7*h**i = 0.
-1, -1/3
Let t(d) be the first derivative of 4*d**5/5 + 191*d**4 + 16128*d**3 + 499712*d**2 - 1048576*d + 600. Suppose t(y) = 0. What is y?
-64, 1
Let n(f) = f**3 + 5*f + 101. Let c be n(0). Factor -7*i**3 + 101*i**2 - c*i**2 - i**4.
-i**3*(i + 7)
Let x(f) be the third derivative of f**6/480 - f**5/120 - 43*f**4/96 - 5*f**3/3 - 994*f**2. Factor x(p).
(p - 8)*(p + 1)*(p + 5)/4
Factor 1/6*q**4 - 10/3*q**3 + 22*q**2 + 0 - 48*q.
q*(q - 8)*(q - 6)**2/6
Let d(c) be the third derivative of -2/27*c**3 - 2*c - 2/135*c**5 + 0 - 1/12*c**4 + 8*c**2. Factor d(o).
-2*(o + 2)*(4*o + 1)/9
Let x(y) be the second derivative of y**6/120 - 3*y**5/16 + 3*y**4/16 + 67*y**3/24 + 21*y**2/4 - 320*y. Let x(j) = 0. Calculate j.
-1, 3, 14
Let u be 16770/(-1989)*(17/5 - 4*7/4). Solve 350/17*i**4 + u*i**2 - 152/17*i - 730/17*i**3 + 16/17 = 0.
2/7, 2/5, 1
Let c(x) = -19*x - 71. Let h be c(4). Let s = 149 + h. Factor -1/3*l**s + 0*l + 4/3.
-(l - 2)*(l + 2)/3
Factor -32/17*t + 0 + 2/17*t**2.
2*t*(t - 16)/17
Suppose 5*p = -5*x - 0*x - 15, 8 = -p - 2*x. Factor 33 + 9*h**3 - h**2 + 69*h + 42*h**2 - 6*h**3 - 2*h**p.
3*(h + 1)**2*(h + 11)
Let d = 4344/13 + -334. Suppose 22*g = 63*g - 123. Find r, given that -d*r**4 + 0*r + 6/13*r**g - 6/13*r**5 + 2/13*r**2 + 0 = 0.
-1, -1/3, 0, 1
Let y(k) = -k**2 - 6*k + 19. Let f be y(-8). Suppose 2*p + q = -4, p - 4*q = -f*p + 16. Factor 1/5*o**2 + p - 2/5*o.
o*(o - 2)/5
Let h(s) be the first derivative of s**5/40 + 31*s**4/8 + 137*s**2 - 209. Let j(d) be the second derivative of h(d). Factor j(k).
3*k*(k + 62)/2
Suppose 626 - 662 = -4*k - 4*v, 5*v - 36 = -2*k. Determine c so that 0 - 14/3*c - 1/3*c**3 - k*c**2 = 0.
-7, -2, 0
Let h(u) be the third derivative of u**7/504 - u**6/12 + 5*u**5/6 - 3*u**4/8 + 37*u**2. Let r(p) be the second derivative of h(p). Find a such that r(a) = 0.
2, 10
Suppose -172620*c**2 + 65032*c + 49202*c + 54000 + 16558*c**3 + 1034*c - 12668*c - 544*c**4 + 6*c**5 = 0. What is c?
-1/3, 1, 30
Suppose -5*z = 12 + 8, -3*z + 592 = 2*a. Let o = a + -287. Factor o*v + 25 + 3*v**2 + 1/5*v**3.
(v + 5)**3/5
Factor 209/9*n + 1/3*n**2 - 70/9.
(n + 70)*(3*n - 1)/9
Let m(s) be the first derivative of s**6/12 - 7*s**5/12 + 15*s**3/2 + 8*s**2 - s - 15. Let c(d) be the second derivative of m(d). Solve c(t) = 0.
-1, 3/2, 3
Let p(o) be the third derivative of 0 + 7/240*o**6 - 1/20*o**5 + 0*o**3 - 23*o**2 - 1/420*o**7 + 0*o + 0*o**4. Suppose p(i) = 0. Calculate i.
0, 1, 6
Let g(a) be the second derivative of 1/110*a**5 - 13/22*a**4 - 361/11*a**2 + 0 + 58*a + 133/11*a**3. Find q such that g(q) = 0.
1, 19
Let j(d) = 7*d**2 - 9*d + 5. Let o be j(2). Factor -o*v**2 - 48*v**4 - 9 - 39*v**2 + 9 + 3*v**5 - 105*v**3.
3*v**2*(v - 18)*(v + 1)**2
Let f be 1/2 + 46/4. Let g be ((-3)/f)/((-2)/16). Factor -51*w**g - 2*w**5 + 2*w - 6*w**4 + 2*w**4 + 55*w**2.
-2*w*(w - 1)*(w + 1)**3
Let i = -413 - -454. What is j in i*j + 116*j + 5*j**2 + 720 - 37*j = 0?
-12
Suppose 6*y - 3*y - 222 = 0. Let s = 78 - y. Find k such that -758 - 3*k - s*k**3 + 774 + 31*k + 8*k**2 = 0.
-1, 4
Factor -23431*o + 21667*o - 7110 - 5*o**2 - 57717 - 7*o**2.
-3*(2*o + 147)**2
Let t(i) be the first derivative of -41/2*i**2 + 26*i - 1/4*i**4 + 217 + 16/3*i**3. Factor t(d).
-(d - 13)*(d - 2)*(d - 1)
Let f(g) be the second derivative of -g**4/3 + 172*g**3/3 - 1520*g**2 - 3918*g + 1. Factor f(a).
-4*(a - 76)*(a - 10)
Let v be -11*2*(-6)/(-7 - -1). Let d = -15 - v. Factor 4*m**4 - 3*m**3 + 0*m**3 - d*m**2 + 4*m**2 + 3*m - m**4.
3*m*(m - 1)**2*(m + 1)
Let g(d) = 149*d**2 + 10*d**3 + 5*d**3 + 3*d - 40*d**2 - 11*d**3. Let h(m) = -8*m**3 - 221*m**2 - 7*m. Let y(f) = 7*g(f) + 3*h(f). Factor y(s).
4*s**2*(s + 25)
Let v be (6*(-6)/(-9))/1. Factor 86*z**3 - v*z**2 - 34*z**3 - 26*z**3 - 28*z**3.
-2*z**2*(z + 2)
Suppose 0 - 67/2*u + 1/2*u**2 = 0. What is u?
0, 67
Let r(v) = v**2 + 6*v**2 + 112 - v**2 - 7*v**2 - 100*v + 4*v**2. Let i(w) = -2*w**2 + 100*w - 110. Let s(a) = 5*i(a) + 4*r(a). Let s(x) = 0. What is x?
-51, 1
Let a(h) be the third derivative of 1/75*h**6 + 0 - 7/15*h**3 - 19/60*h**4 + 12*h**2 - 4/75*h**5 + 2*h. Suppose a(b) = 0. Calculate b.
-1, -1/2, 7/2
Let s(g) be the second derivative of g**4/20 + 431*g**3/10 + 1287*g**2/5 - 1096*g. Factor s(a).
3*(a + 2)*(a + 429)/5
Let j(o) be the second derivative of 100/3*o**2 - 10/9*o**3 + 0 + 1/72*o**4 - 19*o. Determine u so that j(u) = 0.
20
Let c(a) = -a**3 + a + 44. Let o be c(0). Suppose f = 3*l - o - 0, -36 = -3*l + 3*f. Factor 6 - 20*p + 2 + 270*p**3 - 274*p**3 + l*p**2.
-4*(p - 2)*(p - 1)**2
Suppose -70*a + 20*a + 725 = 95*a. Let s(q) be the second derivative of -1/5*q**a - 32*q**3 - 72*q**2 - 13/3*q**4 + 47*q + 0. Factor s(w).
-4*(w + 1)*(w + 6)**2
Let n be (-12)/330*5 - (-312)/22. Suppose -4*k + g = k - 14, k - n = 3*g. Factor -16/7*p**k + 4/7*p**4 - 4/7 + 4/7*p**3 + 2*p - 2/7*p**5.
-2*(p - 1)**4*(p + 2)/7
Let l(k) be the first derivative of -k**6/450 - 17*k**5/200 + 13*k**4/120 + 81*k**3 + 197. Let t(p) be the third derivative of l(p). Factor t(x).
-(x + 13)*(4*x - 1)/5
Let k(m) be the first derivative of m**4 - 1180*m**3/3 - 1784*m**2 - 2384*m + 6006. Suppose k(b) = 0. What is b?
-2, -1, 298
Let j(z) = 9*z**2 + 7*z - 2. Let p(q) = -q**2 - 22*q - 36*q**2 - 6*q + 8 - q. Let w(b) = 9*j(b) + 2*p(b). Factor w(h).
(h + 1)*(7*h - 2)
Find s such that 290/7*s - 1/7*s**3 + 0 + 19/7*s**2 = 0.
-10, 0, 29
Determine w, given that 14*w - 7/8*w**3 - 1/4*w**2 + 4 = 0.
-4, -2/7, 4
Find v such that -52 + 3/2*v**2 + 77*v - 1/2*v**4 - 26*v**3 = 0.
-52, -2, 1
Let q(z) be the second derivative of 4*z**2 + 8/3*z**3 + 29/10*z**5 - 3/7*z**7 + 7/15*z**6 - 5*z - 13/2*z**4 + 0. Let q(k) = 0. Calculate k.
-2, -2/9, 1
Let j(b) = -29*b**2 - 316*b - 862. Let h(v) = 20*v**2 + 210*v + 575. Let f(z) = -7*h(z) - 5*j(z). Solve f(p) = 0.
-19, -3
Let o be (-30)/24 - 37389/(-15972). Let -4/11 + 1/11*i**2 - o*i + 3/11*i**3 = 0. Calculate i.
-2, -1/3, 2
Let h(c) be the third derivative of c**5/570 + 127*c**4/38 - 1124*c**2. Let h(t) = 0. Calculate t.
-762, 0
Let r = 38 + -36. Factor 11*g**r + g**2 - 11*g**2 + g + g.
g*(g + 2)
Let t be -4 + -5 + 7 - 484. Let w = t - -488. Factor 0*i + 0*i**3 + 1/2*i**4 + 0*i**w + 9/4*i**5 + 0.
i**4*(9*i + 2)/4
Let o(z) be the second derivative of 0*z**2 - 2*z - 2/15*z**3 - 1/90*z**4 + 4. Factor o(q).
-2*q*(q + 6)/15
Let n = 12 + 0. Let t be (-16 + n)/(0 - 2). Factor -38*o**4 + 34*o**4 + 6*o**2 - 2*o**t.
-4*o**2*(o - 1)*(o + 1)
Let n(w) be the third derivative of w**8/756 + 4*w**7/945 - 2*w**5/135 - w**4/54 - 840*w**2. Factor n(i).
4*i*(i - 1)*(i + 1)**3/9
Suppose 20*u - 27*u = -84. Let a be 3/u*(-9)/((-108)/80). Find c such that 1/3 + a*c**2 - 2*c = 0.
1/5, 1
Solve 2876/11*a - 6/11*a**2 - 958/11 = 0 for a.
1/3, 479
Let g(t) be the third derivative of t**7/525 - t**6/75 - 89*t**5/150 - 7*t**4/5 - 7285*t**2. Suppose g(z) = 0. Calculate z.
-7, -1, 0, 12
Let l(c) be the second derivative of -c**4/16 + 3*c**3/2 + 21*c**2/2 - 4*c - 8. Determine j, given that l(j) = 0.
-2, 14
Let 0 - 16/7*z + 214/7*z**3 - 60*z**2 = 0. Calculate z.
-4/107, 0, 2
Suppose 16 = -9*f + 52. Determine g, given that -92*g**2 - 10*g**3 - 6*g**3 - 2*g**f + 40*g**3 + 120*g - 50 = 0.
1, 5
Factor 41 - 3/2*u**2 - 121/2*u.
-(u + 41)*(3*u - 2)/2
Let j = 76704/31985 - -12/6397. Let c(p) be the first derivative of 45 + 8/15*p**3 - j*p - 23/5*p**2. Solve c(v) = 0 for v.
-1/4, 6
Determine u, given that 17 - 2*u**4 + 109*u**3 + 26 - 85*u**3 + 5 - 76*u + 6*u**2 = 0.
-2, 1, 12
Let o be 3*1 + 16*1*-12. Let u be 36/10 - -1 - o/(-315). Factor -14*d**3 + 22*d**u - 29*d**4 + 6*d**2 + 11*d**4.
2*d**2*(d - 3)*(2*d - 1)
Let r(g) be the second derivative of g**7/560 + 7*g**6/480 + g**5/20 + g**4/12 + g**3/6 + 8*g + 6. Let w(b) be the third derivative of r(b). Factor w(d).
3*(d + 1)*(3*d + 4)/2
Let y = -16827 - -50483/3. Let o(m) be the first derivative of -5 + y*m**3 + 1/8*m**4 + m**2 + 0*m. Factor o(q).
q*(q + 2)**2/2
Suppose -5*j = 2*u + 5, 3 = -4*j - 1. Suppose u = 9*b - 13*b + 32. Factor 0*x - 14*x**2 + x - 4 - 7*x - 4*x**3 - b*x.
-2*(x + 1)*(x + 2)*(2*x + 1)
Let v = -241 - -245. What is b in 28 + 4*b**3 + 62*b**v - 17*b - 61*b**4 + 21*b - 21*b**2 = 0?
-7, -1, 2
Let v = -23753 + 23756. Let w(b) be the first derivative of -13 + b**v + 27/7*b + 45/14*b**2 + 3/28*b**4. Suppose w(z) = 0.