h + 2/15*h**2 + 0 + 2/15*h**3 - 2/15*h**4 = 0. Calculate h.
-1, 0, 1
Let o(h) be the second derivative of h**4/12 - 41*h**3/3 + 1681*h**2/2 - 3*h - 25. Factor o(j).
(j - 41)**2
Let l = -5 + 10. Let s(m) = -15*m**2 + 1 + 11*m**2 + l*m**2. Let k(v) = 3*v**2 - 2*v + 5. Let p(b) = -2*k(b) + 10*s(b). Factor p(a).
4*a*(a + 1)
Let p(n) be the third derivative of -n**6/540 + n**4/36 + 11*n**3/6 - 2*n**2. Let d(i) be the first derivative of p(i). Let d(h) = 0. What is h?
-1, 1
Suppose 4 = 36*l - 33*l + p, -2*p + 8 = 2*l. Let r(z) be the third derivative of l*z**3 + 0 + 0*z + 1/24*z**6 + 1/30*z**5 + 0*z**4 - 4*z**2. Factor r(y).
y**2*(5*y + 2)
Suppose 2*g + 37 = 41. Factor -1 + 8*i**g - i**3 + 2 + 5 - 13*i.
-(i - 6)*(i - 1)**2
Let v(j) be the second derivative of -j**8/4480 + j**7/1680 + 3*j**4/4 + 27*j. Let d(w) be the third derivative of v(w). Factor d(f).
-3*f**2*(f - 1)/2
Let p(h) be the third derivative of 1/12*h**5 + 0*h - 5/24*h**4 + 0*h**3 - 11*h**2 + 0. Factor p(s).
5*s*(s - 1)
Find z such that 0 + 1/3*z**3 + 0*z + 38/3*z**2 = 0.
-38, 0
Let b be (-1 + 0)*(-3)/(-18)*-320. Let z = b + -50. Factor -2*m**2 - z*m**3 + 4/3*m + 0.
-2*m*(m + 1)*(5*m - 2)/3
Let o(s) be the first derivative of 4*s**3/3 + 12*s**2 + 32*s - 293. Determine r so that o(r) = 0.
-4, -2
Factor 4716 - 9482 + 84*f + 4*f**2 + 4918.
4*(f + 2)*(f + 19)
Let q be 96/15 - 4/10. Let l be (2/4)/(2/16). Suppose i**3 + 2*i - 3*i - q*i**l + 4*i + 6*i**2 - 4*i**3 = 0. What is i?
-1, -1/2, 0, 1
Let w be 0 + 10/(-6) + (-85)/(-51). Let s(j) be the third derivative of 0*j**4 + w + 0*j**3 + 1/60*j**5 + 2*j**2 + 0*j. Solve s(d) = 0.
0
Suppose -2*j - 2*m + 8 = 0, 4*j = 5*m - 0*m - 11. Let w = 5/3 - j. Find n such that 0*n + 0 - w*n**2 + 2*n**3 = 0.
0, 1/3
Let l(r) be the second derivative of 3/40*r**5 - 3/4*r**4 + 0 - 16*r + 9/4*r**3 + 0*r**2. Factor l(f).
3*f*(f - 3)**2/2
Let q = 53945/3 + -17979. Factor -2/3*f**3 - 2*f + 0 + q*f**2.
-2*f*(f - 3)*(f - 1)/3
Let y = -10271 + 154219/15. Find j, given that 64/15*j**2 - y*j**3 + 98/15*j**4 + 0 - 8/15*j = 0.
0, 2/7, 1
Factor 82/3*q**2 - 26*q**3 + 0 + 22/3*q**4 + 2/3*q**5 - 28/3*q.
2*q*(q - 1)**3*(q + 14)/3
Let v be -6 + 8/(-12) + (-78)/(-9). Let m be (-4)/18 - (-2)/9. Factor 0*w**4 + 0 + 3/2*w**3 - 3/2*w**5 + m*w + 0*w**v.
-3*w**3*(w - 1)*(w + 1)/2
Suppose 3*j = 9 - 51. Let k = j + 32. Let d(q) = q**4 + q**2. Let l(n) = -3*n**5 - 12*n**4 - 24*n**2 + 3*n. Let y(t) = k*d(t) + l(t). Find x such that y(x) = 0.
-1, 0, 1
What is z in -3/5*z**3 + 29/5*z + 2*z**2 + 16/5 = 0?
-1, 16/3
Let k = -17 - -19. Let g(j) be the second derivative of 8/7*j**k + 1/7*j**4 + 0 + 4/7*j**3 + 2*j + 1/70*j**5. Solve g(z) = 0 for z.
-2
Let w(y) be the first derivative of -4*y**3/15 - 12*y**2/5 + 28*y/5 - 263. Find t such that w(t) = 0.
-7, 1
Let a be (7 + 1)*(-1)/(-2). Factor -11*i**3 - 6*i**4 + a*i**3 + 0*i**3 + 4*i**3 - 3*i**5.
-3*i**3*(i + 1)**2
Suppose 74 = 54*q - 142. Let i(f) be the third derivative of 0*f**3 - 1/200*f**6 - 10*f**2 + 0*f**q + 0 + 0*f + 0*f**5. Factor i(p).
-3*p**3/5
Suppose 79*h = 76*h. Let w(c) be the second derivative of 14/5*c**3 + 12/5*c**2 + 11/10*c**4 + 6*c + h + 3/20*c**5. Factor w(k).
3*(k + 2)**2*(5*k + 2)/5
Let q = 0 - -8. Suppose -5*v = -9*v + q. Let -5*c**3 + 3*c**2 + v*c**5 + 2*c**3 + c**5 - 3*c**4 = 0. What is c?
-1, 0, 1
Suppose 0 = -5*u + 3*j + 20, -u - 8*j + 3*j + 4 = 0. Let z(p) be the third derivative of 0*p**u + 0*p - 1/36*p**3 + 0 + 1/360*p**5 - 5*p**2. Solve z(r) = 0.
-1, 1
Let k(x) = -2*x - 50. Let y be k(-24). Let w be 70/(-84)*y/5. Let c**4 - c**2 + w*c - 1/3*c**3 + 0 = 0. Calculate c.
-1, 0, 1/3, 1
Suppose 0 = -2*q - 2*q. Suppose 2*j = -q*j. Solve j*g**3 + 0 - 18/7*g**4 + 4/7*g + 2*g**2 = 0.
-2/3, -1/3, 0, 1
Suppose -4*u + 16 = -3*i, i + 0*u + 2*u - 8 = 0. Suppose -5*z + 40 = -i*z. What is w in -6*w + z*w**2 + 0*w + w**4 + 10*w + 5*w**3 = 0?
-2, -1, 0
Let o(b) be the first derivative of -1/10*b**4 - 7/5*b**2 - 6/5*b - 2/3*b**3 + 3. Factor o(h).
-2*(h + 1)**2*(h + 3)/5
Let f(u) be the first derivative of 2*u**6/15 - 12*u**5/25 + 541. Factor f(j).
4*j**4*(j - 3)/5
Let y(g) = 2*g + 4. Let k be y(-10). Let x(o) = 2*o**2 + 4*o + 2. Let z(t) = -6*t**2 - 12*t - 6. Let m(h) = k*x(h) - 5*z(h). Determine c, given that m(c) = 0.
-1
Let 0 + 3/4*w**4 + 3/4*w**5 + 0*w - 3/4*w**3 - 3/4*w**2 = 0. Calculate w.
-1, 0, 1
Let f = -36 - -66. Factor 4*r**3 + r**3 - f*r**2 + 19*r + 9*r**3 - r - 2*r**4.
-2*r*(r - 3)**2*(r - 1)
Let p(u) = u**2 + 10*u + 13. Let f(j) be the second derivative of 7*j**2 + 1/12*j**4 + 11/6*j**3 + 0 - 3*j. Let r(c) = -4*f(c) + 5*p(c). Factor r(x).
(x + 3)**2
Let b(w) = 9*w**2 - 7*w + 3. Let r(z) = 44*z**2 - 36*z + 16. Suppose -2*l - 21 = 3*x, -x - l = 2*l + 14. Let i(u) = x*r(u) + 24*b(u). What is h in i(h) = 0?
1, 2
Let l(w) be the first derivative of 7/5*w**2 + 2/25*w**5 + 6/5*w**3 + 1/2*w**4 + 11 + 4/5*w. Solve l(a) = 0.
-2, -1
Determine x, given that -42/11*x**5 + 0 - 120/11*x**4 - 24/11*x**2 - 108/11*x**3 + 6/11*x = 0.
-1, 0, 1/7
Let j = 82591/55062 - -1/27531. Factor -j*g - 1/8*g**2 - 9/2.
-(g + 6)**2/8
Let j be (-13 - -3) + 9 + 19. Factor j*c**2 - 15*c - 9*c**3 + 3/2*c**4 + 9/2.
3*(c - 3)*(c - 1)**3/2
Let j(n) be the first derivative of -n**7/147 - n**6/105 - 29*n + 4. Let a(t) be the first derivative of j(t). Let a(v) = 0. What is v?
-1, 0
Let k = 10 - 8. Suppose -7*d = -k*d - 10. Let d*l**2 + l + 4*l - 3*l - 4*l**2 = 0. What is l?
0, 1
Let y(b) be the second derivative of b**7/189 + 14*b**6/135 - 4*b**5/45 - 184*b**4/27 + 1040*b**3/27 - 800*b**2/9 + 2*b - 44. Suppose y(z) = 0. What is z?
-10, 2
Let a = 1960/849 - -7/283. Factor 3 - 5*m + a*m**2 - 1/3*m**3.
-(m - 3)**2*(m - 1)/3
Find q, given that 5*q**3 - 4*q**3 - 4227*q**2 + 4316*q**2 + 1840*q - 6348 = 0.
-46, 3
Suppose -7*g + 224 = 9*g. Let y(p) = p**2 + 8*p - 9. Let o(a) = -a + 1. Let n(q) = g*o(q) + 2*y(q). Factor n(u).
2*(u - 1)*(u + 2)
Let w(m) be the first derivative of -m**6/12 + 3*m**5/10 - m**4/8 - m**3/2 + m**2/2 - 24. Suppose w(y) = 0. Calculate y.
-1, 0, 1, 2
Suppose -3*t = 11*d - 8*d, 2*t = 5*d. Let l(v) be the third derivative of d*v + 1/30*v**5 + 0*v**3 - 1/60*v**6 + 1/6*v**4 + 0 + 3*v**2. Factor l(i).
-2*i*(i - 2)*(i + 1)
Let z(b) be the third derivative of 5*b**8/672 - b**7/84 - b**6/4 - b**5/6 + 5*b**4/3 - 67*b**2. Solve z(x) = 0 for x.
-2, 0, 1, 4
Let k(m) = m**2 - 5*m + 3. Let l be k(5). Suppose -11 - 1 = -o + n, -4*n - 41 = -l*o. Suppose o*c**3 - 1 + c - 8*c**3 + 1 = 0. Calculate c.
-1, 0, 1
Solve 17936/3*o - 11552/3 + 4*o**3 - 920/3*o**2 = 0.
2/3, 38
Let d be (495/456)/(-5)*-2. Let r = d + 6/19. Solve 1/4*u - 1/4*u**4 + r*u**3 + 0 - 3/4*u**2 = 0.
0, 1
Let p(j) = 75*j**3 + 5*j - 2. Let q be p(2). Suppose -117*z**2 + q*z**3 + 135*z**5 - 66*z + 339*z**2 - 504*z**4 - 24 - 233*z**3 + 6*z = 0. What is z?
-1/3, 2/5, 2
Let v(y) be the third derivative of -1/180*y**6 - 1/30*y**5 - 1/12*y**4 + 0*y + 0 + 4*y**2 - 1/9*y**3. Solve v(k) = 0.
-1
Suppose 5*h = -6*p + 3*p + 11, 2*h = p. Suppose -6 + p = -2*n. Factor v**n - 4*v**3 + 3*v**3 - 13*v + 13*v.
-v**2*(v - 1)
What is o in 5/2*o**2 + 1960 - 140*o = 0?
28
Let w(m) be the first derivative of -5*m**6/3 - 44*m**5/5 - 23*m**4/2 + 28*m**3/3 + 28*m**2 + 16*m + 76. Solve w(y) = 0 for y.
-2, -1, -2/5, 1
Let l = 2/401 + 748/10827. Let t(i) be the first derivative of -l*i**3 + 4/9*i + 5 + 1/9*i**2. Suppose t(g) = 0. What is g?
-1, 2
Let t(u) be the third derivative of 17*u**5/140 + 19*u**4/56 + u**3/7 + 94*u**2 - 1. What is r in t(r) = 0?
-1, -2/17
Let n(u) = -u**3 - 9*u**2 + 15*u + 3. Let b be n(-11). Factor 31*l**2 - 36*l**2 - b + 59*l - 19*l.
-5*(l - 4)**2
Let g(t) be the first derivative of 2*t**5/55 - 18*t**4/11 + 324*t**3/11 - 2916*t**2/11 + 13122*t/11 - 108. Find v such that g(v) = 0.
9
Factor 0 + 7/4*q**2 + 2*q - 1/4*q**3.
-q*(q - 8)*(q + 1)/4
Let s(b) be the first derivative of 5*b**7/42 + b**6/3 + b**5/4 + 17*b + 8. Let v(h) be the first derivative of s(h). Factor v(a).
5*a**3*(a + 1)**2
Let d(n) be the first derivative of -n**5/5 - 3*n**4/4 + n**3/3 + 3*n**2/2 - 72. Suppose d(a) = 0. Calculate a.
-3, -1, 0, 1
Determine s, given that -75/4 + 39/2*s - 3/4*s**2 = 0.
1, 25
Let f(t) be the first derivative of -8/7*t**2 + 0*t + 4/7*t**3 + 1/7*t**4 + 18. Suppose f(l) = 0. What is l?
-4, 0, 1
Suppose -7*t = -4*r