= 0.
-77, 2
Suppose -388*q + 267*q + 236 = -127. Let j be (-2)/(-7) + 2/(-7). Solve -4/3*o + 2*o**2 - 2/3*o**4 + j*o**q + 0 = 0.
-2, 0, 1
Let s(q) be the second derivative of -7/18*q**4 - 2/9*q**3 - 2/15*q**5 - 43*q + 29/2*q**2 + 0. Let b(t) be the first derivative of s(t). Factor b(m).
-4*(m + 1)*(6*m + 1)/3
Determine d so that -7322*d - 3*d**3 - 10*d**2 - d**3 - 7318*d + 3 + 9 + 14642*d = 0.
-2, -3/2, 1
Let n(j) = 149*j**5 - 1690*j**4 + 6340*j**3 - 6965*j**2 - 2880*j - 251. Let x(l) = -l**5 + 2*l**4 + l**2 - 1. Let w(k) = n(k) + 5*x(k). Factor w(y).
4*(y - 4)**3*(6*y + 1)**2
Let x(w) be the third derivative of -w**8/336 + 47*w**7/105 + 4*w**6/5 - 47*w**5/30 - 95*w**4/24 - 91*w**2 - w + 15. Factor x(h).
-h*(h - 95)*(h - 1)*(h + 1)**2
Let v(a) be the second derivative of -5/2*a**3 + 17/2*a**2 - 1/6*a**4 + 0 + 11*a. Let p(j) = 2*j**2 + 16*j - 18. Let r(f) = 3*p(f) + 2*v(f). Factor r(n).
2*(n - 1)*(n + 10)
Let l(p) = -p**3 + 15*p**2 + 20*p - 59. Let z be l(16). Determine q, given that -q - 4*q + 0*q - 6*q**3 + 8*q + 0*q**z + 3*q**5 = 0.
-1, 0, 1
Let f(k) be the first derivative of -16/9*k**3 + 17/3*k**2 - 49 - 20/3*k + 1/6*k**4. Factor f(u).
2*(u - 5)*(u - 2)*(u - 1)/3
Suppose 40 = 3*v - r, -25 = 6*v - 9*v + 4*r. Let l be (-10 + v)/1 + -2. What is u in -u**l - 2/3 - 10/3*u**2 - 3*u = 0?
-2, -1, -1/3
Factor 5/2*j**4 - 15/2*j**2 - 35/2*j**3 + 35 + 95/2*j.
5*(j - 7)*(j - 2)*(j + 1)**2/2
Let u = -99980 - -99982. Suppose 130/3*k**3 - 1300*k - 545/3*k**u - 5/3*k**4 - 1500 = 0. Calculate k.
-2, 15
Factor -8 + 2/9*d**4 + 16/3*d + 10/9*d**2 - 4/3*d**3.
2*(d - 3)**2*(d - 2)*(d + 2)/9
Let g(i) be the first derivative of i**7/168 - i**6/72 - i**5/12 - 30*i**3 - 74. Let x(f) be the third derivative of g(f). Solve x(p) = 0.
-1, 0, 2
Suppose -5*c - 20 + 30 = 0. Factor -9*b**2 + b - 16 - 49 + 5*b**c - 15 + 47*b.
-4*(b - 10)*(b - 2)
Determine w, given that w**4 - 232311*w + 856551*w - 663255 + 6*w**4 - 2*w**4 + 38250*w**2 + 760*w**3 = 0.
-51, 1
Let l(g) be the first derivative of 5 - 3/16*g**4 + 0*g**2 + 0*g + 1/2*g**3. Factor l(p).
-3*p**2*(p - 2)/4
Let v(w) = 11*w**3 - 3*w**2 + w - 5. Let d(j) = 2*j**3 - j**2 - 1. Let f be 440/132*(1 + 2). Let g(p) = f*d(p) - 2*v(p). Factor g(r).
-2*r*(r + 1)**2
Let c(b) be the second derivative of -b**8/3360 - b**7/630 + b**6/45 - 209*b**4/12 + 8*b + 1. Let f(j) be the third derivative of c(j). Solve f(d) = 0 for d.
-4, 0, 2
Let k(j) be the third derivative of j**5/630 + j**4/14 + 80*j**3/63 + 660*j**2. Factor k(t).
2*(t + 8)*(t + 10)/21
Let c(a) = a**2 + 112*a + 2180. Let i be c(-25). Let x(m) be the second derivative of 0*m**2 - 5/4*m**4 - 3/20*m**i + 0 + 0*m**3 + 11*m. Factor x(k).
-3*k**2*(k + 5)
Suppose 4*n - 95 = h, 5*n - h - 47 = 3*n. Let b be 23/2 - n/(-16). Factor 12*l**2 - 4 + b - 9*l - 9 - 3*l**3.
-3*l*(l - 3)*(l - 1)
Let z = -55 + 57. Suppose -5*r = -7*r + b - z, 3*r = b - 2. Solve -2/5*w**5 + 2/5*w**3 + 2/5*w**2 + r*w - 2/5*w**4 + 0 = 0 for w.
-1, 0, 1
Let g = -14227/348 - -1188/29. Let l(b) be the third derivative of 0 + 5/6*b**4 - 10/3*b**3 + 0*b + 40*b**2 - g*b**5. Solve l(o) = 0.
2
Let h = -4/1771 - -9871/1771. Let -6*a + h + 3/7*a**2 = 0. What is a?
1, 13
Let n be 30/4*12/(-18). Let a be -5 + 9 + n/((-15)/(-6)). Solve -4/25 - 2/5*o - 8/25*o**a - 2/25*o**3 = 0.
-2, -1
Let n be (6/15*3)/(103/(7210/56)). Determine g, given that 1/2*g**4 + 0 + n*g - 3/2*g**3 - 1/2*g**2 = 0.
-1, 0, 1, 3
Let w(p) be the first derivative of 560/3*p**2 + 10 - 196/9*p**3 - 1600/3*p. Determine y, given that w(y) = 0.
20/7
Let u be (-8)/(32/6) + (-9)/(-2). Solve 28*n**3 + 2*n**2 - u*n + n - 10*n**2 - 2*n - 16*n**4 = 0 for n.
-1/4, 0, 1
Let t(r) be the third derivative of -r**8/1008 + 4*r**7/315 - r**6/72 - 7*r**5/90 + 50*r**2 - 26*r. Find a, given that t(a) = 0.
-1, 0, 2, 7
Let p(l) be the first derivative of l**5/2 + 3*l**4/16 - 5*l**3/6 - 3*l**2/8 - 1057. Factor p(v).
v*(v - 1)*(v + 1)*(10*v + 3)/4
Determine o so that 15/4*o - 3/4*o**2 + 375 = 0.
-20, 25
Let h(d) be the second derivative of d**4/36 - 5*d**3/18 - 25*d**2 + 2157*d. Factor h(z).
(z - 15)*(z + 10)/3
Let t = 30847/123356 + -2/30839. Let v(y) be the second derivative of t*y**4 + 0 - 19*y + 5/2*y**3 - 9*y**2. Factor v(m).
3*(m - 1)*(m + 6)
Find h such that 268/3*h + 40*h**3 - 28 - 296/3*h**2 - 4/3*h**4 - 4/3*h**5 = 0.
-7, 1, 3
Suppose -3*c + 13 = -d, -3*c - 2 + 7 = d. Suppose 4*s = -4*u, 4*s - c*u = -8*u - 4. Factor -32*k - 128/7 + s*k**3 - 2/7*k**4 - 66/7*k**2.
-2*(k - 8)**2*(k + 1)**2/7
Let -2408*o**2 + 778 - 197*o + 165*o + 2407*o**2 - 355*o = 0. What is o?
-389, 2
Let h be 24*1/2 - 5. Determine x so that -3*x**5 + 9 - 3*x - h*x**4 + 22*x**2 - 8*x**3 + x**5 + 33*x + 4*x**5 = 0.
-1, -1/2, 3
Let -1980/7*i**4 + 0 + 6768/7*i**2 + 5616/7*i - 75/7*i**5 - 528/7*i**3 = 0. Calculate i.
-26, -6/5, 0, 2
Let x = 5217 + -5213. Let m(k) be the first derivative of 3/5*k**5 + 2*k**3 + 3*k**x - 6*k**2 - 9*k - 12. Determine r so that m(r) = 0.
-3, -1, 1
Let z(i) = -22*i**2 - 6*i + 13. Let d be z(-4). Let r be 56/d*6/(-8)*5. Factor 0*l**2 + 0*l + 2*l**4 - 4/3*l**3 - r*l**5 + 0.
-2*l**3*(l - 2)*(l - 1)/3
Let d(w) be the first derivative of -175 - 4*w + 8/9*w**3 - 1/3*w**2 - 1/6*w**4. Determine r, given that d(r) = 0.
-1, 2, 3
Let y(v) be the first derivative of 45/2*v**2 - 3/20*v**5 - 3/8*v**4 - 22 + 0*v - 1/40*v**6 - 1/2*v**3. Let t(k) be the second derivative of y(k). Factor t(l).
-3*(l + 1)**3
Let b = 5627/16 - 39293/112. Let 24/7 + b*j - 3/7*j**2 = 0. What is j?
-2, 4
Let i(l) be the first derivative of -l**4/6 + 10*l**3/9 - 2*l**2 + 2496. Determine q so that i(q) = 0.
0, 2, 3
Let m(s) be the third derivative of s**9/26880 - s**8/3840 + s**7/3360 + 67*s**5/60 + 40*s**2. Let f(g) be the third derivative of m(g). Factor f(v).
3*v*(v - 2)*(3*v - 1)/4
Let p(q) be the second derivative of -q**9/22680 - q**8/1680 + q**7/3780 + q**6/180 + 11*q**4/4 - 82*q. Let y(v) be the third derivative of p(v). Factor y(k).
-2*k*(k - 1)*(k + 1)*(k + 6)/3
Let i(r) = -r**3 - 5*r**2 - r + 3. Let a be i(-5). Let m be a*1 + -7 + 3. Factor -11*c**3 + 13*c**3 - 4*c**2 + 0*c**5 + 6*c**m - 2*c**2 - 4*c + 2*c**5.
2*c*(c - 1)*(c + 1)**2*(c + 2)
Let i(a) = a**3 + 15*a**2 + 51*a + 15. Let b be i(-9). Let c be ((-36)/b)/(312/(-392)). Solve 12/13*m + 2/13*m**2 - c = 0.
-7, 1
Let -21*n**2 - 14*n**3 + 540*n + 740 - 285*n + 43 - 4*n**3 + 105*n = 0. Calculate n.
-3, 29/6
Let u = -55801/243 - 8/243. Let w = 231 + u. Solve -w*j + 0 + 6*j**2 = 0 for j.
0, 2/9
Let u(j) be the second derivative of 0 + 0*j**2 + 1/135*j**6 + 16/27*j**3 + 41*j + 0*j**5 - 2/9*j**4. Factor u(v).
2*v*(v - 2)**2*(v + 4)/9
Let k = 2/458027 + 4580264/1374081. Suppose 124/3*a**2 - 52/3 + 82/3*a - k*a**3 = 0. Calculate a.
-1, 2/5, 13
Suppose -29*c - 2*c + 2945 = 0. Suppose -186*z**2 + 18*z + c*z**2 + 89*z**2 - 40 = 0. What is z?
4, 5
Let h(s) be the first derivative of -104 - 1/36*s**6 + 0*s + 1/3*s**2 + 4/9*s**3 - 1/15*s**5 + 1/8*s**4. Let h(w) = 0. What is w?
-2, -1, 0, 2
Let a(m) be the first derivative of 2/21*m**3 - 2/21*m**6 - 2/35*m**5 + 3/14*m**4 + 0*m - 1/7*m**2 + 74. Solve a(g) = 0 for g.
-1, 0, 1/2, 1
Factor -w**3 + 340*w**2 + 172 + 170 - 276*w - 290*w + 2*w**3 - 117*w.
(w - 1)**2*(w + 342)
Let k(b) = -2 - 1131*b**2 - 54*b + 1137*b**2 + 4. Let d be k(9). Factor -72/5 - 2/5*f**d - 24/5*f.
-2*(f + 6)**2/5
Let a(j) be the first derivative of -75*j**4/4 + 895*j**3/3 + 1035*j**2/2 + 65*j - 8118. Suppose a(s) = 0. What is s?
-1, -1/15, 13
Let q(n) be the second derivative of -n**5/10 + 8*n**4/3 + 77*n**3/3 + 60*n**2 + 3*n + 1079. Find c such that q(c) = 0.
-3, -1, 20
Let o(l) be the first derivative of -l**5/25 + 9*l**4/20 + 4*l**3/5 - 16*l**2 + 4472. Let o(w) = 0. What is w?
-4, 0, 5, 8
Let t(i) be the third derivative of 5*i**8/336 + i**7/14 - i**6/24 - i**5/4 - 3*i**2 - 72*i. Solve t(s) = 0.
-3, -1, 0, 1
Factor 4471*l - 1956*l**2 - 8614225 + 1399*l + 1955*l**2.
-(l - 2935)**2
Let p(f) be the second derivative of -f**6/24 + 87*f**5/80 + 9*f**4/8 - 654*f. Factor p(w).
-w**2*(w - 18)*(5*w + 3)/4
Find f such that -20/3*f**2 - 16/9*f**3 + 448/9*f + 490/9 + 2/9*f**4 = 0.
-5, -1, 7
Let u(b) be the first derivative of 89 + 56/11*b - 8/33*b**3 - 111/11*b**2. Factor u(m).
-2*(m + 28)*(4*m - 1)/11
Let g be 3*(175/161 + 6/(-69)). Let c(h) be the first deriv