ose -171/2*f**4 - 497/2*f**2 + 334 + 336*f - 671/2*f**3 - 1/2*f**5 = 0. What is f?
-167, -2, -1, 1
Let p(o) = -12*o**3 + 339*o**2 + 475*o + 160. Let h(t) = -110*t**3 + 3050*t**2 + 4274*t + 1440. Let f(z) = 6*h(z) - 52*p(z). Factor f(j).
-4*(j - 20)*(3*j + 2)**2
Let j be (600/240)/((-5)/(-2)). Suppose w = 2*u - 5, 2 = w - j. Suppose 5/3*y**u - 20/3*y**3 + 20/3*y - 20/3 + 5*y**2 = 0. What is y?
-1, 1, 2
Determine h so that 6397*h**3 - 393*h**2 - 47*h - 6409*h**3 - 331*h + 3*h**4 = 0.
-9, -1, 0, 14
Let r(g) be the first derivative of 1/4*g**4 + 34 - 5/3*g**3 + 5*g - 1/2*g**2. Find d such that r(d) = 0.
-1, 1, 5
Suppose -21*f = 253 - 673. Let w be (13/(-5) - (17 - f))*4. Let -w + 36*d**3 - 8*d - 162/5*d**4 + 6*d**2 = 0. What is d?
-1/3, -2/9, 2/3, 1
Solve -172*r**2 - 20276*r - 3484*r + 0*r**3 - 3*r**3 - 5572 + 703*r**2 + 28804 = 0.
1, 88
Let k(t) be the first derivative of 3/17*t**2 + 0*t + 2/51*t**3 - 80. Factor k(a).
2*a*(a + 3)/17
Let f(j) be the third derivative of 1083*j**5/80 + 95*j**4/16 + 25*j**3/24 + 2*j**2 - 125*j. Factor f(h).
(57*h + 5)**2/4
Let u(l) = -l - 9. Let n be u(-11). Let g be ((-12285)/162 - -42) + 34. Let 7/6 - g*c**n - c = 0. Calculate c.
-7, 1
Suppose 1547 = 2*w + 11*w. Let 21*t - w*t**4 - 5*t**5 - 16*t + 109*t**4 + 10*t**2 = 0. What is t?
-1, 0, 1
Let i(u) be the third derivative of 2*u**7/105 + 7*u**6/30 + 2*u**5/5 - 25*u**2 + 23. Factor i(z).
4*z**2*(z + 1)*(z + 6)
Let a(f) = 2*f**2 - f + 1. Let g(s) = -1. Let c(v) = -16*v**2 + v - 4. Let t(z) = c(z) + 3*g(z). Let o(k) = -14*a(k) - 2*t(k). Let o(h) = 0. Calculate h.
-3, 0
Let x = -2078 + 2074. Let i(j) = -j - j + 3*j**2 - j. Let l(h) = 13*h**2 - 13*h. Let g(f) = x*l(f) + 18*i(f). What is p in g(p) = 0?
0, 1
Let y = -165 + -53. Let q = y - -656/3. Find r, given that -4/3*r**2 - 2/3*r**5 - q*r + 2/3 + 2/3*r**4 + 4/3*r**3 = 0.
-1, 1
Let r(b) be the first derivative of b**6/14 - 264*b**5/35 + 1452*b**4/7 - 138. What is u in r(u) = 0?
0, 44
Let d = -209 + 213. Let x(o) be the third derivative of 0*o - 1/30*o**5 + 1/336*o**8 - 1/6*o**3 - 4*o**2 - 1/8*o**d + 0 + 1/60*o**6 + 1/70*o**7. Factor x(a).
(a - 1)*(a + 1)**4
Let j(g) be the second derivative of -g**6/180 - 4*g**5/45 + 19*g**4/36 - 10*g**3/9 + 55*g**2/2 - 64*g. Let n(x) be the first derivative of j(x). Factor n(r).
-2*(r - 1)**2*(r + 10)/3
Let y(w) be the first derivative of w**3 - 120*w + 191 + 117/2*w**2. Factor y(v).
3*(v - 1)*(v + 40)
Let h(u) be the third derivative of u**5/330 + 25*u**4/132 + 28*u**3/11 - 1505*u**2. Factor h(v).
2*(v + 4)*(v + 21)/11
Let r(w) be the second derivative of -w**6/15 + 73*w**5/10 - 203*w**4 - 4180*w**3/3 - 2888*w**2 + 1162*w. Factor r(x).
-2*(x - 38)**2*(x + 1)*(x + 2)
Let h(a) = 23063*a + 23063. Let t be h(-1). Determine b so that b**2 + t + 4/5*b**3 + 2/5*b + 1/5*b**4 = 0.
-2, -1, 0
Let m(h) = 2*h**2 + 3*h - 18. Let w be m(-4). Find j such that 35 - 7*j**2 - 23*j**2 + 1 - 2*j**w - 84*j = 0.
-3, 3/8
Let h(n) be the second derivative of -n**5/20 + n**4/12 - n**3/6 + 2*n**2 - 21*n. Let l be h(0). Factor 0*t - t**5 - 2*t + 0*t**5 + 4*t**2 - 4*t**l + 3*t**5.
2*t*(t - 1)**3*(t + 1)
Let h(r) = r**2 - 127*r + 3729. Let x be h(46). Factor 0 - 1/4*d**4 + d**x + 1/2*d - 5/4*d**2.
-d*(d - 2)*(d - 1)**2/4
Let u be (-21)/(-42)*(2 + 1012). What is x in -24*x**3 - 5*x**4 - 72 - 112*x**2 + 4*x**5 - u*x + 336*x + 29*x**4 + 351*x = 0?
-6, -3, 1
Let n(v) = 2*v - 9. Let f(l) = 2*l - 8. Let g(i) = -7*f(i) + 6*n(i). Let j be g(0). Factor 43*s - 96*s**3 - 7*s - 12 - 9*s**j + 81*s**3.
-3*(s - 1)*(s + 2)*(5*s - 2)
Let x be (77/21 - 1) + (-20 - -19). Find b such that 7/3*b - 13/3*b**2 + x*b**3 + 1/3*b**4 + 0 = 0.
-7, 0, 1
Suppose 2*d = -4*a + 170, 0 = 2*d - 0*d - 5*a - 188. Let h = d + -87. Factor -39 + 6*z**h + 15*z - 11*z**2 + 29.
-5*(z - 2)*(z - 1)
Solve -62*x**2 + 11 - 1 + 5 + 270*x + 15*x**3 + 7*x**2 - 245*x = 0.
-1/3, 1, 3
Suppose 20 = 3*k + k. Let w(o) = -5*o**2 + 5. Let s(i) be the second derivative of -i**4/4 + 3*i**2/2 - 8*i - 3. Let r(u) = k*s(u) - 2*w(u). Factor r(x).
-5*(x - 1)*(x + 1)
Let j = -852453 + 1704907/2. Solve -2/3*d - 2*d**2 + 0 - j*d**3 + 5/6*d**4 = 0.
-1, -2/5, 0, 2
Let v(x) be the third derivative of 2*x - 1/1470*x**7 + 1/105*x**5 + 0 + 97*x**2 + 1/42*x**4 - 1/840*x**6 + 0*x**3. Factor v(w).
-w*(w - 2)*(w + 1)*(w + 2)/7
Let b(u) be the second derivative of -3*u**5/20 - 9*u**4/4 + 149*u**3 - 828*u**2 + 5292*u. Factor b(y).
-3*(y - 12)*(y - 2)*(y + 23)
Suppose w - 41 = 5*y, 3*y = w - y - 36. Let g be -7 + 3 - (0 - w). Factor g*u**2 + 15*u**2 - 4 - 23*u**2.
4*(u - 1)*(u + 1)
Let l(f) = -f**3 + 16*f**2 + 17*f + 128. Let i be l(17). Let r = -507/4 + i. Solve 1/4*w**2 + 0 - r*w = 0.
0, 5
Let m = -3513 - -3513. Let j(u) be the first derivative of 0*u + u**3 + m*u**2 + 1/2*u**6 + 9/5*u**5 + 9/4*u**4 - 1. Factor j(h).
3*h**2*(h + 1)**3
Let z = -18341/3 + 55031/9. Let -2/9*c**2 + 2/9 - 8/9*c**3 + z*c = 0. What is c?
-1, -1/4, 1
Factor 72*z**2 + 364/5 - 2/5*z**3 + 726/5*z.
-2*(z - 182)*(z + 1)**2/5
Suppose 645 = 2*s + 631, 2*s - 10 = 2*u. Factor 4/5*i**3 + 9/5*i**u + 2/5*i + 0.
i*(i + 2)*(4*i + 1)/5
Let j(z) be the second derivative of z**4/15 - 5192*z**3/15 + 3369608*z**2/5 + 895*z. Determine i so that j(i) = 0.
1298
Suppose 5*b = 5*r - 40, 138 = 5*r - 4*b + 103. Factor 0 - 9/2*y + 3/4*y**r - 15/4*y**2.
3*y*(y - 6)*(y + 1)/4
Let h(a) = 44*a**2 - 53*a + 6. Let t(j) = 250*j**2 - 319*j + 34. Let s(u) = 34*h(u) - 6*t(u). Factor s(y).
-4*y*(y - 28)
Let d(r) be the third derivative of r**5/120 - 107*r**4/48 + 53*r**3/6 + 45*r**2 + 3*r. Let d(x) = 0. What is x?
1, 106
Let d(m) = -14*m**3 + 6321*m**2 + 3163*m + 452. Let i be d(452). Factor i*w**3 + 0*w**2 + 1/5*w**4 + 0*w - 1/5*w**5 + 0.
-w**4*(w - 1)/5
Suppose 144 - 144 = 2*h. Suppose -4*o = 4*c + 4, 13*c - 9*c - 4*o - 20 = h. Find w such that 2/9*w**c + 4/9 - 2/3*w = 0.
1, 2
Let c(k) be the third derivative of -k**7/7980 + k**6/3420 + k**5/1140 - k**4/228 + 7*k**3/3 - 72*k**2. Let s(i) be the first derivative of c(i). Factor s(q).
-2*(q - 1)**2*(q + 1)/19
Let x be (-38)/3 + (66/(-9))/(-11). Let w be (-25)/x - ((-143)/39 + 5). Factor -1/4*f**2 + 0 + w*f.
-f*(f - 3)/4
Let s = 581 - 569. Factor 3*a**2 - s*a + 4*a - 6*a**2 + 0*a**2 - 7*a.
-3*a*(a + 5)
Factor -1599*s - 115*s**2 + 429*s**2 - 72*s**3 + 1200 + 3*s**4 + 238*s**2 + 159*s.
3*(s - 10)**2*(s - 2)**2
Let z(n) be the second derivative of -n**7/315 + 13*n**6/225 + 11*n**5/50 - 37*n**4/90 - 116*n**3/45 - 4*n**2 + 1937*n. Determine t, given that z(t) = 0.
-2, -1, 2, 15
Let z(f) be the first derivative of -605*f**6/24 + 539*f**5/4 - 2355*f**4/16 - 1735*f**3/12 + 370*f**2 - 240*f - 1381. What is q in z(q) = 0?
-1, 8/11, 1, 3
Let o be ((3/16)/(45/(-30) + 3))/((-18)/(-72)). Factor 23/2*c + 21 + o*c**2.
(c + 2)*(c + 21)/2
Let t be (-4176)/(-15) - 4/10. Let m = -832/3 + t. Determine u so that 2/3 - m*u**2 - 1/3*u + 1/3*u**3 = 0.
-1, 1, 2
Factor -606*b**3 - 161*b**2 - b - 91*b**4 - 71*b - 499*b**2 - 56*b**4.
-3*b*(b + 2)**2*(49*b + 6)
Let m = -297737/13804 + -5/1972. Let j = -21 - m. Suppose 0*c - j*c**4 + 0 + 12/7*c**3 + 0*c**2 = 0. Calculate c.
0, 3
Let p(s) = s**2 + 2*s - 3. Let t be p(1). Suppose t = 3*b - 24. Factor -11*h**4 + 20*h**4 + 20*h**2 - b*h + 7*h**4 + 44*h**3.
4*h*(h + 1)*(h + 2)*(4*h - 1)
Let x(k) be the third derivative of 5*k**8/336 - k**7/7 - 9*k**6/8 + 19*k**5/3 + 20*k**4 + 3602*k**2. Let x(l) = 0. Calculate l.
-4, -1, 0, 3, 8
Let q(m) = -31*m**3 - 7*m**2 + 428*m - 399. Let o(y) = -9*y**3 - y**2 + 8*y - 1. Let x(b) = 3*o(b) - q(b). Let x(j) = 0. What is j?
-11, 1, 9
Suppose -2*b**4 - 16000 + 76*b**3 + 3664*b - 2633*b - 1080*b**2 + 5769*b = 0. Calculate b.
8, 10
What is o in 192 - 28/3*o**2 - 232/3*o = 0?
-72/7, 2
Let i(h) = 93*h**2 + 4281*h + 140. Let v be i(-46). Solve 0 + 4/3*k**5 + 20/3*k**3 + 8/3*k**v + 0*k + 16/3*k**4 = 0 for k.
-2, -1, 0
Let j(t) = -605*t**2 - 8976*t - 34845. Let d(y) = -596*y**2 - 8976*y - 34846. Let v(f) = -3*d(f) + 2*j(f). Factor v(r).
2*(17*r + 132)**2
Let n(o) be the third derivative of -11*o**2 - 13/1155*o**7 + 1/20*o**6 - 41/330*o**5 + 0*o + 0 - 2/11*o**3 + 1/924*o**8 + 25/132*o**4. What is a in n(a) = 0?
1, 3/2, 2
Let s(g) = -2*g**3 + 3*g**2 + g. Let c(w) = 2*w**3 + 99*w**2 + 117*w - 224. Let u(o) = c(o) + 3*s(o). Factor u(n).
-4*(n - 28)*(n - 1)*(n + 