve -31*p**2 - o*p - 4*p + 32*p**2 = 0 for p.
0, 6
Let j(t) be the second derivative of t**4/9 - 2*t**3/9 - 140*t**2 - 544*t. Determine b, given that j(b) = 0.
-14, 15
Suppose 3*y - y = -5*v + 206, v - 3*y - 48 = 0. Let r = v - 38. Factor r*l**2 - l + 2*l + 2*l**3 - l**2.
l*(l + 1)*(2*l + 1)
Let f(p) be the second derivative of p**7/7 + 26*p**6/15 + 73*p**5/10 + 37*p**4/3 + 8*p**3 + 742*p + 2. Suppose f(n) = 0. Calculate n.
-4, -3, -1, -2/3, 0
Let -221556222*k + 998001*k**2 + 3/2*k**4 + 36889110963/2 - 1998*k**3 = 0. What is k?
333
Let h(v) = 3*v**2 - 3*v. Let u(g) = -2*g - 1077*g**2 - 3*g + 4*g + 1078*g**2. Let w = 6 - 8. Let y(o) = w*h(o) + 9*u(o). Let y(r) = 0. What is r?
0, 1
Determine g, given that -63*g**3 + 6*g**2 - g**4 - 2*g**2 + 2*g**2 + 64*g**3 = 0.
-2, 0, 3
Factor 1527*l + 967*l + 2*l**2 + 1152 - 1914*l.
2*(l + 2)*(l + 288)
Let t(q) be the first derivative of -3*q**5/5 - 27*q**4/2 + 85*q**3 - 99*q**2 + 3162. Suppose t(m) = 0. Calculate m.
-22, 0, 1, 3
Suppose -2*a = -a + 4*h + 3, -5*a = 3*h - 19. Suppose 0 = -a*q - 8 + 23. Factor -149*y**4 - 3*y**2 - 3*y + 6*y**q + 6*y**2 + 146*y**4 - 3*y**3.
-3*y*(y - 1)**2*(y + 1)
Let t(v) be the second derivative of v**7/378 - 251*v**6/270 + 581*v**5/5 - 5292*v**4 - 10976*v**3 + 91*v + 17. Let t(y) = 0. Calculate y.
-1, 0, 84
Let f(b) be the third derivative of -7*b**7/45 - 7357*b**6/45 - 3077*b**5/6 - 4793*b**4/9 - 2396*b**3/9 + b**2 + 58*