3
Let s = 1053427/2 + -526389. What is v in 121 - 5/2*v**3 + 56*v**2 - s*v = 0?
2/5, 11
Suppose 0 = -21*r + 36649 - 36649. Let i(a) be the third derivative of -5/96*a**4 + 1/6*a**3 + 1/240*a**5 + r*a + 0 + 19*a**2. Suppose i(z) = 0. Calculate z.
1, 4
Let m be (12/8 + -1)*0. Determine b so that -b**2 + m*b - 314 - 10 + 36*b = 0.
18
Let i be (-1 - 6/(-4))/(186/(-341)). Let y = -1/6 - i. Find h, given that -y - 3/8*h**2 - 9/8*h = 0.
-2, -1
Let c(q) be the first derivative of q**4/6 - 62*q**3/3 + 446*q**2/3 - 352*q - 770. Factor c(i).
2*(i - 88)*(i - 3)*(i - 2)/3
Suppose -4*x = -16, -3*d - x = -10 - 0. Suppose 4*b - 3*i = -0*b + 9, 0 = -2*b + d*i + 6. Factor -5/6*u + b + 5/6*u**3 - 5/6*u**4 + 5/6*u**2.
-5*u*(u - 1)**2*(u + 1)/6
Let a(d) be the third derivative of d**5/120 + 75*d**4/16 + 219*d**3/2 - 348*d**2 - 3*d + 2. Factor a(j).
(j + 6)*(j + 219)/2
Let s(f) be the third derivative of 0 - f + 0*f**6 - 1/30*f**4 + 1/525*f**7 - f**2 - 1/50*f**5 + 0*f**3. Factor s(g).
2*g*(g - 2)*(g + 1)**2/5
Suppose 0 = -8*d - 69*d + 15*d + 1054. Let n(p) be the third derivative of 0*p**3 - 1/40*p**6 - d*p**2 + 0*p**5 + 1/70*p**7 + 0 + 0*p + 0*p**4. Factor n(y).
3*y**3*(y - 1)
Let y = 22 - 30. Let a(u) = -u**2 - 8*u + 3. Let i be a(y). Factor -9 - 2*s**2 - 8*s + 5 - 5*s**2 + i*s**2.
-4*(s + 1)**2
Let v = -39 + 38. Let z be (-3)/(-1 + 0/(2 + v)). Solve 0*n**3 + 6*n - 2*n**3 - 8*n**2 - 2 + 2*n**2 + 4*n**z = 0 for n.
1
Suppose -2*c = -5*s + 2206, 3*c - 327 = 3*s - 1647. Let l = s - 440. Factor -1/8*v**4 - 1/4*v**l + 0 + 0*v + 3/8*v**3.
-v**2*(v - 2)*(v - 1)/8
Let j(z) be the first derivative of z**3/3 + 3*z**2 + 13*z - 37. Let v(a) = -2*a - 7. Let i(o) = -3*j(o) - 5*v(o). Find d, given that i(d) = 0.
-2, -2/3
Find w such that -8 - 3*w**2 + 9*w + 1/4*w**3 = 0.
2, 8
Let z(w) = 7*w**2 + 759*w + 712. Let o(q) = -30*q**2 - 3290*q - 3085. Let p(j) = -8*o(j) - 35*z(j). Suppose p(d) = 0. What is d?
-48, -1
Let c = 11163 - 22319/2. Determine d, given that 3 + 13/2*d + c*d**3 - 13*d**2 = 0.
-2/7, 1, 3
Factor -40/3 + 34/9*p - 2/9*p**2.
-2*(p - 12)*(p - 5)/9
Factor -c**4 + 22*c**3 + 88*c**2 + 42*c**2 - 1207 + 1207 - c**3.
-c**2*(c - 26)*(c + 5)
Factor 12/7 - 1/7*j**2 - 4/7*j.
-(j - 2)*(j + 6)/7
Let p(u) be the first derivative of 5*u**3 + 0*u - 15/4*u**4 - 5/2*u**2 + u**5 - 57. What is g in p(g) = 0?
0, 1
Let x be ((-7)/2)/(-2 - -1). Let v = -19861283/4 - -4965333. Factor -v - 1/4*s**2 - x*s.
-(s + 7)**2/4
Let x be 0/4 + 50/(-16) + 0. Let f = x + 7/2. Suppose f*v**3 + 3*v + 3/2 + 15/8*v**2 = 0. Calculate v.
-2, -1
Find a, given that 38*a**3 + 26*a**2 + 39*a**3 - 156*a**3 - 162 + 38*a**3 - 33*a + 42*a**3 = 0.
-27, -2, 3
Suppose z - 175 = -3*y, -22 = y + z - 77. Factor 1 + 51*s - 29*s**2 - 137*s**2 - 545*s**3 + 722*s**3 - y*s**4 - 5*s**2 + 2.
-3*(s - 1)**3*(20*s + 1)
Let y be 1/3*6/4. Let z be (-22)/4*334/(-14696). Solve -3/8*x - z*x**2 + y = 0 for x.
-4, 1
Suppose 8*a - 349 = 3683. Let u be 1 + -1 + -5 + a/72. Find r such that -2/7*r**u - 72/7 + 24/7*r = 0.
6
Suppose 0 = -2*c - c - 3, -3*c = 5*n - 37. Let 34*b**2 + 4*b - 64*b**4 + 114*b**4 + 18*b**3 - 70*b**4 + n*b**2 = 0. Calculate b.
-1, -1/10, 0, 2
Let w be 1/(-20)*25*6/(-30). Factor w*r**2 - 11/4 - 5/2*r.
(r - 11)*(r + 1)/4
Let p(y) be the first derivative of -1/2*y**2 + 5/12*y**3 - 1/16*y**4 + 0*y - 74. Factor p(g).
-g*(g - 4)*(g - 1)/4
Let j(a) be the third derivative of a**8/40320 + a**7/5040 - a**6/96 - 11*a**5/15 + a**4/12 + 77*a**2. Let p(m) be the third derivative of j(m). Factor p(d).
(d - 3)*(d + 5)/2
Let c(j) = j**3 - 6*j**2 + 9*j - 11. Let h be c(6). Let k = h - 41. Find l, given that -6*l + 3*l - k*l**2 + 0*l + l**3 = 0.
-1, 0, 3
Let c(w) be the first derivative of -24 + 5/2*w**2 + 5/2*w**3 + 0*w - 25/24*w**4 - 1/6*w**5. Let d(a) be the second derivative of c(a). Solve d(s) = 0.
-3, 1/2
Let m = -123 + 126. Factor 15*c**2 + 190*c**2 + 170*c + 5*c**4 - 25*c**2 + 55 + 70*c**m.
5*(c + 1)**3*(c + 11)
Let k(b) = b**3 - 18*b**2 + 58*b - 19. Let i be k(11). Let a be 3 - (6 + i/18) - -1. What is g in 22/3*g - 98/3*g**3 + 8/3*g**2 - 112/3*g**4 - a*g**5 - 4/3 = 0?
-2, -1, 1/4
Suppose -5*t = -203*t + 1023 - 429. Let b(x) be the third derivative of 0*x + 7/180*x**5 + 0 + 1/8*x**4 + 1/9*x**t + 26*x**2. Factor b(n).
(n + 1)*(7*n + 2)/3
Let b(x) be the second derivative of 1/35*x**6 - 2/21*x**4 + 0*x**3 - 1/147*x**7 + 0*x**5 + 1 + 0*x**2 - x. Determine l so that b(l) = 0.
-1, 0, 2
Let l be 0 + (-5 - (-10)/(-5)) + 19. Let i(w) = -w**3 + 16*w**2 - 42*w - 68. Let g be i(l). Suppose -20/3*o - g*o**2 + 100/9 - 4/9*o**3 = 0. Calculate o.
-5, 1
Let b be (-1 + -1)*(-9)/2. Let f(p) = 0*p - p + b + 3*p - p + 6*p**2. Let j(l) = -7*l**2 - 2*l - 10. Let i(c) = -6*f(c) - 5*j(c). Suppose i(d) = 0. What is d?
2
Suppose -7*d = -14 - 0. Suppose -d = y, 0 = 2*g + 5*y - 1 - 1. Factor -5*j**2 - g*j - 4*j - 15*j.
-5*j*(j + 5)
Let c(w) = 4*w**2 + 40*w + 174. Let r(m) = m**2 - m + 3. Let l(g) = c(g) - 6*r(g). Solve l(j) = 0 for j.
-3, 26
Suppose 58*l = 55*l + 2*p - 4, 2*p - 10 = 0. Suppose 2*z = 7*z + 3*h + l, 4*h = -16. Factor 4/13 + 0*v**z + 6/13*v - 2/13*v**3.
-2*(v - 2)*(v + 1)**2/13
Let p(v) be the second derivative of 196249*v**5/20 + 147076*v**4/3 - 5315*v**3/24 + 3*v**2/8 + 3*v + 23. Solve p(h) = 0.
-3, 1/886
Let a(s) = 13*s**2 - 2800*s - 4557. Let t be a(217). Let -2/5*h**2 + t - 62/5*h = 0. Calculate h.
-31, 0
Let b be (54/(-15) - 2)*1110/(-37). Suppose -165*h + b*h = 0. Find q, given that -4/5*q + h - 2/5*q**4 - 8/5*q**3 - 2*q**2 = 0.
-2, -1, 0
Let z(x) be the first derivative of 4*x**4 + 312*x**2 - 156 + 396*x - 4/5*x**5 + 248/3*x**3. Solve z(y) = 0.
-3, -1, 11
Let y(l) be the third derivative of 0 - 9/200*l**6 + 0*l + 0*l**4 + 93*l**2 + 1/1050*l**7 + 0*l**3 + 1/6*l**5. Factor y(k).
k**2*(k - 25)*(k - 2)/5
Let c(t) be the third derivative of -t**7/63 - 7*t**6/45 + 17*t**5/90 + 7*t**4/9 - 4*t**3/3 - 31*t**2 - 16. Let c(p) = 0. What is p?
-6, -1, 2/5, 1
Let s(f) be the third derivative of f**5/60 + 31*f**4/48 + 65*f**3/12 + 4692*f**2. Suppose s(g) = 0. What is g?
-13, -5/2
Let p be 2*(2/2 + -9). Let m(s) = -4*s**3 - 40*s**2 - 16. Let z = -512 - -517. Let k(b) = -b**3 - 13*b**2 - 5. Let a(h) = p*k(h) + z*m(h). Factor a(v).
-4*v**2*(v - 2)
Let l = 3105 - 3101. Let y(h) be the second derivative of 0*h**2 - 1/48*h**l + 1/8*h**3 - 3*h + 0. Find i, given that y(i) = 0.
0, 3
Let g(l) be the third derivative of l**8/840 + l**7/105 - l**6/180 - l**5/15 - 269*l**3/6 + 45*l**2 + 2. Let y(x) be the first derivative of g(x). Factor y(j).
2*j*(j - 1)*(j + 1)*(j + 4)
Factor -124 - 74/3*b - 2/3*b**2.
-2*(b + 6)*(b + 31)/3
Find t, given that -203*t**2 - 148*t**3 + 87*t**4 - 144*t - 117*t**4 - 26*t**2 - 2*t**5 - 35*t**2 = 0.
-6, -2, -1, 0
Let f(b) be the second derivative of -b**5/10 + 157*b**4/6 - 1917*b**3 - 32805*b**2 + 55*b + 3. Factor f(z).
-2*(z - 81)**2*(z + 5)
Let y = -38 - -25. Let f(l) = -l**3 - 10*l**2 + 40*l + 17. Let b be f(y). Determine q, given that -12*q**b + 18*q**3 + 0 - 9/4*q - 15/4*q**2 = 0.
-1/4, 0, 3/4, 1
Let a = 677670 + -2710659/4. Determine n so that 63/4*n**2 - 75*n**3 + a*n**4 + 75*n - 21 = 0.
-1, 2/7, 1, 14
Let -2/11*s**4 + 2/11*s**2 + 0 + 4/11*s**3 - 4/11*s = 0. What is s?
-1, 0, 1, 2
Let y(w) be the second derivative of w**4/6 + 32*w**3/3 + 60*w**2 - 12*w - 27. Solve y(x) = 0.
-30, -2
Let z(w) be the first derivative of -w**4/8 - 55*w**3/6 - 52*w**2 - 102*w + 1461. Find a such that z(a) = 0.
-51, -2
Let y = 1287952 - 16743252/13. Solve 1922/13 + 2/13*t**2 + y*t = 0 for t.
-31
Let y = -427 - -430. Suppose -o - 7 = -y*s + 4, 20 = 5*o. Solve 312/5*g + 807/5*g**3 - 147/5*g**s + 873/5*g**2 + 36/5 + 63/5*g**4 = 0.
-1, -2/7, 3
Let d(u) be the first derivative of u**4/4 + 8*u**3/3 - 10*u**2 - 97*u - 581. Let i be d(-9). Determine j so that -2*j + 2/7*j**i + 24/7 = 0.
3, 4
Let j(a) = 9*a**3 + 2*a + 1. Let w(v) = 50*v**3 + 84*v**2 - 212*v + 150. Let g(m) = 6*j(m) - w(m). Determine p so that g(p) = 0.
1, 2, 18
Let 0 + 27817*c**2 + 0 + 28278*c**2 - 25*c**5 + 210*c**4 - 505*c**3 - 100*c - 55675*c**2 = 0. What is c?
0, 2/5, 1, 2, 5
Let n(t) = -t**3 - 68*t**2 - 62*t + 335. Let s be n(-67). Let d(m) be the third derivative of s*m - 20*m**2 - 1/2*m**4 - 5/2*m**3 + 0 + 1/20*m**5. Factor d(g).
3*(g - 5)*(g + 1)
Let n be -33*1 - (-147735)/4355. S