1/13*v**2 + 14 - 28/39*v**3. Let x(m) = 0. What is m?
-1, 3
Suppose -6*y + 5*y = -3. Let f be 2/y*75/10. Factor -5*h**2 + f*h - 5*h - 28*h**3 + 13*h**2.
-4*h**2*(7*h - 2)
Let g(x) be the first derivative of x**6/2880 - x**5/320 + x**4/96 + 20*x**3/3 + 17. Let o(y) be the third derivative of g(y). Factor o(m).
(m - 2)*(m - 1)/8
Let m(f) be the third derivative of 1/70*f**5 + 0*f + 5/28*f**4 + 6/7*f**3 + 0 + 13*f**2. Factor m(t).
6*(t + 2)*(t + 3)/7
Let o be 9/(-12) - (-40)/(-32). Let m be ((-1)/o)/((-2)/(-52)). Determine s so that -m*s**3 + 481*s - 5*s**2 - 2*s**3 - 466*s + 5*s**4 = 0.
-1, 0, 1, 3
Let n = -4941/2 + 24711/10. Solve -18/5*t + 12/5*t**3 + 0 - n*t**4 - 3/5*t**2 = 0.
-1, 0, 2, 3
Let o(c) be the second derivative of 12*c + 3/5*c**2 + 0 - 1/20*c**4 + 1/10*c**3. Factor o(d).
-3*(d - 2)*(d + 1)/5
Let j(v) = 5*v**4 - 17*v**3 - 40*v**2 - 54*v + 6. Let o(a) = -a**4 + a**3 + a - 1. Let k(g) = 5*j(g) + 30*o(g). Factor k(d).
-5*d*(d + 3)*(d + 4)**2
Let f(w) = 2*w**4 + 134*w**3 - 126*w**2 - 134*w + 124. Let c(v) = -v**4 - 133*v**3 + 125*v**2 + 133*v - 124. Let x(n) = -6*c(n) - 5*f(n). What is l in x(l) = 0?
-1, 1, 31
Let v(l) be the third derivative of l**5/5 - 33*l**4/8 + 4*l**3 + 66*l**2. Let v(w) = 0. What is w?
1/4, 8
Let a(r) = -21*r**3 + 2*r**2 + r. Let j be a(-1). Let o be j/(-33) + (-28)/(-6). Factor 5*i**2 + o*i**3 + 0*i**3 + 6*i + 4*i**2 - i**3.
3*i*(i + 1)*(i + 2)
Let k(l) be the second derivative of l**6/90 + l**5/60 - 5*l**4/18 - 2*l**3/9 + 4*l**2 - 271*l - 2. Solve k(p) = 0.
-3, -2, 2
Let q(c) be the third derivative of 0*c + 1/25*c**5 + 8/45*c**3 + 1/9*c**4 + 7/900*c**6 - 6*c**2 + 1/1575*c**7 + 0. Suppose q(k) = 0. Calculate k.
-2, -1
Let u be (-192)/26 - (-35 - (-21 - 6)). What is j in -2/13*j**2 + u*j + 0 = 0?
0, 4
Let a(k) = -6*k**2 + 2*k + 6. Let j = -26 - -28. Let q(s) = -s**2 + s + 1. Let d(l) = j*q(l) - a(l). Factor d(h).
4*(h - 1)*(h + 1)
Let v be 0 + 204/24 - 7. What is x in -3/2*x**2 + 0*x + v*x**3 + 0 = 0?
0, 1
Let v = 8338 - 8336. Suppose 0*y**3 + 0 - 1/6*y**4 + 0*y + 2/3*y**v = 0. Calculate y.
-2, 0, 2
Let b(z) be the second derivative of -49*z**4/18 + 112*z**3/9 - 64*z**2/3 - 8*z - 9. Factor b(p).
-2*(7*p - 8)**2/3
Suppose 5*z + 12 = 3*i, -i - 3*i + 3*z + 16 = 0. Suppose -15 = -i*q - 3. Factor -4*h**4 + h**4 + 0*h**4 + 9*h**3 - 3*h**2 - q*h**3.
-3*h**2*(h - 1)**2
Suppose -3*j - 21 = -3*r, -4*j + 13 = 2*r - 19. Suppose 0 = 15*i - r - 20. What is s in -3*s + 3 + 3/4*s**i = 0?
2
Let o(t) be the second derivative of t**7/3780 - t**6/270 + t**5/60 + 3*t**4/4 - 9*t. Let q(l) be the third derivative of o(l). Suppose q(c) = 0. Calculate c.
1, 3
Let p(j) be the third derivative of -j**5/210 + 31*j**4/84 - 58*j**3/21 - 3*j**2 + 19. Determine y so that p(y) = 0.
2, 29
Let z(i) be the first derivative of 5*i**4/4 + 20*i**3/3 - 55*i**2/2 + 30*i + 475. Factor z(p).
5*(p - 1)**2*(p + 6)
Suppose 8/9*k + 10/9*k**2 + 2/9*k**3 + 0 = 0. Calculate k.
-4, -1, 0
Let u(a) be the first derivative of 0*a + 2/5*a**3 + 3/4*a**4 - 12 + 0*a**2 - 21/25*a**5. Solve u(j) = 0 for j.
-2/7, 0, 1
Let q(p) be the second derivative of -1/30*p**5 - 1/135*p**6 + 1/9*p**3 - 1/54*p**4 - 12*p + 2/9*p**2 + 0. Solve q(g) = 0 for g.
-2, -1, 1
Let x(d) = -d**3 + d**2 - 1. Let u(a) be the first derivative of 5*a**6/6 - a**4/2 - a**3 + 3*a - 8. Let z(w) = -u(w) - 3*x(w). Factor z(o).
-5*o**3*(o - 1)*(o + 1)
Let g = -5206 - -10447/2. Factor -20/3*j**2 + 5/6*j**3 + g*j - 15.
5*(j - 3)**2*(j - 2)/6
Let m(d) be the third derivative of d**9/35280 + d**8/15680 - d**7/1176 + d**6/560 - 7*d**4/12 - d**2. Let q(z) be the second derivative of m(z). Factor q(c).
3*c*(c - 1)**2*(c + 3)/7
Let l(h) be the third derivative of -h**6/30 - h**5/5 + 3*h**4/2 - 10*h**3/3 - 8*h**2. Determine s, given that l(s) = 0.
-5, 1
Let y(s) = -s**3 - 6*s**2 + 9*s + 13. Let b be y(-7). Let m(k) = 5*k + 8. Let n be m(b). Solve -1/6*l**n + 0 + 0*l + 0*l**2 - 1/6*l**5 + 1/3*l**4 = 0 for l.
0, 1
Let r(o) be the first derivative of o**4/26 - 46*o**3/39 + 7*o**2 + 78*o - 272. Factor r(u).
2*(u - 13)**2*(u + 3)/13
Let 1/3*h**4 - 140/3*h**3 + 4900/3*h**2 + 0 + 0*h = 0. Calculate h.
0, 70
Suppose -7*j + 6 = -4*j. Solve -19*u + 7*u - u**j + 6*u + 3*u = 0.
-3, 0
Let m(u) = -16*u**4 + 46*u**3 + 6*u**2 - 36*u + 20. Let k(z) = 5*z**4 - 15*z**3 - 2*z**2 + 12*z - 6. Let s(x) = 10*k(x) + 3*m(x). Let s(p) = 0. Calculate p.
-1, 0, 1, 6
Let m(c) = c**2 - 25*c - 28. Let b(w) = 24*w + 30. Let u(f) = 4*b(f) + 3*m(f). Factor u(x).
3*(x + 3)*(x + 4)
Determine z so that -316*z**3 - 641*z - 813*z**3 - 881*z**3 - 703*z + 256 + 2352*z**2 + 638*z**3 = 0.
4/7
Find w such that -242/17 - 46/17*w**2 + 2/17*w**3 + 286/17*w = 0.
1, 11
Let z = -86/139 + 814/417. Solve -4/3*o**3 + z*o**2 + 0*o + 0 = 0 for o.
0, 1
Let v = -31 + -181. Let j = v - -217. Factor -88/5*k**3 + 72/5*k**2 + 4/5 - 28/5*k - 12/5*k**j + 52/5*k**4.
-4*(k - 1)**4*(3*k - 1)/5
Let y(r) be the first derivative of 3*r**5/20 + 57*r**4/16 + 35*r**3/4 + 51*r**2/8 + 67. Factor y(j).
3*j*(j + 1)**2*(j + 17)/4
Find m, given that -12/17*m - 2*m**2 - 30/17*m**3 - 6/17*m**4 + 0 + 2/17*m**5 = 0.
-1, 0, 6
Let h(l) = l**3 - l**2 - l. Let k(m) = -4*m**3 + 4*m**2 - 3. Suppose 0*s + 4*s = 20. Let g(f) = s*h(f) + k(f). Suppose g(p) = 0. Calculate p.
-1, 3
Let y = 353/900 + 7/900. Find m, given that 0 + 8/5*m + 2*m**3 + 16/5*m**2 + y*m**4 = 0.
-2, -1, 0
Let b(s) be the first derivative of -s**6/210 + s**4/42 - s**2/14 + 17*s - 44. Let w(g) be the first derivative of b(g). Factor w(t).
-(t - 1)**2*(t + 1)**2/7
Let w(p) be the third derivative of p**6/480 - 7*p**5/120 + 7*p**4/32 + 3*p**3/2 - 291*p**2. Solve w(h) = 0 for h.
-1, 3, 12
Suppose 9*t = -5*t + 84. Let g be 6/((0 - (-4)/t)*3). Factor 0 + 0*k + 2/9*k**g + 4/9*k**2.
2*k**2*(k + 2)/9
Factor 209*y - 433*y + 126*y**2 - 3*y**3 + 2400 - 30*y - 1186*y.
-3*(y - 20)**2*(y - 2)
What is i in 8/13*i**3 + 0 - 2/13*i**4 - 6/13*i**2 + 0*i = 0?
0, 1, 3
Suppose 166 - 79 = 52*k + 87. Solve k - 3/7*p**2 - 12/7*p = 0.
-4, 0
Suppose 5*z + 0 - 20 = 0. Let t**4 - 5*t + 9*t**2 + 6*t**2 - 5*t**z + 5*t**3 - 10 - t**4 = 0. Calculate t.
-1, 1, 2
Let y = -76/3 + 26. Let q(d) = -2*d**3 - 21*d**2 + 10*d - 9. Let f be q(-11). Determine v, given that y*v - 1/3*v**f - 1/3 = 0.
1
Suppose 0 - 1/6*v**5 + 35/3*v**4 + 0*v**2 - 1225/6*v**3 + 0*v = 0. What is v?
0, 35
Let z(f) = f - 1. Let c(q) = -q**2 - q + 8. Let o(d) = -c(d) - 3*z(d). Let y be o(9). Determine j so that -18*j**2 + 66*j - 34*j**2 - y*j = 0.
0, 2/13
Factor -2307*f + 572*f - 2*f**5 - 1560*f**2 + 40*f**4 - 44*f**3 - 1307*f.
-2*f*(f - 13)**2*(f + 3)**2
Determine j, given that -1/4*j**3 + 135/2 - 1/4*j**4 + 63/4*j**2 - 243/4*j = 0.
-10, 3
Let t(h) = h**2 + 31*h + 11. Let u(l) = -3*l - 2 - 3*l + 6*l - 6*l. Let o(r) = 2*t(r) + 11*u(r). Factor o(d).
2*d*(d - 2)
Let z(a) be the first derivative of -20 - 7/4*a**4 + 0*a - 4/3*a**3 - 2/7*a**2. Determine i, given that z(i) = 0.
-2/7, 0
Let a(p) be the first derivative of -4*p + 3/40*p**5 + 1/8*p**4 + 3 - 1/4*p**3 - 3/4*p**2. Let k(z) be the first derivative of a(z). Factor k(s).
3*(s - 1)*(s + 1)**2/2
Suppose -2*k + 7 = d, -k - 5*d + 1 = 2. Suppose -10 = -c - k*c. Solve -10*u + 34*u**c - 8*u**2 - 18*u**2 + 2 = 0 for u.
1/4, 1
Let h(t) = 0*t**2 - 208 - t**2 + 35*t + 178. Let k be h(34). Solve k*l**2 + 1/4*l**5 + 3/2*l**4 + 1/2 + 7/2*l**3 + 9/4*l = 0.
-2, -1
Factor 2/7*p**2 + 172/7*p + 170/7.
2*(p + 1)*(p + 85)/7
Let t be 84/10 - (320 - 312). Solve t*r**2 + 4/5*r - 4/5*r**3 + 1/5*r**4 - 3/5 = 0 for r.
-1, 1, 3
Let m(s) = -s**3 + 19*s**2 + 7*s + 46. Let o be m(19). Let f = o + -179. Factor -2/5*l**3 + f*l**2 + 1/5*l**4 - 1/5 + 2/5*l.
(l - 1)**3*(l + 1)/5
Let g(u) be the first derivative of 1/10*u**5 - 1 + 0*u**4 - 2*u**2 - u**3 - 5*u. Let o(r) be the first derivative of g(r). Factor o(h).
2*(h - 2)*(h + 1)**2
What is a in -3/5*a**2 - 15 + 78/5*a = 0?
1, 25
Let l(z) be the first derivative of z**4/24 + z**3/6 - 3*z**2/2 - 37. Solve l(v) = 0 for v.
-6, 0, 3
Let q = -134 + 137. Let n(l) = 2*l - 4. Let b be n(q). Determine s so that -10/3*s - 2/3*s**3 + 8/3*s**b + 4/3 = 0.
1, 2
Let k(j) = -2*j**2 + 55*j - 53. Let n(v) = -9*v**2 + 219*v - 210. Let d(o) = 21*k(o) - 5*n(o). Factor d(y).
3*(y - 1)*(y + 21)
Suppose -246 = -p - 3*w, 0*p + 4*p - 977 = -5*w. Let l = -2669/