1)
Let 10/9 - 8/9*q - 2/9*q**2 = 0. What is q?
-5, 1
Let i(g) be the second derivative of g**4/8 - 39*g**3/2 + 4563*g**2/4 + 20*g + 2. Solve i(w) = 0 for w.
39
Let v(n) be the third derivative of n**7/210 - 122*n**2. Find a, given that v(a) = 0.
0
Let p(x) be the second derivative of 0 - 1/240*x**5 - 1/24*x**3 + 7*x + 9/2*x**2 - 1/48*x**4. Let l(o) be the first derivative of p(o). Factor l(q).
-(q + 1)**2/4
Let a(w) be the third derivative of w**5/510 - 5*w**4/51 + 19*w**3/51 - 108*w**2. Factor a(q).
2*(q - 19)*(q - 1)/17
Let w(i) be the second derivative of -i**4/42 + 2*i**3/21 + 8*i**2/7 + i + 50. Factor w(s).
-2*(s - 4)*(s + 2)/7
Let k(c) be the third derivative of -c**8/112 + 9*c**7/70 - 9*c**6/20 - 11*c**5/10 + 51*c**4/8 + 45*c**3/2 + 50*c**2 - c. Solve k(r) = 0.
-1, 3, 5
Let n(o) be the first derivative of o**4/12 - 47*o**3/9 + 23*o**2/3 - 35. Factor n(l).
l*(l - 46)*(l - 1)/3
What is w in -140*w + 16 + 84 + 319*w**2 + 5*w**3 - 284*w**2 = 0?
-10, 1, 2
Let b be (8/(-16))/((-2)/76). Let n = b - 17. Find z, given that z**4 - 41*z**2 - 18*z**3 - 4*z**4 - 12 - 36*z + n*z**2 = 0.
-2, -1
Let w(g) be the first derivative of g**2 + 2/15*g**3 + 8/5*g - 13. Determine z so that w(z) = 0.
-4, -1
Let l(f) = 5*f - 20. Let b be l(4). Suppose 4*s + 43 - 55 = b. Suppose -12/7*u**4 + s*u**3 - 3/7*u - 6/7*u**2 + 0 = 0. What is u?
-1/4, 0, 1
Determine t, given that -2*t**3 + 17*t + 16*t**2 + 28*t - 118*t + 41*t = 0.
0, 4
Factor -1107/7*m**2 - 136161/7*m - 5582601/7 - 3/7*m**3.
-3*(m + 123)**3/7
Suppose -25*y = -9*y - 79*y + 126. Factor 0 + 1/3*f + 1/6*f**y - 1/3*f**3 - 1/6*f**4.
-f*(f - 1)*(f + 1)*(f + 2)/6
Let q(k) be the third derivative of k**6/200 - 29*k**2. Let q(t) = 0. What is t?
0
Let s(k) be the third derivative of 1/40*k**4 + 0*k**3 - 1/100*k**5 + 35*k**2 + 0*k + 0. Let s(v) = 0. Calculate v.
0, 1
Let w be (-322)/92 + 5/1. Factor -w + 1/2*h + 2*h**2.
(h + 1)*(4*h - 3)/2
Factor 5618/3 + 212/3*c + 2/3*c**2.
2*(c + 53)**2/3
Let g(x) be the first derivative of x**4/10 - 28*x**3/15 + 24*x**2/5 + 58. Find p such that g(p) = 0.
0, 2, 12
Suppose 0*w + w = 6. Let l = -4 + w. Solve -y**3 + y**l + 0*y**3 + 3*y**3 + y**4 = 0 for y.
-1, 0
Suppose 3*p - 104 = -4*q, 11*q - 30 = -p + 12*q. Solve 15*a - 2*a**2 + p*a - 37*a = 0 for a.
0, 5
Let h(d) be the third derivative of -d**5/210 - 5*d**4/28 + 16*d**3/21 + 78*d**2. Solve h(l) = 0.
-16, 1
Suppose -5*i - h = -2 + 13, -h + 9 = -5*i. Let t be 4*(1 - (2 + i)/1). Find k, given that -2/3*k**4 + t*k**5 + 0*k**2 + 0 + 0*k - 4/3*k**3 = 0.
-1/2, 0, 2/3
Suppose -b + 10 = -y + 6*y, -3*b - 4*y = -19. Find w, given that -46*w**3 + 56*w**2 - 11*w**5 - 24*w + 16*w**4 + 27*w**b - 18*w**5 = 0.
0, 1, 2, 3
Let 4*p**3 + 272 - 76*p**2 + 288*p - 32*p**2 + 192*p**2 = 0. What is p?
-17, -2
Let m(t) be the first derivative of -t**4/3 + 2*t**3 - 4*t**2 + 36*t + 3. Let d(w) be the first derivative of m(w). Factor d(x).
-4*(x - 2)*(x - 1)
Let l be 328/(-41)*5/(-8). Let y(z) be the second derivative of -1/6*z**4 + 1/6*z**l - 2/45*z**6 + 1/3*z**2 - 1/9*z**3 - 11*z + 0. Factor y(i).
-2*(i - 1)**3*(2*i + 1)/3
Let l = 48557/3 + -16185. Factor 0*p**3 + 2/3 + 0*p + l*p**4 - 4/3*p**2.
2*(p - 1)**2*(p + 1)**2/3
Let t(y) be the second derivative of 3*y**5/160 - 5*y**4/32 + 3*y**3/16 + 27*y**2/16 + y + 2. Solve t(f) = 0.
-1, 3
Suppose 3*w - 120 - 597 = 0. Solve 122*o - w*o + 117*o + o**4 = 0.
0
Let f(i) be the first derivative of -4*i**6/9 - 52*i**5/15 - 10*i**4 - 112*i**3/9 - 16*i**2/3 - 566. Factor f(l).
-4*l*(l + 2)**3*(2*l + 1)/3
Let a(u) = u**3 + 14*u**2 + 14*u - 1. Let w be a(-13). Let g = w + 18. Determine k, given that -5*k - 13 - g*k**2 - 3*k + 9 = 0.
-1
Suppose 272*u - 274*u - 8 = 4*z, z + 9 = 3*u. Factor -2/3*o**u + 2*o - 4/3.
-2*(o - 2)*(o - 1)/3
Factor 0 + 5/3*z**4 + 0*z + 12*z**2 - 1/3*z**5 + 32/3*z**3.
-z**2*(z - 9)*(z + 2)**2/3
Factor -198*h**2 + 46*h + 195*h**2 + 74*h - 12*h - 972.
-3*(h - 18)**2
Let l(o) be the third derivative of -o**7/1120 - o**6/480 + o**3/3 + 11*o**2. Let d(c) be the first derivative of l(c). Suppose d(x) = 0. What is x?
-1, 0
Suppose 0 = -2*a - a + 4*v + 43, 5*v - 10 = 0. Find f such that f**2 - 60 - 5*f**2 + 18*f - f**2 + a*f = 0.
3, 4
Let b(i) = -i**2 - 4*i + 23. Let m be b(-7). Let l(q) be the first derivative of 1/6*q**4 + 0*q - m - 2/9*q**3 - 2/3*q**2. What is y in l(y) = 0?
-1, 0, 2
Let r = 383 - 378. Suppose 0 - 2/11*t**r + 0*t**4 + 0*t**2 + 2/11*t**3 + 0*t = 0. What is t?
-1, 0, 1
Let d(u) = 4*u + 19. Let a be d(-4). Let t(q) be the first derivative of 3/4*q**2 + 0*q - 1/4*q**a - 5. What is m in t(m) = 0?
0, 2
Suppose 0 = -2*i - 3*t + 25, 0 = -5*t + 10*t - 35. Factor -18/17 - 2/17*a**3 + 10/17*a**i - 6/17*a.
-2*(a - 3)**2*(a + 1)/17
Let -45 - 3/2*r**5 + 36*r**3 + 6*r**4 + 267/2*r - 129*r**2 = 0. What is r?
-5, 1, 6
Let n(d) be the third derivative of d**6/1260 - d**4/84 - d**3 - 4*d**2. Let x(p) be the first derivative of n(p). Determine g, given that x(g) = 0.
-1, 1
Suppose -10 = -2*i - 5*r, -2 = -2*i - 4*r + 3*r. Let f = i + 23. Factor f*m**3 + m**4 - 25*m**3 + 4 + m - 2*m**2 + m**5 - 3.
(m - 1)**2*(m + 1)**3
Suppose 0 = -29*z + 26*z. Let s(n) be the first derivative of z*n - 1/16*n**4 - 1/20*n**5 + 3 + 1/12*n**3 + 1/8*n**2. What is w in s(w) = 0?
-1, 0, 1
Suppose -2*l - 1 = -p, 2*p - 8 = -l + 4. Factor -15*k**2 - 1 + 3/2*k**p + 13/2*k - 8*k**4 + 16*k**3.
(k - 2)*(k - 1)**3*(3*k - 1)/2
Let q(b) = -b**3 + 6*b**2 + 8*b - 5. Let u be q(7). Let n = -4463 - -4463. Factor 0*d**3 + d**u - 1/2*d**4 + n*d - 1/2.
-(d - 1)**2*(d + 1)**2/2
Suppose 4*f - m = -f - 4, 4*f = -3*m + 12. Let b(l) = -l**2 - 3*l + 2. Let s be b(f). Factor -2/7*n**s - 4/7*n + 6/7.
-2*(n - 1)*(n + 3)/7
Factor 0 - 1/2*q**5 + 0*q**2 + 0*q + 1/2*q**3 + 0*q**4.
-q**3*(q - 1)*(q + 1)/2
Factor -1/11*a**3 - a**2 - 39/11*a - 45/11.
-(a + 3)**2*(a + 5)/11
Let u(h) be the first derivative of -2*h**3/9 + h**2/3 + 55. Factor u(r).
-2*r*(r - 1)/3
Let a = 9903 - 49513/5. Find p such that -2/5*p - 1/10*p**2 - a = 0.
-2
Let u(n) be the first derivative of n**6/42 + 17*n**5/35 + 99*n**4/28 + 81*n**3/7 + 108*n**2/7 + 284. Factor u(i).
i*(i + 3)**3*(i + 8)/7
Suppose 4/5*n**4 - 48/5 - 28/5*n**2 - 16*n + 8/5*n**3 = 0. What is n?
-2, -1, 3
Suppose -7*b + 6*b = -4. Factor -12*r**3 - 5*r**2 - r**4 + 17*r**2 + b*r**4.
3*r**2*(r - 2)**2
Let g = 2329 - 6979/3. Let w = -36 + 110/3. Factor g + w*f**2 + 8/3*f.
2*(f + 2)**2/3
Let h = -6652 + 6654. Factor 6/5 - 6/5*g**h + 3/5*g - 3/5*g**3.
-3*(g - 1)*(g + 1)*(g + 2)/5
Suppose 8*v + 65 = 105. Let a(x) be the first derivative of -1/5*x**v + 0*x + 3/4*x**4 - 4 - 2/3*x**3 + 0*x**2. Factor a(s).
-s**2*(s - 2)*(s - 1)
Let y be 7 - (112/35 + -2 - 70/(-25)). Factor 2/3*v**2 + 8/15 + 2/15*v**y + 16/15*v.
2*(v + 1)*(v + 2)**2/15
Let z(d) be the third derivative of d**8/25200 - d**7/1260 + d**5/5 + 5*d**2. Let f(j) be the third derivative of z(j). Let f(t) = 0. What is t?
0, 5
Factor -3*v - 56*v**2 + v**5 - 62*v**2 + 4*v**4 + 114*v**2 - 12*v**3 + 14*v**3.
v*(v - 1)*(v + 1)**2*(v + 3)
Let u(f) = f**2 + 99*f + 2440. Let g be u(-46). Let -1/8*b - 1/8*b**g + 3/4 = 0. Calculate b.
-3, 2
Let o be (14 + 1810/(-125))*(-5)/3. Suppose -o*j - 24/5*j**3 + 8/5*j**4 + 0 + 18/5*j**2 = 0. What is j?
0, 1/2, 2
Suppose -4*m + 8*m = -14*m. Let a(l) be the third derivative of 3*l**2 + 1/12*l**4 - 1/30*l**5 + 0 + m*l + 0*l**3. Factor a(f).
-2*f*(f - 1)
Let m = -72 + 81. Suppose m = 3*u - 6. Factor -2 - 100*v**4 + 19*v + 485/4*v**3 - 139/2*v**2 + 125/4*v**u.
(v - 1)**2*(5*v - 2)**3/4
Let f be 20/16*(-32)/(-20). Let a(z) be the first derivative of -4*z**f - 8 + 2/3*z**3 + 8*z. What is o in a(o) = 0?
2
Let v(s) be the first derivative of s**4 + 80*s**3/3 + 234*s**2 + 648*s - 129. Factor v(z).
4*(z + 2)*(z + 9)**2
Let q be 282/(-658) + (144/14)/3. Determine k, given that 0 + 6/7*k**2 + 10/7*k**4 + 2/7*k**5 + 2*k**q + 0*k = 0.
-3, -1, 0
Let i(g) be the first derivative of -4*g**2 + 0*g + 10/3*g**3 - 34 - 1/2*g**4. Factor i(f).
-2*f*(f - 4)*(f - 1)
Suppose -4*x + 4*l - 17 = -3*x, -1 = 3*x - 2*l. Let z be 12/(1 - 2/(-4)). Factor x*k**3 - 3*k - z + 8.
3*k*(k - 1)*(k + 1)
Suppose -47*w = -44*w - 54. Let o = 21 - w. Solve 24/5*z**2 + 8/5*z**o + 16/5 + 32/5*z + 1/5*z**4 = 0 for z.
-2
Let b = 134/153 - -70/153. Find j such that -b*j + 0 - 4/3*j**2 = 0.
-1, 0
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