(m + 1)*(7*m - 2)
Let x(u) be the first derivative of -2*u**3/27 - 40*u**2/9 - 74*u/3 + 699. Factor x(t).
-2*(t + 3)*(t + 37)/9
Let n(c) = 3*c**2 - 41*c + 14. Let v be n(13). Let w be (108/(-240))/(v/16). Suppose w*p**2 - 2/5 + 1/5*p = 0. What is p?
-1, 2/3
Determine g so that -182/5*g**3 + 2/5*g**4 + 542/5*g + 364/5 - 6/5*g**2 = 0.
-1, 2, 91
Suppose -9*u - 23 = -104. Factor 16*h**3 - 45*h**3 + 104*h**3 - 24*h**2 - u*h**4.
-3*h**2*(h - 8)*(3*h - 1)
Let f(n) be the third derivative of n**5/210 + 367*n**4/21 + 538756*n**3/21 + 6*n**2 + n - 24. Factor f(l).
2*(l + 734)**2/7
Suppose -495*n - 484 = -506*n. Suppose 0*o + 6 = 3*o. Factor -4*g + 4 + 25*g**2 + 20*g**2 - n*g**o.
(g - 2)**2
Let a(y) = 2*y**2 - 17*y - 3. Let k be a(9). Suppose 2*u = 5*u - k. Factor 5*m**3 + 20 + m**2 + u*m**4 - 7*m**4 + 55*m + 44*m**2.
-5*(m - 4)*(m + 1)**3
Factor 37*t**2 + 79 - 161*t - 115*t - 3*t**3 - 11*t**2 + 305 - 131*t**2.
-3*(t - 1)*(t + 4)*(t + 32)
Let y(a) be the third derivative of a**8/112 + 37*a**7/350 - 129*a**6/50 - 193*a**5/25 - 28*a**4/5 + 3477*a**2. Find t such that y(t) = 0.
-14, -1, -2/5, 0, 8
Factor -48*p - 2*p**2 + 10*p**2 - 87 + 7 + 30 - 6*p**2.
2*(p - 25)*(p + 1)
Find s such that -19/2*s + 6 - 1/2*s**3 + 4*s**2 = 0.
1, 3, 4
Let y(m) be the third derivative of 3*m**6/10 - m**5/5 + m**4/18 - 4*m**3/3 - 120*m**2. Let x(l) be the first derivative of y(l). Find j, given that x(j) = 0.
1/9
Let r(l) be the second derivative of l**4/18 - 35*l**3/9 + 304*l**2/3 - l - 88. Factor r(v).
2*(v - 19)*(v - 16)/3
Let h = -291 - -293. Let -h - 12*q - 10*q - 2*q**2 - 16*q + 34*q = 0. Calculate q.
-1
Let -36/5 + 19104/5*h - 2534464/5*h**2 = 0. Calculate h.
3/796
Let d = 54 + -51. Suppose -d*u = 11 - 20. Suppose 4*j**u - 6 + 15*j**2 - 30*j - 6*j**3 + 6*j - 10 = 0. Calculate j.
-1/2, 4
Let f = -1022 + 1141. Suppose -102*d = -f*d + 34. Factor 4/3 - 6*x - 22/3*x**d.
-2*(x + 1)*(11*x - 2)/3
Factor 1/5*n**2 + 226/5*n + 0.
n*(n + 226)/5
Let f(l) be the third derivative of l**6/12 - 7*l**5/30 - 7*l**4/4 - 3*l**3 - 610*l**2. Factor f(m).
2*(m - 3)*(m + 1)*(5*m + 3)
Suppose 0 = 7*o - 6*o - 7. Suppose 3 = 2*q - o, 3*v + q = 5. Suppose -10*n**3 + 6*n**4 + 6*n**5 + v*n**5 + 9*n - 6*n**2 - 4*n**5 - n = 0. What is n?
-4, -1, 0, 1
Let d = 347 - 343. Suppose 6*f**2 - f**5 + 7*f**3 + 118*f**4 - 118*f**d = 0. What is f?
-2, -1, 0, 3
Let a(h) be the third derivative of -h**8/1176 + 239*h**7/735 - 19651*h**6/420 + 17215*h**5/6 - 140602*h**4/3 + 1043504*h**3/3 - 290*h**2 + 1. Factor a(f).
-2*(f - 77)**3*(f - 4)**2/7
Let r = -5409 - -5445. Let b(j) be the first derivative of r*j + 1/3*j**3 - 1 - 6*j**2. Determine c so that b(c) = 0.
6
Let x(h) = -h**2 - h + 1. Let b(k) = 11*k**2 - 2920*k + 1168. Let l(r) = b(r) - 4*x(r). Let l(n) = 0. Calculate n.
2/5, 194
Let b(p) = 3*p**4 + p**3 + 18*p**2 + 8*p. Let s(q) = -q**4 - 2*q**2. Let d(g) = -b(g) - 4*s(g). Find h such that d(h) = 0.
-2, -1, 0, 4
Let f = 1697 + -1695. Let x(p) be the first derivative of -4/3*p**3 - f*p**2 + 1/2*p**6 + 2*p**5 + 7/4*p**4 + 0*p + 13. Suppose x(q) = 0. Calculate q.
-2, -1, 0, 2/3
Factor -2/17*v**2 + 32/17*v - 126/17.
-2*(v - 9)*(v - 7)/17
Let s(t) be the first derivative of 4*t**5/5 - 13*t**4 + 184*t**3/3 - 24*t**2 - 288*t - 3577. Factor s(x).
4*(x - 6)**2*(x - 2)*(x + 1)
Let k(n) = -3*n**2 + 1. Let b(c) = 4*c**2 - 148*c - 148. Let s(d) = -b(d) - 2*k(d). Suppose s(g) = 0. What is g?
-73, -1
Let y(q) be the second derivative of q**4/16 - 123*q**3/4 - 741*q**2/8 - 5823*q. Factor y(d).
3*(d - 247)*(d + 1)/4
Suppose 7*v - 2085 = -1924. Suppose v = 9*g + 5. Suppose -1/2*w**2 + 1/4*w**3 - w + g = 0. What is w?
-2, 2
Let a(u) be the third derivative of -u**7/945 - u**6/135 + 8*u**5/135 + 4*u**4/27 - 16*u**3/9 - 7974*u**2. Determine l so that a(l) = 0.
-6, -2, 2
Let -5/4*m**5 + 15/4*m**3 + 0 + 25/2*m**2 - 5*m**4 - 10*m = 0. What is m?
-4, -2, 0, 1
Let s(x) be the second derivative of 4*x**4/27 - 3862*x**3/27 - 322*x**2/3 - 36*x - 27. Solve s(a) = 0.
-1/4, 483
Let a be 189/(-42)*9896/(-18). Suppose 0 = a*y - 2465*y - 18. Find j, given that 1/5 + 1/5*j**y - 2/5*j = 0.
1
Let a be (44/(-7) - 0)/(144/(-1848)). Factor -140/3*v - a*v**3 + 4 + 451/3*v**2.
-(2*v - 3)*(11*v - 2)**2/3
Let b(m) be the first derivative of -4*m**3/39 - 49*m**2/13 + 50*m/13 - 2549. Factor b(x).
-2*(x + 25)*(2*x - 1)/13
Let f(w) be the second derivative of -12*w - 1/8*w**4 - 3 + 3*w**2 - 3/4*w**3. Let f(l) = 0. What is l?
-4, 1
Let p be -2 + (296/370)/((-4)/(-10)). Factor 1/2*n**2 + 14*n + p.
n*(n + 28)/2
Let v(h) = 33*h**2 + 909*h + 3486. Let q(p) = 7*p**2 + 180*p + 697. Let a(f) = 24*q(f) - 5*v(f). Factor a(d).
3*(d - 78)*(d + 3)
Factor 416/15 - 58/15*u + 2/15*u**2.
2*(u - 16)*(u - 13)/15
Let g(z) be the third derivative of -3*z**2 + 32*z**3 + 1/40*z**6 - 2*z**4 + 0*z - 1/5*z**5 + 4. Factor g(a).
3*(a - 4)**2*(a + 4)
Suppose 2*g + 4*j = -516, 5*j - 237 = -7*g + 8*g. Let i be (-1 - 3/(-7))*g/90. Factor 0 + i*y - 4/5*y**2 + 52/5*y**4 - 36/5*y**3 - 4*y**5.
-4*y*(y - 1)**3*(5*y + 2)/5
Let f(p) be the second derivative of -p**5/25 + 54*p**4/5 + 986*p**3/15 + 132*p**2 + 1926*p - 1. Solve f(x) = 0.
-2, -1, 165
Let z = -1037 + 17636/17. Let s(i) be the first derivative of z*i**2 - 6/17*i**3 - 2/85*i**5 - 4/17*i + 5/34*i**4 + 21. Factor s(l).
-2*(l - 2)*(l - 1)**3/17
Let g be (136/(-16))/(26/4). Let h = g + 255/26. Find o, given that -1/2*o**3 + h*o**2 + 32 - 40*o = 0.
1, 8
Suppose -348*o - 14*o = 193*o - 18315. Factor o*t**3 + 189/2*t + 81*t**2 + 1/2*t**5 + 13/2*t**4 + 81/2.
(t + 1)*(t + 3)**4/2
Let t(y) be the third derivative of -y**7/70 - 3*y**6/20 + 177*y**5/20 - 85*y**4/4 + 4945*y**2. Let t(f) = 0. Calculate f.
-17, 0, 1, 10
Let a = -568 + 661. Determine o so that -635 - 108*o**3 - 336*o**2 + 317 - 84*o**3 + a*o + 312 = 0.
-2, 1/8
Factor 2044 + 1706 - 3991*j - 159*j**3 - 1934*j + 3*j**4 + 2331*j**2.
3*(j - 25)**2*(j - 2)*(j - 1)
Suppose -b = t - 4, 27*t - 23*t - 16 = -2*b. Suppose 22*v - 26*v + 28 = 4*q, -3*v = -t*q + 14. Factor -4/11*m - 8/11*m**3 + 10/11*m**v + 0 + 2/11*m**4.
2*m*(m - 2)*(m - 1)**2/11
Let g be (2 - 14)*21/(-14)*(-2)/(-12). Factor 0 + 3/8*t**g - 3*t**2 - 9/2*t + 3/8*t**4.
3*t*(t - 3)*(t + 2)**2/8
Let y = -4124 + 4127. Let a(v) be the second derivative of 1/12*v**4 + 3/20*v**5 + 0 + 0*v**2 - 1/30*v**6 - 1/42*v**7 + 7*v - 1/3*v**y. Factor a(b).
-b*(b - 1)**2*(b + 1)*(b + 2)
Let 0 + 455/8*d**3 + 169/8*d**4 + 3/2*d - 19*d**2 = 0. Calculate d.
-3, 0, 2/13
Let z(m) = -488*m + 160 + 39*m + 2715*m**2 - 791*m. Suppose 0 = 6*q - 3*q - 60. Let o(j) = 388*j**2 - 177*j + 23. Let g(f) = q*o(f) - 3*z(f). Factor g(b).
-5*(7*b - 2)*(11*b - 2)
Let l(p) = -p**3 - 10*p**2 - 5*p + 68. Let v be l(-9). Suppose 2*c + v = 36. Suppose 1/6*g + 0 + 1/6*g**c = 0. What is g?
-1, 0
What is m in 33*m**4 - 45*m**4 - 84*m**2 - 94*m**4 - 164*m**4 + 27*m**5 + 45*m**4 + 264*m**3 = 0?
0, 2/3, 7
Let i(u) be the first derivative of -9/2*u - 27/8*u**4 - 29/10*u**5 + 19/3*u**3 + 7/24*u**6 + 47/8*u**2 + 40. Suppose i(h) = 0. What is h?
-1, 2/7, 1, 9
Suppose -16 = 3*v - 4*w - 425, 0 = -5*v + 4*w + 695. Solve -22 + 2*n**2 + 215*n + v*n - 9*n**2 - 437*n = 0.
-11, -2/7
Let i(s) be the first derivative of -1/27*s**6 + 0*s**2 - 7 + 0*s - 2/27*s**3 - 2/15*s**5 - 1/6*s**4. Factor i(q).
-2*q**2*(q + 1)**3/9
Determine p so that 28*p**2 - 27552*p - 23873 - 9*p**3 + 974*p**2 + 5057 = 0.
-2/3, 56
Let x(h) be the second derivative of h**6/240 - 3*h**5/80 - 9*h**4/32 + 506*h. What is v in x(v) = 0?
-3, 0, 9
Let n(b) be the first derivative of -7*b**6/15 - 18*b**5 - 377*b**4/2 + 338*b**3/3 + 72*b - 67. Let u(t) be the first derivative of n(t). Factor u(d).
-2*d*(d + 13)**2*(7*d - 2)
Let z be -1*-18*25/(-10). Let c = 47 + z. Factor 5*v - c*v**3 + 2*v**4 - 3*v**4 + 1 - 3*v.
-(v - 1)*(v + 1)**3
Let j be 6/4 - 2 - (-3419)/1578. Let q(r) be the first derivative of -15*r + 10*r**2 - 25 - j*r**3. Suppose q(h) = 0. Calculate h.
1, 3
Suppose -19*k + 25204 - 25166 = 0. Let n(h) be the second derivative of -17/3*h**4 + 0 + 6*h**k - 12/5*h**5 + 16*h - 4/3*h**3. Factor n(u).
-4*(u + 1)*(3*u - 1)*(4*u + 3)
Let d = -12259 + 12262. Find b such that 4 + 1/2*b**2 - d*b = 0.
2, 4
Let t(n) be the second derivative of -n**6/6 - 27*n**5/2 - 4145*n**4/12 - 2250*n**3 - 6250*n**2 + 2*n - 121. Let t(j) = 0. What is j?
-2