v**2 - 1451*v + 90*v**3 - 680*v**3 = 0. What is v?
-24, -2, -1/4, 3
Let n(m) be the first derivative of -m**4/16 - 511*m**3/12 - 1019*m**2/8 - 509*m/4 + 2753. Factor n(f).
-(f + 1)**2*(f + 509)/4
Let u be (-1)/23*(89 + -135). Factor -27556/7*m**3 + 28884/7*m**u + 16/7 - 192*m.
-4*(m - 1)*(83*m - 2)**2/7
Let o = 8977/60 - 2233/15. Solve 3/2*p + o - 9/4*p**2 = 0.
-1/3, 1
Let q(g) be the third derivative of -1/1440*g**6 - 11/2*g**3 + 0*g + 0 + 1/80*g**5 - 14*g**2 + 7/96*g**4. Let l(z) be the first derivative of q(z). Factor l(c).
-(c - 7)*(c + 1)/4
Let m(s) = 4*s**2 - 216*s - 403. Let p(h) = 11*h**2 - 464*h - 807. Let f(q) = -7*m(q) + 3*p(q). Factor f(x).
5*(x + 4)*(x + 20)
Factor -4*g**3 - 956484*g + 2847*g**2 + 6405*g**2 - 5340*g**2.
-4*g*(g - 489)**2
Let q(b) be the second derivative of -41*b**7/98 + 22*b**6/35 + 195*b**5/28 - 129*b**4/7 + 18*b**3/7 - 4472*b. Let q(m) = 0. Calculate m.
-3, 0, 3/41, 2
Let q(h) be the second derivative of -143*h**6/105 + 153*h**5/70 - 5*h**4/21 + 2179*h. Factor q(f).
-2*f**2*(f - 1)*(143*f - 10)/7
Let s(k) be the third derivative of k**7/11340 + k**6/810 - 145*k**4/12 + 113*k**2. Let r(b) be the second derivative of s(b). Determine q, given that r(q) = 0.
-4, 0
Factor -20*p**2 + 118*p**2 - 43*p**2 - 120*p + 20.
5*(p - 2)*(11*p - 2)
Suppose -3*u + 4*i = -24 - 16, -15 = -u + i. Suppose 6*j - u + 2 = 0. Let -1/2*x**2 + 0*x - 5/8*x**5 + x**j + 0 + 7/8*x**4 = 0. What is x?
-1, 0, 2/5, 2
Let k = -192 - -199. Let x(s) = -3*s**3 - 31*s**2 + 132*s - 151. Let u(i) = -i**3 - 10*i**2 + 44*i - 50. Let w(f) = k*u(f) - 2*x(f). Factor w(l).
-(l - 2)**2*(l + 12)
Solve -52 + 2/5*f**2 + 6/5*f = 0 for f.
-13, 10
Solve -712*o + 12*o**4 - 323796*o**2 - 80 + 324144*o**2 + 1072*o**3 + 80 = 0 for o.
-89, -1, 0, 2/3
Let m(y) = -3*y**2 + y + 2. Let v(o) = o**2 - 1. Let c(k) = -m(k) - 2*v(k). Let u(d) = d**2 - 2*d + 1. Let q(f) = 2*c(f) - u(f). Factor q(l).
(l - 1)*(l + 1)
Let l(d) be the second derivative of d**7/6300 + d**6/150 - 71*d**4/6 - 2*d + 37. Let h(q) be the third derivative of l(q). Let h(w) = 0. Calculate w.
-12, 0
Let d(g) be the first derivative of -g**8/1176 + g**6/140 + g**5/105 + 7*g**2/2 - 10. Let i(x) be the second derivative of d(x). Factor i(b).
-2*b**2*(b - 2)*(b + 1)**2/7
Let n(c) be the first derivative of c**5/10 + 7*c**4/54 - 2*c**3/27 - 87*c + 155. Let f(d) be the first derivative of n(d). Factor f(i).
2*i*(i + 1)*(9*i - 2)/9
Let v(g) be the second derivative of g**5/20 - 3*g**4/2 - 7*g**3/2 + 19*g**2 + 2*g + 469. Find j such that v(j) = 0.
-2, 1, 19
Let i(y) be the third derivative of y**5/240 - 113*y**4/32 - 85*y**3/6 - 1638*y**2. Factor i(r).
(r - 340)*(r + 1)/4
Let p be (12/(-2))/((24/16*-1)/(55/30)). Let -p*y**3 + 4*y**2 + 0*y + 2/3*y**5 + 8/3*y**4 + 0 = 0. What is y?
-6, 0, 1
Let g be 4 + (-2713)/(-67)*(-15)/135. Let f = 1/1206 - g. Suppose -f*p**2 + 2*p - 3/2 = 0. What is p?
1, 3
Let l(c) = -5*c**3 + 404*c**2 + 597*c + 260. Let y(d) = -4*d**2 + d - 4. Let f(i) = 2*l(i) + 16*y(i). Factor f(m).
-2*(m - 76)*(m + 1)*(5*m + 3)
Let n(j) be the second derivative of -j**6/15 + 163*j**5/5 - 643*j**4/2 + 2884*j**3/3 - 1280*j**2 - 3943*j. Suppose n(q) = 0. What is q?
1, 4, 320
Let -11174 - 9634*z - z**3 - 273*z**2 - 9134*z - 7322 = 0. Calculate z.
-136, -1
Let u be 12/(-30) + 66/15. Factor 0*c - 3*c + 3*c**2 - 3*c**u + 6*c - 3*c**3.
-3*c*(c - 1)*(c + 1)**2
Suppose 0 = 23*i - 24*i + 2, -2*i - 4136 = 5*h. Let c = h + 828. Factor c*j**2 - 1/6*j**3 + 1/6*j + 0.
-j*(j - 1)*(j + 1)/6
Let a(o) = -5*o**2 - 501*o. Let u(b) = -3*b**2 - 504*b. Let d(y) = 3*a(y) - 4*u(y). Let d(s) = 0. What is s?
0, 171
Let k(c) = -45*c**2 + 40*c + 140. Let t(f) = f**3 - 44*f**2 + 43*f + 132. Let x(r) = -4*k(r) + 5*t(r). Factor x(z).
5*(z - 5)*(z - 4)*(z + 1)
Let l(p) = -2*p**4 - 3*p**3 - p**2 - p - 2. Let u(k) = k**4 + 3476*k**3 - 1161*k**2 - k - 2. Let c(r) = 3*l(r) - 3*u(r). Let c(y) = 0. Calculate y.
-1160, 0, 1/3
Let y(b) = b**3 + 636*b**2 - 26460*b + 370446. Let q(x) = x**3 + 1906*x**2 - 79380*x + 1111336. Let m(a) = 3*q(a) - 8*y(a). Suppose m(i) = 0. Calculate i.
42
Let i be -144 + 139 + (-66)/(-20) - (-88)/40. Find v such that -i*v**2 + 0 + 16*v = 0.
0, 32
Let s be 3 + 2 - 37/((-2072)/(-280)). Solve s + 46/7*v**3 + 1/7*v**5 + 16/7*v**4 - 144/7*v**2 + 81/7*v = 0.
-9, 0, 1
Suppose -2*s - 16 = -113*r + 117*r, 0 = -2*r + 2*s + 16. Factor 0 + 2/7*v**2 + r*v - 1/7*v**3.
-v**2*(v - 2)/7
Suppose 48 = -4*r + 16*r. Factor 113*g**r - 24*g - 24*g**2 - 107*g**4 - 6*g**3 + 3*g - 6 + 3*g**5.
3*(g - 2)*(g + 1)**4
Let s = -218/27 + 1198/135. Factor -6/5*y**5 + 0*y**2 + 2*y - 4*y**3 + s - 4*y**4.
-2*(y + 1)**4*(3*y - 2)/5
Suppose -2*w - 6 + 104 = g, 0 = 5*g + 2*w - 506. Determine y, given that -y**2 + 3*y**5 + 6*y**4 - 102 + g - 3*y**3 - 5*y**2 = 0.
-2, -1, 0, 1
Suppose -35*d - 4*d**5 - 27*d**3 + 12*d - 19*d**2 - 7*d**4 + 5*d**5 - 10*d**2 + 13*d = 0. Calculate d.
-1, 0, 10
Suppose 3/8*n**3 + 77017125 + 783225/2*n + 2655/4*n**2 = 0. Calculate n.
-590
Let m(s) = -55*s**4 + 105*s**3 - 30*s**2 - 95*s + 125. Let i(t) = -2*t**4 + 3*t**3 - t**2 + t + 1. Let v(u) = 25*i(u) - m(u). Determine o, given that v(o) = 0.
-2, 1, 2, 5
What is q in -256*q - 1/3*q**3 - 16*q**2 - 4096/3 = 0?
-16
Let v = 2778677/4 + -694669. Find u such that v*u**4 - 4*u - 5/4*u**2 + 5*u**3 - u**5 + 1 = 0.
-2, -1, 1/4, 1, 2
Suppose -69 = 7*l - 83. Find z such that -11*z**2 + 23*z**4 - z**l + 19*z**4 - 30*z**4 + 32*z**3 = 0.
-3, 0, 1/3
Let t(s) be the second derivative of s**6/165 - 3*s**5/110 - s**4/66 + s**3/11 + 764*s. Determine f, given that t(f) = 0.
-1, 0, 1, 3
Let v(f) = 2*f**5 + f**3 - f**2 + 2*f + 1. Let j(r) = -11*r**5 - 8*r**4 - 20*r**3 + 54*r**2 - 39*r - 6. Let m(u) = j(u) + 6*v(u). Factor m(p).
p*(p - 9)*(p - 1)**2*(p + 3)
Let 4178769*o - 74*o**2 + 236*o**2 + 2*o**4 - 4179437*o - 664 + 2*o**4 + 167*o**3 - 3*o**4 = 0. Calculate o.
-166, -2, -1, 2
Find s such that -15*s**5 + 30*s**4 + 24*s**3 - 66*s**3 + 18*s**5 + 138436 - 138370 - 96*s**2 + 39*s = 0.
-11, -1, 1, 2
Let w(h) = 3*h**2 - 2*h + 3. Let q(y) = 3*y**2 + 32*y + 20. Let o be q(-10). Let r be w(o). Factor 6/5*k**4 + 2/5*k**2 + 0*k + 0 + 6/5*k**r + 2/5*k**5.
2*k**2*(k + 1)**3/5
Let n(o) be the second derivative of -o**7/294 + 9*o**6/70 + 59*o**5/70 + 13*o**4/6 + 41*o**3/14 + 31*o**2/14 + 309*o. Factor n(y).
-(y - 31)*(y + 1)**4/7
Let m(i) = -i**3 + 7*i**2 + 7*i + 5. Let f = -14 + 22. Let g be m(f). Let l(y) = -y**2 + y. Let s(k) = 2*k**2 - 2*k. Let o(x) = g*s(x) - 10*l(x). Factor o(v).
4*v*(v - 1)
Let p(d) be the first derivative of -d**3/8 - 1929*d**2/16 - 1923*d/4 + 4938. Factor p(f).
-3*(f + 2)*(f + 641)/8
Let 64/5*r + 564/5*r**3 - 64*r**2 - 406/5*r**4 + 0 + 98/5*r**5 = 0. Calculate r.
0, 4/7, 1, 2
Let h(w) be the second derivative of -w**7/1785 - w**6/510 + 77*w**2/2 - 79*w. Let z(u) be the first derivative of h(u). What is t in z(t) = 0?
-2, 0
Let l(a) = -7*a - 27. Let r be l(-3). Let z(d) = -d**3 - 5*d**2 + 5*d + 1. Let o be z(r). Let 14*s + 2*s**3 - 6*s**2 + 3 - o - 8*s + 2 = 0. Calculate s.
1
Let n(i) = -898*i + 22452. Let h be n(25). What is u in -39/2*u**3 + 0 - 15/8*u**4 - 15/2*u**h + 0*u = 0?
-10, -2/5, 0
Let a = -1951 - -3903/2. Factor a*u**2 + 5/3*u**3 + 0*u - 13/6*u**4 + 0.
-u**2*(u - 1)*(13*u + 3)/6
Let d(q) be the second derivative of q**6/30 + 2*q**5/5 + 5*q**4/4 - 4*q**3/3 - 8*q**2 - 23*q + 3. Solve d(t) = 0.
-4, -1, 1
Factor 207/2*a**3 + 0 + 1/4*a**5 + 134*a - 73/4*a**4 - 203*a**2.
a*(a - 67)*(a - 2)**3/4
Let d(h) be the first derivative of -5/38*h**4 + 2/95*h**5 + 0*h + 9/19*h**2 + 2/19*h**3 - 20. Suppose d(n) = 0. What is n?
-1, 0, 3
Factor 304*t + 2019*t - 6*t**3 - 44 - 623*t - 845*t**2 + 36*t**3 - 216.
5*(t - 26)*(t - 2)*(6*t - 1)
Let k = -21350/23 - -64073/69. Factor 9 + k*f**2 + 28/3*f.
(f + 1)*(f + 27)/3
Let n(m) = m**3 - 51 - m**2 - 43 + 92. Let y(r) = -2*r - 42. Let x be y(-18). Let f(w) = -27*w**3 - 93*w**2 - 96*w + 48. Let j(v) = x*n(v) - f(v). Factor j(g).
3*(g + 2)*(g + 3)*(7*g - 2)
Let b = 56 + -103. Let m = 164 + b. Factor -m + 5*k - 5*k**2 - 116 + 263.
-5*(k - 3)*(k + 2)
Let s be ((-4)/(-12) + -3)/((-10)/30). Factor -r**3 + 551*r + s*r**2 - 18 + 548*r - 1088*r.
-(r - 9)*(r - 1)*(r + 2)
Let k(i) = 3*i + 7. Let j be k(-1). Suppose 0 = 9*g - 22 + j. Suppose p**4 - 5*p**3 + 142*p**2 - 140*