- 29*f**3/42 + 50*f**2/7 - 6*f + 1. Determine d, given that j(d) = 0.
4, 25
Let -846/7 - 120*s**3 - 2536/7*s - 2532/7*s**2 + 2/7*s**4 = 0. What is s?
-1, 423
Factor -552*k**4 - 340*k**3 + 578*k**2 + 11 - 11 - 332*k + 90*k**2 + 556*k**4.
4*k*(k - 83)*(k - 1)**2
Suppose 92*u = -39*u - 25*u + 624. Let h(o) be the second derivative of 0 + 1/8*o**3 + 1/16*o**u + 10*o + 1/80*o**5 + 1/8*o**2. Factor h(v).
(v + 1)**3/4
Let l(y) = 135*y**4 + 10235*y**3 - 150*y**2 - 100*y + 100. Let i(d) = 8*d**4 + 602*d**3 - 9*d**2 - 6*d + 6. Let g(m) = 50*i(m) - 3*l(m). Factor g(p).
-5*p**3*(p + 121)
Factor -1/3*v**3 - 20 + 3*v**2 + 16/3*v.
-(v - 10)*(v - 2)*(v + 3)/3
Factor -338*f + 422/5 + 8/5*f**2.
2*(f - 211)*(4*f - 1)/5
Let s(b) be the third derivative of -19/180*b**5 - 1/360*b**6 + 0*b**3 - 2*b - 17/36*b**4 + 0 - 101*b**2. Determine n, given that s(n) = 0.
-17, -2, 0
Let i = -1519 - -1523. Suppose 6*m + 5*u + i = 3*m, m = -2*u - 2. Factor 0 + 32*h**m + 256/3*h + 1/6*h**4 + 4*h**3.
h*(h + 8)**3/6
Suppose 7*c - 2315 = 1255. Suppose -7*x = -12*x + c. Solve -8 - x*w**2 - 12*w - 101*w**2 + 199*w**2 = 0 for w.
-2, -1
Suppose 4*y + 53 = f, 1236*f + y - 73 = 1219*f. Let 2/7*s**f - 6/7*s - 12/7*s**3 + 16/7*s**2 + 0 + 0*s**4 = 0. Calculate s.
-3, 0, 1
Determine v, given that 116*v**2 - 2*v**4 - 880 + 295 + 400*v + 296 + 289 - 46*v**3 = 0.
-25, -2, 0, 4
Factor 4/3*s**2 + 28/3 + 113/3*s.
(s + 28)*(4*s + 1)/3
Let i(z) = -6*z**2 - 33*z + 23. Let d be i(-6). Let t be (-18)/22 - 3*d/(-15). Factor 0*v + 0 + 0*v**3 + 0*v**2 + t*v**5 + 2/11*v**4.
2*v**4*(v + 1)/11
Let p be ((-20)/(-8))/((171/(-864))/19). Let c be p/(-1036) - (-64)/1184. Determine m, given that -c*m**5 - 8/7*m - 26/7*m**2 + 0 - 2*m**4 - 30/7*m**3 = 0.
-4, -1, 0
Let l(s) be the first derivative of s**4/2 - 34*s**3/3 + 16*s**2 - 1010. Factor l(z).
2*z*(z - 16)*(z - 1)
Let d(v) = -v**2 + 13*v + 55. Let s be d(16). Let f(m) = 4*m - 24. Let c be f(s). Factor 2*r**4 - 6 - c - 4*r**3 - 9*r - 16*r - 24*r**2 - 3*r.
2*(r - 5)*(r + 1)**3
Suppose -x + 16*t - 15*t = -6, 3*x + 6 = -3*t. Let b be -2*18/x*4/(-16). Factor -3/2*j**3 - 3 + 0*j**2 + b*j.
-3*(j - 1)**2*(j + 2)/2
Let b(u) = -76*u - 2. Let y be b(0). Let j be 1035/460 + 3/y. Let -j*f**2 - 15/2*f - 27/4 = 0. Calculate f.
-9, -1
Let f = 316 + -323. Let w(m) = -m**2 - 14*m - 46. Let p be w(f). Find v, given that -4/11*v**p + 2/11*v + 2/11*v**5 + 2/11 + 2/11*v**4 - 4/11*v**2 = 0.
-1, 1
Let k(r) = 4*r**3 - 120*r**2 - 4*r + 156. Let w(z) = -4*z**3 + 124*z**2 + 4*z - 154. Let d(c) = -5*k(c) - 6*w(c). Determine i so that d(i) = 0.
-1, 1, 36
Let d = -87008/21 + 12431/3. Let -3/7*c**3 + d*c - 6/7 + 6/7*c**2 = 0. What is c?
-1, 1, 2
Let n(k) be the second derivative of 37/180*k**6 + 7/10*k**5 + 4/9*k**3 + 17/18*k**4 + 0 + 227*k + 5/252*k**7 + 0*k**2. Determine z, given that n(z) = 0.
-4, -2, -1, -2/5, 0
Let g = -6315/19 + 31613/95. Let u = 86 + -428/5. Factor -u*n**3 - 2/5 + 2/5*n + g*n**2.
-2*(n - 1)**2*(n + 1)/5
Let y = -9 - 78. Let w = y + 90. Factor 0*g**3 + g + 11*g - 2*g**3 + 5*g**w + 12*g**2.
3*g*(g + 2)**2
Let t(r) = r**4 + 3*r**2 + r - 3. Let b(m) = 2*m**5 + 20*m**4 - 26*m**3 + 68*m**2 + 118*m + 6. Let j(n) = 2*b(n) - 44*t(n). Determine a so that j(a) = 0.
-2, -1, 3
Let m(d) = -18*d**3 + 42*d**2 - 376*d - 480. Let r(a) = -3*a**3 + 9*a**2 - 76*a - 96. Let k(f) = -2*m(f) + 11*r(f). Factor k(x).
3*(x - 4)*(x + 1)*(x + 8)
Solve 2614/7*t - 1308/7 - 2/7*t**3 - 1304/7*t**2 = 0 for t.
-654, 1
Suppose -13*m - 44 = 346. Let p be -5*(m/(-9) - 3)*-3. Find c such that -7/6*c**2 - 3/2*c**3 - 1/6*c**p - 5/6*c**4 + 0 - 1/3*c = 0.
-2, -1, 0
Let z(n) be the second derivative of n**5/10 - n**4/12 + n**3/3 - 11*n**2/2 + 77*n. Let m be z(2). Factor 0*r + 16/3*r**4 - 32/3*r**3 - 2/3*r**m + 0 + 0*r**2.
-2*r**3*(r - 4)**2/3
Let d(x) be the first derivative of -x**6/40 + 3*x**5/80 + x**4/8 + 13*x + 53. Let h(c) be the first derivative of d(c). Let h(n) = 0. What is n?
-1, 0, 2
Let g(c) be the third derivative of 0 + 77/10*c**6 - 8*c**3 + 4/5*c**5 - 21/10*c**7 + 54*c**2 - 10*c**4 + 0*c. Determine b so that g(b) = 0.
-2/7, 2/3, 2
Let b = 1363577/294118 - -9/5071. Let z = -62/29 + b. What is u in 0 + z*u**2 - 5/2*u**3 + 5/6*u**4 - 5/6*u = 0?
0, 1
Let q be 2/(-5) - 12/(-5). Let k = 7600 - 7594. Factor 27*m - 23*m**q - 13*m**2 - k - 26*m**3 + 41*m**3 + 0*m.
3*(m - 1)**2*(5*m - 2)
Let m(l) be the first derivative of -1/2*l**4 - 2*l**2 - 2*l**3 + 0*l + 117. Suppose m(j) = 0. What is j?
-2, -1, 0
Let a(h) be the third derivative of h**8/12 + 46*h**7/105 - 53*h**6/15 + 52*h**5/15 + 4*h**4 + 73*h**2 + 3. Solve a(k) = 0 for k.
-6, -2/7, 0, 1, 2
Factor -160/3 - 1/3*t**2 + 161/3*t.
-(t - 160)*(t - 1)/3
Let b(t) be the third derivative of t**8/4032 - 5*t**7/336 - t**6/9 + t**5/60 + 5*t**3/2 + 83*t**2. Let y(i) be the third derivative of b(i). Factor y(a).
5*(a - 16)*(a + 1)
Let d(g) be the second derivative of -g**8/47040 + g**7/8820 - g**6/5040 + 3*g**4/4 + 77*g. Let f(n) be the third derivative of d(n). What is l in f(l) = 0?
0, 1
Let o(y) be the second derivative of y**4/54 + 140*y**3/27 - 47*y**2/3 - 2571*y. What is v in o(v) = 0?
-141, 1
Suppose 57*h = 77*h - 80. Let k(o) be the second derivative of 0*o**h + 1/30*o**5 - 2*o + 0 + 0*o**2 + 0*o**3 - 1/135*o**6. Solve k(p) = 0 for p.
0, 3
Let n be (-480)/504*7/(-8). Determine h so that 0 + 5/2*h**3 + n*h**4 + 0*h - 10/3*h**2 = 0.
-4, 0, 1
Suppose 0 = 1768*w - 1764*w. Let v(b) be the second derivative of 6*b + 15/2*b**3 - 5/2*b**4 + 1/4*b**5 + 0 + w*b**2. Find g, given that v(g) = 0.
0, 3
Let u(b) be the first derivative of -b**4/3 + 92*b**3/3 - 770*b**2 - 4900*b/3 - 889. Suppose u(y) = 0. Calculate y.
-1, 35
Let a(b) be the second derivative of -b**4/18 - 1669*b**3/9 + 1670*b**2/3 + 9636*b. Factor a(y).
-2*(y - 1)*(y + 1670)/3
Let m(s) be the third derivative of -1/168*s**8 - 4/3*s**3 + 0*s - 1/12*s**4 + 4/15*s**5 + 1/30*s**6 + 0 + 118*s**2 - 4/105*s**7. Suppose m(x) = 0. Calculate x.
-4, -1, 1
Let j be 3*-2*-1*13/13. Let i(u) = u**4 + 9*u**3 + 9*u**2 - 5*u - 6. Let f(x) = x**4 + x**2 - 2. Let k(n) = j*f(n) - 2*i(n). Factor k(b).
2*b*(b - 5)*(b + 1)*(2*b - 1)
Factor -4/15*c**3 + 2/15*c + 2/15*c**5 + 0*c**4 + 0 + 0*c**2.
2*c*(c - 1)**2*(c + 1)**2/15
Let k(x) = x**3 - 8*x**2 - 5*x - 25. Let j be k(9). Factor 6*a**2 + j*a**4 + 17*a + 14*a**4 + 3*a - 12*a**3 - 23*a**4.
2*a*(a - 5)*(a - 2)*(a + 1)
Let o be 384/204 - (-3 - (-98)/34). Factor 0*m - 524 + 4*m**o + 516 + 4*m.
4*(m - 1)*(m + 2)
Let d(f) = 2*f**2 - 51*f - 1790. Let b(r) = -2*r**2 + 64*r + 1792. Let n(p) = -7*b(p) - 6*d(p). Let n(m) = 0. What is m?
-11, 82
Let n(g) = -g**3 - 10*g**2 - 17*g - 6. Let k be ((-4)/10)/(6/120). Let d be n(k). Factor 8/11*q - 2/11*q**d + 10/11.
-2*(q - 5)*(q + 1)/11
Let q(b) be the second derivative of 5*b**7/42 - 161*b**6/3 + 6480*b**5 + 805*b**4/6 - 129605*b**3/6 - 3116*b. Find o such that q(o) = 0.
-1, 0, 1, 161
Suppose 5*s = -7*s. Solve -16*k**3 + 60 + 5*k**4 + 200*k + 165*k**2 + 66*k**3 + 20 + s*k**4 = 0.
-4, -1
Let o(t) be the first derivative of t**3/6 - 332*t**2 + 220448*t - 872. Factor o(a).
(a - 664)**2/2
Let n(b) be the first derivative of 4*b**6/45 + b**5/20 - 2*b**4/9 - b**3/6 + 28*b - 66. Let w(h) be the first derivative of n(h). Factor w(x).
x*(x - 1)*(x + 1)*(8*x + 3)/3
Suppose -3*m + 2648 = -3412. Let n be m/40 + (-1)/2. Solve -6*u**3 + 2*u**4 - 51*u - n*u + 99*u + 6*u**2 = 0.
0, 1
Let b(g) be the first derivative of g**4/4 - 7*g**3/3 + g**2 - 11*g + 39. Let f be b(7). Solve 20*x + 10*x**3 + 0*x**4 - 25*x**f + 5*x**4 = 0 for x.
-1, 0, 2
Let r = 1137127/65 + -227402/13. Factor r*x - 1/5*x**3 - 18/5 + 2/5*x**2.
-(x - 3)*(x - 2)*(x + 3)/5
Let h be ((-76)/(-10) - 4) + 6/(-10). Suppose 151*s**h + 5*s - 4 + 14 - 156*s**3 - 10*s**2 = 0. What is s?
-2, -1, 1
Let i = 22754 + -117287/5. Let g = 705 + i. Factor -2/5*n**2 - 6/5 - g*n.
-2*(n + 1)*(n + 3)/5
Let p = 1277722970009/4081 - 313090655. Let z = p + 6/583. Let -12/7*i**3 - 3/7*i**5 - 6/7*i**2 + 15/7*i - 6/7 + z*i**4 = 0. Calculate i.
-1, 1, 2
Let p(g) = g**3 - g**2 - g + 1. Suppose -25*w + 21 = -29. Let b(i) = 16*i**2 - 14*i - 2. Let s(o) = w*p(o) + b(o). Determine m so that s(m) = 0.
-8, 0, 1
Let d(m) = -m**3 + 11*m**2 + 2*m - 19. Let l be d(11). Suppose -5 = v + 4*t - l*t, 0 = 5*t + 25. Factor v - 1/2*k**5 - 1