/4, 2/3
Find d such that 0 + 0*d**2 - 54/5*d**3 + 2/5*d**5 + 0*d - 52/5*d**4 = 0.
-1, 0, 27
Let s(h) be the first derivative of -91*h**6/3 + 8*h**5/5 + 91*h**4 - 16*h**3/3 - 91*h**2 + 8*h - 482. Solve s(o) = 0.
-1, 4/91, 1
Let -1696*z**2 - 100983 + 216809 - 4*z**5 - 856*z**3 + 2944*z - 106098 - 116*z**4 = 0. What is z?
-19, -4, 2
Let w(p) = 25*p**2 - 755*p + 1080. Let m(x) = 145 - 2*x**2 - 28*x - 2*x**2 - 105 + 5*x**2. Let t(l) = -55*m(l) + 2*w(l). Suppose t(h) = 0. What is h?
2, 4
Let t(n) be the second derivative of 9*n**5/50 + 103*n**4/5 - 71*n**3/5 - 414*n**2/5 + n - 2504. Determine d so that t(d) = 0.
-69, -2/3, 1
Let u(g) be the second derivative of g**8/56 + 11*g**7/105 + g**6/10 + 6*g**2 + 69*g - 2. Let q(t) be the first derivative of u(t). Let q(l) = 0. What is l?
-3, -2/3, 0
Let b(s) = -s**3 - 10*s**2 - s. Let l be b(-10). Suppose 0 = -0*h - 5*h + l. What is i in -52*i**2 + 4 + 51*i**h - 3 = 0?
-1, 1
Let i(p) = -4*p**3 + 123*p**2 - 479*p + 498. Let l(w) = w**3 - 5*w + 2. Let z(t) = -2*i(t) - 10*l(t). What is y in z(y) = 0?
-127, 2
Let c(b) be the second derivative of b**7/14 + 2*b**6 + 33*b**5/10 - 195*b**4 + 1521*b**3/2 - 1629*b. Factor c(a).
3*a*(a - 3)**2*(a + 13)**2
Let g = -232 - -728. Suppose -5*v + 3*v + g = 0. Factor -52*c - v*c**2 - 21*c**5 - 47*c**5 + 73*c**4 - 341*c**4 - 392*c**3 + 4.
-4*(c + 1)**4*(17*c - 1)
Let r(g) be the first derivative of -g**5 - 25*g**4 - 95*g**3/3 - 2286. What is i in r(i) = 0?
-19, -1, 0
Let i be (-9)/(-3)*(-6)/(-9). Let r(s) be the first derivative of -15*s**4 + 5 - 2*s**i + 32*s**4 - 16*s**4. Factor r(n).
4*n*(n - 1)*(n + 1)
Let o(d) be the third derivative of 57*d**2 - 4/15*d**3 + 152/525*d**7 - 2 + 0*d - 29/100*d**6 + 6/35*d**8 + 11/20*d**4 - 29/75*d**5. What is q in o(q) = 0?
-1, 1/4, 4/9
Let f(l) be the first derivative of 5*l**4/4 - 190*l**3/3 + 350*l**2 - 680*l + 679. Factor f(s).
5*(s - 34)*(s - 2)**2
Let o = 96141/2 + -48068. Factor -1/2*p**3 - o*p**2 + 9/2 - 3/2*p.
-(p - 1)*(p + 3)**2/2
Let q = 4177 + -133663/32. Let n(f) be the third derivative of -1/20*f**5 + 0*f + 27*f**2 - q*f**4 - 1/160*f**6 + 0 + 3/4*f**3. Factor n(t).
-3*(t - 1)*(t + 2)*(t + 3)/4
Let n(l) = -11*l**4 + 66*l**3 + 1079*l**2 - 264*l - 4344. Let r(x) = 2*x**4 + x**2 - 2. Let u(g) = -n(g) - 6*r(g). Factor u(a).
-(a - 2)*(a + 2)*(a + 33)**2
Let i = -321 + -105. Let u = i - -428. Solve -8/9*a + 2/9*a**u - 10/9 = 0.
-1, 5
Let t be (-210)/(-9)*-3 + -3 + 1. Let r = -71 - t. What is a in 75*a**3 - 27*a + 2 + 45*a**2 - r + 2 = 0?
-1, 1/5
Let i(o) be the first derivative of -3*o**4/4 + 1787*o**3 - 2397705*o**2/2 + 2392347*o + 842. What is y in i(y) = 0?
1, 893
Suppose 3*j = -x + 20, 2*x + 40*j = 36*j + 28. Suppose 2/5*s**4 - 4*s + 6/5 + 24/5*s**x - 12/5*s**3 = 0. What is s?
1, 3
Let s(m) be the second derivative of -m**5/4 + 545*m**4/6 - 2150*m**3/3 + 2140*m**2 + 7310*m. Factor s(r).
-5*(r - 214)*(r - 2)**2
Solve 14*b**4 - 48*b**4 - 74*b**3 + 114*b**3 - 116*b + 8*b + 204*b**3 + 570*b**2 = 0 for b.
-2, 0, 3/17, 9
Let w be (-17)/35*8/6. Let o = w - -46/35. Determine c, given that 0 - o*c - 4/3*c**2 = 0.
-1/2, 0
Solve -499*c**4 - 712*c**3 - 1164*c**2 - 435 + 8*c**5 + 900*c + 1429*c**4 + 669 - 196*c = 0 for c.
-117, -1, -1/4, 1
Suppose -62*f = -49*f + 338. Let z be -13*3/7 - 156/f. Let -48/7 - 27/7*s**2 - 72/7*s - z*s**3 = 0. Calculate s.
-4, -1
Let i(n) = -2*n**2 - 32*n + 13. Let s(x) be the first derivative of x**3 + 31*x**2 - 25*x - 35. Let u(g) = -7*i(g) - 3*s(g). Factor u(j).
(j + 8)*(5*j - 2)
Suppose 19*b = 5*b. Suppose 5*c - 2*v = -b*v + 40, -c + 4*v + 26 = 0. Let 10*w**3 - 12*w + 0*w**2 + 11*w**3 - c*w**4 - 7*w**2 - 5*w**2 = 0. Calculate w.
-1/2, 0, 2
What is x in 1024/7 - 60/7*x**2 + 2/7*x**3 + 384/7*x = 0?
-2, 16
Let r = -189 - -192. Suppose 6*x - 5*x**3 + x + x + 16*x**r - 10*x**2 - 9*x**3 = 0. What is x?
0, 1, 4
Let b be ((-6)/(-8))/(5/1420). Suppose -15*d + 222 + b = 0. Let 30 - 3*i**2 + d*i - 75 - 77*i = 0. What is i?
-15, -1
Factor -7602*y + 5479*y**2 - 2731*y**2 - 2895*y**2 - 98283.
-3*(7*y + 181)**2
Let b(h) be the third derivative of -h**6/480 - h**5/3 - 123*h**4/32 + 75*h**3/4 - 944*h**2 - 2*h + 3. Factor b(k).
-(k - 1)*(k + 6)*(k + 75)/4
Let b(c) = -c**3 + 17*c**2 - 32*c + 52. Let m be b(15). Let t(s) be the third derivative of 0 - m*s**2 + 0*s - 2*s**3 - 1/20*s**5 - 1/2*s**4. Factor t(w).
-3*(w + 2)**2
Suppose -4*s - 22 = -30. Let -24 + 3*o - 14*o**4 + o + 38*o**s + 16*o**3 - 11*o - 9*o = 0. Calculate o.
-1, -6/7, 1, 2
Let q(d) = 3*d**2 - 20*d - 5. Let m be q(7). Find i such that -599*i**2 + 132*i + 1202*i**m - 600*i**2 = 0.
-44, 0
Let w = 1577/3176 + 11/3176. What is k in w*k**2 - 9*k - 19/2 = 0?
-1, 19
Let a(w) be the third derivative of w**6/160 + 77*w**5/80 + 19*w**4/8 - 2*w**2 + 12. Let a(c) = 0. What is c?
-76, -1, 0
Factor -1/7*x**2 + 814/7 + 405/7*x.
-(x - 407)*(x + 2)/7
Solve 804/5*m + 2/5*m**2 + 80802/5 = 0 for m.
-201
Let l(j) be the first derivative of 5*j**3/3 + 65*j**2/2 - 150*j + 1527. What is w in l(w) = 0?
-15, 2
Let t(i) be the third derivative of -i**5/15 + 610*i**4/3 - 1624*i**3 + 557*i**2. Determine w so that t(w) = 0.
2, 1218
Suppose -4*h = 5*k - 31, -2*k + 2*h = -0*k + 2. Suppose k*m = -3*m + 78. Factor 41*p**2 - 15*p - 10 + m*p**2 - 29*p**2.
5*(p - 1)*(5*p + 2)
Let z(a) = 129*a - 4*a**4 - 2*a**4 + 21*a**2 - 3*a**3 - 141*a. Let o(c) = 19*c**4 + 10*c**3 - 64*c**2 + 35*c. Let p(w) = -6*o(w) - 17*z(w). Factor p(k).
-3*k*(k - 1)*(k + 2)*(4*k - 1)
Let x(d) be the third derivative of 0*d**3 + 0*d - 289*d**2 - 1/12*d**6 + 0 + 5/4*d**4 + 5/12*d**5 - 1/42*d**7. Factor x(q).
-5*q*(q - 2)*(q + 1)*(q + 3)
Suppose -d + 2 = -2*p + 13, 5*d - 17 = -2*p. Let i(k) = k**2 - 7*k + 8. Let z be i(p). Factor 42*c**2 - 1 + 35*c**z - 26*c - 55*c**2 + 5.
2*(c - 1)*(11*c - 2)
Let p(t) be the first derivative of -2*t**5/5 - 39*t**4/2 - 50*t**3 - 37*t**2 - 1309. Find i, given that p(i) = 0.
-37, -1, 0
Let b(l) be the first derivative of -4*l**3/21 + 2402*l**2/7 + 9624*l/7 + 2330. Let b(f) = 0. What is f?
-2, 1203
Let r(z) be the first derivative of -z**3/12 + 883*z**2/8 + 221*z + 3848. Factor r(q).
-(q - 884)*(q + 1)/4
Let h be (9/48 + 0)/(((-160)/(-11520))/((-1)/(-6))). Suppose 15/4*a**2 - 3/2 - h*a = 0. What is a?
-2/5, 1
Suppose 51 = 220*a - 203*a. Determine x, given that 18/7*x**5 + 9*x**a + 0 - 57/7*x**4 - 27/7*x**2 + 3/7*x = 0.
0, 1/6, 1
Suppose 22110 = -6*o + 3*o + 22116. Determine q, given that -1624/3*q**o + 43732/9*q + 172/9*q**3 - 2/9*q**4 + 48778/9 = 0.
-1, 29
Suppose 0 = 12*h - 8109 - 2583. Let y = -1781/2 + h. Solve 1/2*s**5 + s - 3/2*s**3 + 1/2*s**4 - y*s**2 + 0 = 0 for s.
-2, -1, 0, 1
Factor 9/2*h**3 + 3/4*h**4 + 3*h + 27 - 81/4*h**2.
3*(h - 2)**2*(h + 1)*(h + 9)/4
Let x(n) be the third derivative of -n**6/60 - 38*n**5/5 + 691*n**4/12 - 154*n**3 + 97*n**2 - 5*n - 4. Let x(j) = 0. Calculate j.
-231, 1, 2
Let t be 7/(84/(-256)) - 5/(-15). Let d = t + 25. Factor -12*a**2 - 12*a**4 + 8*a**d - 16*a**3 - 4*a + 4*a.
-4*a**2*(a + 1)*(a + 3)
Let n(j) = 96*j**2 + 958*j + 848. Let c be n(-9). Let k be 2/3 - (-7)/3. Factor 0 - 1/3*g**k + g**c + 0*g.
-g**2*(g - 3)/3
Suppose 0 = 4*a + 22*s - 27*s - 32, 0 = -5*a + 4*s + 31. What is g in -4*g + 4*g**5 - 32 - 16*g**4 - 549*g**a - 12*g + 40*g**2 + 553*g**3 = 0?
-1, 2
Let j(h) be the first derivative of -220*h + 5/4*h**4 + 120*h**2 - 25*h**3 + 145. Factor j(k).
5*(k - 11)*(k - 2)**2
Let i(s) = -s**5 + s**4 + s**3 - 1. Let q(g) = -12*g**5 - 150*g**4 + 802*g**3 - 1400*g**2 + 1082*g - 322. Let p(r) = 14*i(r) - q(r). Let p(j) = 0. Calculate j.
1, 2, 77
Let r = -441 + 436. Let f be r/3*(-7 + (-319)/(-55)). Suppose 4/11 - 4/11*o**4 + 14/11*o + 12/11*o**f - 2/11*o**3 = 0. Calculate o.
-1, -1/2, 2
Factor 9392*c + 340 - 17*c**2 + c**2 - 9644*c.
-4*(c + 17)*(4*c - 5)
Let o be 3*(-10)/60 + (-2)/8*-2. Factor o + 15/4*g - 3/4*g**3 - 3*g**2.
-3*g*(g - 1)*(g + 5)/4
Let d(i) = -24*i + 506. Let l be d(21). Suppose 7*a - 3*a**4 - 25916*a**3 + 2*a**l + a**4 + 4*a**4 - 4 + 25908*a**3 + a**5 = 0. Calculate a.
-4, -1, 1
Factor 4/5*p - 4/5*p**3 + 4/5*p**2 - 4/5.
-4*(p - 1)**2*(p + 1)/5
Suppose 0 = -2*l - 4*s - 10 + 4, -5*s = -l + 18. Factor -6*o + 75*o**4 + 2*o + 411*o**3 + 3*o**5 + 4*o + 432*o**2 + 93*o**l.
3*o**2*(o + 1)*(o + 12)**2
Let f = -176452 + 529586/3. Suppose -86*v**3 - 32/3*