 1. Let y(q) = 5*q**3 + 11*q**2 + q - 23. Let w = 214 - 208. Let l(h) = w*z(h) + y(h). Factor l(r).
-(r - 17)*(r - 1)*(r + 1)
Suppose 702*k - 707*k = -455. Suppose 0 = -k*s + 63*s + 56. Solve -4/9 + 8/9*f**3 + 2/9*f**5 + 8/9*f**4 - 4/9*f**s - 10/9*f = 0 for f.
-2, -1, 1
Suppose -438*h - 357 + 314 + 1357 = 0. Let f(r) be the first derivative of 147/5*r**5 + 24*r - 28 + 18*r**h - 357/4*r**4 + 66*r**2. Factor f(m).
3*(m - 2)*(m - 1)*(7*m + 2)**2
Let r(p) = p**3 + 5*p**2 - 4*p - 4. Let o be r(-6). Let c = o - -19. Factor -3*b**2 - 84*b**3 - c*b**2 + 87*b**3.
3*b**2*(b - 2)
Let w(q) = 26*q**3 - q**2 + q + 1. Let z(c) = -129*c**3 + 166*c**2 + 6859*c + 30415. Let j(u) = -5*w(u) - z(u). Factor j(y).
-(y + 5)*(y + 78)**2
Let c(n) be the third derivative of -30*n**2 + 0*n**4 + 0 - 1/15*n**6 - 1/15*n**5 + 0*n**3 + 0*n - 2/105*n**7. Solve c(t) = 0.
-1, 0
Let b(q) be the third derivative of -q**7/945 - 11*q**6/540 - 11*q**5/90 - 37*q**4/108 - 14*q**3/27 + 1945*q**2. Find w such that b(w) = 0.
-7, -2, -1
Let c be ((-12)/(-10))/(-3) - (-43358)/70. Factor -p**3 - c + 619 + p - p**2 + p**4.
p*(p - 1)**2*(p + 1)
Let h(k) be the third derivative of -k**8/1008 - k**7/45 - k**6/30 + 7*k**5/90 + 13*k**4/72 + 3*k**2 - 22*k + 11. Let h(a) = 0. Calculate a.
-13, -1, 0, 1
Let t(k) be the second derivative of 5/3*k**3 - 1/24*k**4 - 1/80*k**5 - 1/720*k**6 + 0*k**2 - 27*k + 0. Let o(l) be the second derivative of t(l). Factor o(q).
-(q + 1)*(q + 2)/2
Let t = -66 + 96. Suppose t*r = 15*r + 45. Factor -6/7*b**r + 0 + 0*b + 4/7*b**2 + 2/7*b**4.
2*b**2*(b - 2)*(b - 1)/7
Let l(n) be the first derivative of n**4/14 - 34*n**3/21 + 80*n**2/7 - 128*n/7 - 7281. Determine t so that l(t) = 0.
1, 8
Let t(l) be the second derivative of 0*l**2 - 16/27*l**3 - 31/54*l**4 + 1/135*l**6 + 0 - 89*l - 7/45*l**5. Suppose t(s) = 0. What is s?
-1, 0, 16
Let d(o) be the second derivative of -o**7/280 + o**5/40 - 29*o**3/6 + 109*o. Let y(m) be the second derivative of d(m). Solve y(q) = 0.
-1, 0, 1
Determine m, given that -161*m**3 - 529/3*m**2 - 1/3*m**5 + 15*m**4 + 0 + 0*m = 0.
-1, 0, 23
Let h(c) = 5*c**2 - 12248*c - 12509316. Let t(y) = -33*y**2 + 85737*y + 87565206. Let u(g) = 27*h(g) + 4*t(g). Factor u(n).
3*(n + 2042)**2
Suppose -3*z = 7459*u - 7462*u - 27, 6*u + 42 = 3*z. Suppose 6*i + 2/3*i**5 + 4/3 + 32/3*i**2 + 28/3*i**3 + z*i**4 = 0. Calculate i.
-2, -1
Let m(t) be the third derivative of 5*t**8/336 - 17*t**7/42 + 11*t**6/3 - 6*t**5 - 90*t**4 + 360*t**3 - 1143*t**2. Solve m(y) = 0 for y.
-2, 1, 6
Let t(v) be the third derivative of -v**7/105 - 19*v**6/60 - 43*v**5/10 - 123*v**4/4 - 126*v**3 - 5*v**2 + 58*v - 3. Solve t(p) = 0 for p.
-7, -6, -3
Suppose 5*k = a - 49, -5*a - 7*k + 47 = -10*k. What is b in 14/5*b**5 + 24/5*b**3 + 4/5*b**2 - 6/5*b + 0 - 36/5*b**a = 0?
-3/7, 0, 1
Determine i, given that 303*i - 91 + 75*i**2 + 12*i**3 - 15 + 40 - 234*i**2 = 0.
1/4, 2, 11
Let m(c) = 2*c**2 + 42*c + 40. Let h be m(-20). Suppose -l + 5 = -h*l + t, 0 = -2*l - t + 7. Let 5*x - 5/4*x**l + 0 = 0. Calculate x.
0, 4
Let y = 1821 - 2025. Let u be 8 + 3 + y/24. Factor 1/2*v**2 - u*v + 0.
v*(v - 5)/2
Let c = -1412196/5 - -282446. Let 32/5*r + c - 2/5*r**2 = 0. What is r?
-1, 17
Suppose 0 = 10122*h - 10183*h + 244. Determine t so that -2/11*t**5 - 6/11*t**h + 0 - 2/11*t**3 + 4/11*t + 6/11*t**2 = 0.
-2, -1, 0, 1
Let n(g) be the first derivative of g**6/10 + 3*g**5/20 - g**4 - 2*g**3 - 37*g - 81. Let q(f) be the first derivative of n(f). Solve q(r) = 0.
-2, -1, 0, 2
Let k(g) be the second derivative of -5*g**7/42 - 2*g**6 - 11*g**5/4 + 115*g**4/3 + 10*g**3 - 200*g**2 - g - 420. What is h in k(h) = 0?
-10, -4, -1, 1, 2
Let o = -1100 + 1100. Let r(j) be the third derivative of -1/72*j**4 + o*j - j**2 - 1/45*j**5 + 1/360*j**6 + 0 + 2/9*j**3. Suppose r(v) = 0. What is v?
-1, 1, 4
What is k in 70/3*k - k**2 + 79 = 0?
-3, 79/3
Let n(y) be the third derivative of y**10/6048 + y**4/24 - 20*y**2. Let l(s) be the second derivative of n(s). Find i, given that l(i) = 0.
0
Determine m, given that 180000 - 2*m**4 + 4*m**4 + 148523*m**2 + 20485*m**2 - 1196*m**3 + 8594*m**2 + 358800*m = 0.
-1, 300
Factor -32/7*d + 96/7*d**2 - 96/7*d**3 + 0 - 6/7*d**5 + 40/7*d**4.
-2*d*(d - 2)**3*(3*d - 2)/7
Let w = -1103 - -837. Let u = 800/3 + w. Factor -14/9*m**4 + 4*m**3 - u + 2/9*m**5 - 44/9*m**2 + 26/9*m.
2*(m - 3)*(m - 1)**4/9
Let r(f) be the second derivative of 0*f**3 + 2/3*f**4 + 1/3*f**6 - 5 + 0*f**2 + 9*f + 6/5*f**5. Factor r(m).
2*m**2*(m + 2)*(5*m + 2)
Let b = 274 - 258. Factor -5*l**2 - 40 - b*l - 10 - 94*l - 55.
-5*(l + 1)*(l + 21)
Let c = 333 + -318. Suppose -1878*k - c*k**4 + 5*k**3 + 15*k**2 + 3*k**5 + 2*k**5 + 1868*k = 0. Calculate k.
-1, 0, 1, 2
Suppose -9*s - 24 + 3/2*s**5 + 75/2*s**2 - 27/2*s**4 + 15/2*s**3 = 0. Calculate s.
-1, 1, 2, 8
Let o(r) = -58*r**4 + 420*r**3 + 1852*r**2 + 12. Let x(d) = -24*d**4 + 168*d**3 + 741*d**2 + 5. Let p(b) = -5*o(b) + 12*x(b). Factor p(y).
2*y**2*(y - 46)*(y + 4)
Let x = 123 - 97. Let -x*u**3 - 70*u**3 - 2*u**5 - 2*u**5 - 64*u - 32*u**4 - 128*u**2 = 0. What is u?
-2, 0
Let h(i) be the first derivative of -1/3*i**3 + 71 - 22*i - 23/2*i**2. What is r in h(r) = 0?
-22, -1
Determine p so that 25 + 11 - 3951*p + 6*p**2 - 6 + 3888*p = 0.
1/2, 10
Let w(k) = -25*k - 98. Let u be w(-4). Determine h, given that 156 - 98 - 28*h + 4*h**u - 90 = 0.
-1, 8
Solve -2*m**3 - 58*m**2 - 49 - 24 - 102 + 24*m**2 + 79 - 128*m = 0 for m.
-12, -4, -1
Find z, given that -676/9*z + 448/9 - 1114/9*z**2 + 10/9*z**3 = 0.
-1, 2/5, 112
Let r(f) be the third derivative of f**5/12 - 25*f**4/4 + 500*f**3/3 + 789*f**2 + f. Factor r(v).
5*(v - 20)*(v - 10)
Factor 231*l**3 - 444*l**3 + 7 - 38*l**2 + 211*l**3 + 90*l + 119.
-2*(l - 3)*(l + 1)*(l + 21)
Determine g, given that 152/3*g - 2/3*g**4 + 40 - 20/3*g**3 + 14/3*g**2 = 0.
-10, -2, -1, 3
Solve -3/4*l**2 + 2277/2*l - 1728243/4 = 0.
759
Let l(w) be the third derivative of -w**5/12 + 145*w**4/2 - 25230*w**3 - 1122*w**2. Suppose l(n) = 0. What is n?
174
Let u(k) = -22*k + 220. Let f be u(10). Suppose f = -835*t + 843*t - 24. Factor -2*j**t + 0 + 0*j**2 - 2/3*j**4 + 8/3*j.
-2*j*(j - 1)*(j + 2)**2/3
Let t(d) be the second derivative of d**4/12 - d**3/6 + 2*d**2 + d. Let q be t(0). Factor 3*b**4 - 154*b**5 - 13*b**q + 149*b**5.
-5*b**4*(b + 2)
Suppose b = -o + 257 + 561, 2*b - 1624 = 4*o. Let p = b + -814. Factor p*x + 3/4*x**2 + 1.
(x + 2)*(3*x + 2)/4
Let a(y) be the first derivative of 9*y**5/5 - 21*y**4/4 - 18*y**3 + 42*y**2 + 72*y + 3934. Find v such that a(v) = 0.
-2, -2/3, 2, 3
Factor 989 - 270 - 133*m + 517*m - 4*m**2 + 1301.
-4*(m - 101)*(m + 5)
Factor -32448/5 - 624/5*r - 3/5*r**2.
-3*(r + 104)**2/5
Let b(l) = l**3 + 15*l**2 - 14*l + 35. Let p be b(-16). Factor 19*i**4 + 2*i + 29*i**4 + 44*i**3 + p*i**5 + 11*i**5 + 4*i**5 + 16*i**2.
2*i*(i + 1)**2*(3*i + 1)**2
Let d(a) be the second derivative of -3*a**5/20 + 49*a**4/4 - 70*a**3 + 138*a**2 + a - 113. Factor d(j).
-3*(j - 46)*(j - 2)*(j - 1)
Let k be (39/104)/(22 - (-1293)/(-60)). Factor 0 - 5*s**2 + 20/3*s + k*s**3.
5*s*(s - 4)*(s - 2)/6
Let l(c) be the second derivative of -c**4/30 + 2*c**3 - 40*c**2 - 1689*c + 1. Solve l(k) = 0 for k.
10, 20
Let b be 6 + (-8 + -1 - -5). Solve 20 + 13*c**b - c - 24*c - 23*c**2 + 15*c**2 = 0.
1, 4
Find k, given that 5547/7 + 3/7*k**2 + 258/7*k = 0.
-43
Let y(s) be the third derivative of s**5/45 - 23*s**4/48 + 53*s**3/18 + 1786*s**2 + 1. Let y(j) = 0. What is j?
2, 53/8
Let l(x) = 3*x**3 + 8*x**2 - x - 5. Suppose 97*z = 89*z - 40. Let o(g) = 4*g**3 + 10*g**2 - 2*g - 6. Let q(p) = z*o(p) + 6*l(p). Solve q(t) = 0 for t.
-2, 0, 1
Let a(f) be the third derivative of -f**7/280 + 11*f**6/120 + 3*f**5/40 - 11*f**4/24 - 5*f**3/8 - 620*f**2. Solve a(g) = 0 for g.
-1, -1/3, 1, 15
Factor 107/3*a - 18 - 1/3*a**3 - 52/3*a**2.
-(a - 1)**2*(a + 54)/3
Suppose 4*s + 41*w - 37*w = 136, -s + 5*w = -40. Suppose -34*l + 5*o - 5 = -29*l, 0 = 5*l + 5*o - s. Factor -2/3*x**2 - 2/9*x**l + 4/9 + 2/9*x**4 + 2/9*x.
2*(x - 2)*(x - 1)*(x + 1)**2/9
Let k be 15/((-22050)/238) - (6/(-14))/1. Let h(o) be the second derivative of -20*o + 7/10*o**2 + 0 + 1/60*o**4 - k*o**3. Factor h(f).
(f - 7)*(f - 1)/5
Let s be 124/6 + (-2)/3. Suppose 3229 = 23*u - 267. Determine z, given that -147*z**5 + s*z + u*z**5 - 23*z**3 - 2