 = -10, -5*f = 3*u - 22. Solve 0 - 8*v - 4*v**2 - u + 4 = 0 for v.
-2, 0
Let c(t) be the first derivative of 1/40*t**6 - 1/20*t**5 - t**2 - 1/8*t**4 + 1/2*t**3 + 3 + 0*t. Let o(l) be the second derivative of c(l). Factor o(p).
3*(p - 1)**2*(p + 1)
Solve 0 + 49/10*j**5 - 49/5*j**4 - 2/5*j + 9/2*j**3 + 4/5*j**2 = 0 for j.
-2/7, 0, 2/7, 1
Let i(g) be the third derivative of g**8/168 + 74*g**7/315 + 41*g**6/30 + 18*g**5/5 + 191*g**4/36 + 14*g**3/3 + 233*g**2. Suppose i(q) = 0. What is q?
-21, -1, -2/3
Let c(j) be the third derivative of -j**7/315 + j**6/90 + 7*j**5/90 - 2*j**4/9 - 4*j**3/3 - 152*j**2. Find w such that c(w) = 0.
-2, -1, 2, 3
Let l(h) = -2*h - 9. Let n be l(8). Let d = n + 29. Factor -d + 4*q**3 + 32*q**2 + 64*q + 4.
4*q*(q + 4)**2
Factor -59/2*s + 1/2*s**4 - 10 - 57/2*s**2 - 17/2*s**3.
(s - 20)*(s + 1)**3/2
Let 15/4 + 61/4*y + y**2 = 0. What is y?
-15, -1/4
Let b(o) be the second derivative of -1/20*o**4 + 0 + 2*o + 0*o**3 + 0*o**2 + 3/50*o**6 - 3/50*o**5. Factor b(r).
3*r**2*(r - 1)*(3*r + 1)/5
Let f = -3879/10 - -390. Let s = 209/90 - f. Factor 0*t**3 - 2/9*t**2 + s*t**4 + 0*t + 0.
2*t**2*(t - 1)*(t + 1)/9
Let k(h) = h**3 + 3*h**2 - 6*h - 5. Let n = 120 - 124. Let x be k(n). Factor 0*i - 8/3*i**2 + 0*i**x + 1/3*i**4 + 16/3.
(i - 2)**2*(i + 2)**2/3
Let n = -76 - -80. Suppose -2*i + n = -0. What is k in 2/5*k + 0 - 2/5*k**i = 0?
0, 1
Let r be 3 + (-34)/8 + (-10 - 60/(-4)). Determine w so that -5/4 - 6*w - r*w**2 + w**3 = 0.
-1, -1/4, 5
Let i(k) = -8*k**3 + 8*k + 8. Suppose 0*t = -5*t + 5. Let d be (3 - 1)/t + -11. Let l(r) = -r**4 + 16*r**3 - 16*r - 17. Let s(y) = d*i(y) - 4*l(y). Factor s(n).
4*(n - 1)*(n + 1)**3
Let s(r) be the first derivative of -1/15*r**5 - 5/2*r**2 - 1/120*r**6 + 1 + 0*r**3 - 1/6*r**4 + 0*r. Let c(o) be the second derivative of s(o). Factor c(q).
-q*(q + 2)**2
Let m = 40 - 31. Factor 6*c**4 - 18*c + 36*c**3 + m*c**4 - 4*c**2 - 29*c**2.
3*c*(c - 1)*(c + 3)*(5*c + 2)
Let i(l) = 4*l**2 - 34*l + 54. Let r be i(2). What is g in 8/3 - 2/3*g**r - 2*g = 0?
-4, 1
Let z = 36 - 32. Determine c so that -4*c**2 + z*c - 4 + 3*c**5 + 6*c - 5*c**5 - 8*c**3 + 8*c**4 = 0.
-1, 1, 2
Suppose n + 3*n + 16 = -4*m, 2*m = -4*n. Let v be (-14)/(-2) - (m - -13). Factor -3/5*g**3 + 0 - 3/5*g**v + 6/5*g.
-3*g*(g - 1)*(g + 2)/5
Let m be 5 + -1 + (-2)/(-2). Let w = -212/5 + 44. Solve -6/5*h**4 + 14/5*h**2 - w + 2/5*h**m + 0*h - 2/5*h**3 = 0 for h.
-1, 1, 2
Let t(p) be the second derivative of p**8/2520 + p**7/630 + 5*p**3/6 + 8*p. Let y(h) be the second derivative of t(h). Factor y(r).
2*r**3*(r + 2)/3
Factor 816*r**2 - 160 + 166 - 818*r**2 - 344 - 52*r.
-2*(r + 13)**2
Let h(u) = -u**2 - 2*u + 63. Let k be h(7). Let p(v) be the third derivative of 11/84*v**4 + 0 + k*v + 5*v**2 + 1/7*v**3 - 2/105*v**5. Factor p(j).
-2*(j - 3)*(4*j + 1)/7
Factor -268*j**3 - j**4 + 271*j**3 - 12*j + 14 + 2*j**2 - 6.
-(j - 2)**2*(j - 1)*(j + 2)
Let b = -26/19 - -301/95. Let k be (-8 + 7)*(2 + -1)*-4. Factor 0*y - b*y**3 + 3/5*y**2 + 0 - 3/5*y**5 + 9/5*y**k.
-3*y**2*(y - 1)**3/5
What is g in -96/5 - 2/5*g**2 + 98/5*g = 0?
1, 48
Let f be (-1*1)/((-26)/78). What is m in 320*m**2 + 52*m + 115*m + 72 + 100*m**f + 109*m = 0?
-2, -3/5
Find i such that -48 - 36/5*i**2 + 2*i**3 - 616/5*i = 0.
-6, -2/5, 10
Let 8/5*f**3 + 16/5*f**2 + 1/5*f**4 + 0*f + 0 = 0. What is f?
-4, 0
Let c(x) be the first derivative of x**4/12 + 8*x**3/9 + 7*x**2/6 - 97. Suppose c(t) = 0. What is t?
-7, -1, 0
Let l(k) be the third derivative of k**5/240 - 7*k**4/32 + 13*k**3/3 - 711*k**2. Factor l(v).
(v - 13)*(v - 8)/4
Let t(a) be the third derivative of -39*a**2 - 8/21*a**3 + 0 + 1/60*a**5 + 1/21*a**4 + 0*a + 1/840*a**6. Suppose t(m) = 0. What is m?
-4, 1
Solve 1/2*l**4 - 9/2*l**2 + 4 + l**3 - l = 0 for l.
-4, -1, 1, 2
Factor -17*q + 1/4*q**2 + 289.
(q - 34)**2/4
Let s(v) = -v**2 - 1. Let q(t) = t**2 + 11*t - 18. Let u(m) = m**2 + 22*m - 35. Let w(k) = -5*q(k) + 3*u(k). Let y(g) = 3*s(g) - w(g). Factor y(f).
-(f - 1)*(f + 12)
Let r = 1043/120 - 26/3. Let u(q) be the third derivative of -1/16*q**4 + 0*q - 5*q**2 + 0*q**3 + 0 + 1/80*q**6 + 1/140*q**7 - r*q**5. Factor u(s).
3*s*(s - 1)*(s + 1)**2/2
Suppose 0 = 4*l + 1 - 21. Factor -5*z**4 - 1 + 10*z**4 + 15*z**3 - 15*z + 0 + l*z**2 - 9.
5*(z - 1)*(z + 1)**2*(z + 2)
Factor -169*l**2 - 13*l - 1/4.
-(26*l + 1)**2/4
Let f(t) be the second derivative of -t**7/6300 + t**6/900 + t**5/100 + t**4/6 + 3*t. Let p(c) be the third derivative of f(c). Factor p(o).
-2*(o - 3)*(o + 1)/5
Let c(y) = -y**2 - 6*y + 43. Let f be c(-10). Let a = 5 - 3. Determine x so that 6*x - 29 - 20*x**a + f*x + 28 = 0.
1/5, 1/4
Factor 200*r**3 - 200*r - 35*r**2 + 205 + 3*r**4 - 156*r**2 - 19*r**2 + 2*r**4.
5*(r - 1)**2*(r + 1)*(r + 41)
Let l(u) = 2*u**3 + 5*u**2 - 8*u - 1. Let g(j) = -j**3 - j. Let t(o) = -3*g(o) + l(o). Let q(r) be the first derivative of t(r). Find w such that q(w) = 0.
-1, 1/3
Factor -2/3*m**2 - 8*m + 26/3.
-2*(m - 1)*(m + 13)/3
Suppose -146 = -10*h + 174. Let l = h + -28. Factor 0 + 1/5*f**l + 0*f + 0*f**2 - 1/5*f**3.
f**3*(f - 1)/5
Let b(c) be the second derivative of -1/20*c**4 + 0 + 0*c**2 + 0*c**3 + 21*c. Factor b(k).
-3*k**2/5
Suppose 60 - 66 = -3*q. Suppose 2*a**5 - 2*a**2 + 2*a**4 - 51 - q*a**3 + 51 = 0. What is a?
-1, 0, 1
Let i(w) be the first derivative of -25/4*w**4 - 16 + 65/2*w**2 + 50*w + w**5 - 5*w**3. Solve i(o) = 0.
-1, 2, 5
Let u(b) be the third derivative of -b**8/48 - 2*b**7/35 + 5*b**6/24 + 5*b**5/6 + b**4/2 - 4*b**3/3 - 17*b**2 - 5. Let u(w) = 0. What is w?
-2, -1, 2/7, 2
Suppose 5*p = 2*i - 4*i + 65, -2*p + 5*i + 26 = 0. Find r such that -7*r**2 - 18*r**2 + 40*r + 5*r**3 - 33 + p = 0.
1, 2
Let u(t) be the first derivative of t**3/9 - 7*t**2/3 + 13*t/3 - 50. Factor u(h).
(h - 13)*(h - 1)/3
Let d(v) be the first derivative of -69/5*v**5 - 7/2*v**6 - 3*v**2 + 0*v + 6 - 81/4*v**4 - 13*v**3. Factor d(m).
-3*m*(m + 1)**3*(7*m + 2)
Let z = -37 + 41. Find f such that -12*f**3 + z*f**3 - 2*f**2 - f**4 + 12*f**3 - f**4 = 0.
0, 1
Let w = -11 + 14. Suppose 5*j + 35 = 3*z, -2*j = -w*z + 2*j + 34. Find p, given that z*p**3 - 5*p**5 - 78 - 5*p + 78 = 0.
-1, 0, 1
Let u = -33 + 21. Let n = u + 15. Factor 42*a**2 - 15*a + 3 + 6 - a**n - 35*a**2.
-(a - 3)**2*(a - 1)
Let c = 1433/1729 + 7/247. Factor 0*w - c*w**2 + 8/7 - 2/7*w**3.
-2*(w - 1)*(w + 2)**2/7
Let -1/4*f**4 + 1/2*f - 15/4 + 4*f**2 - 1/2*f**3 = 0. What is f?
-5, -1, 1, 3
Let x be 2 + ((-132)/176)/(0 - 27/(-24)). Factor 4*r - x*r**3 + 0*r**2 - 8/3.
-4*(r - 1)**2*(r + 2)/3
Suppose -4*f + 3 = 7. Let d(c) = c**5 + c**4 - c**2 + c. Let g(v) = 4*v**5 - 8*v**4 + 6*v**3 + 5*v**2 - 8*v + 3. Let q(b) = f*d(b) + g(b). Factor q(w).
3*(w - 1)**4*(w + 1)
Let h = 76 - 71. Let m(c) be the second derivative of 5*c + 6*c**2 + 1/5*c**h + 5/3*c**4 + 14/3*c**3 + 0. Factor m(a).
4*(a + 1)**2*(a + 3)
Let r(n) = -51*n**4 - 18*n**3 + 309*n**2 - 150*n + 12. Let x(m) = -103*m**4 - 34*m**3 + 618*m**2 - 301*m + 22. Let t(g) = -7*r(g) + 3*x(g). Factor t(b).
3*(b - 2)*(b + 3)*(4*b - 1)**2
Find x such that -39/4*x**3 - 37/4*x**2 + 0 + 1/2*x = 0.
-1, 0, 2/39
Factor -1/3*u**2 + 52*u - 2028.
-(u - 78)**2/3
Let l(k) = -5*k**3 - 8*k**2 - 5*k + 6. Let w(d) = d + 5*d**3 + 8*d**2 + 3*d - 32 + 27. Let s(z) = 3*l(z) + 4*w(z). Factor s(i).
(i + 1)**2*(5*i - 2)
Suppose 2*v + 264 = m, 4*m - 2*v - 1288 = -m. Let -228*b**4 + 41*b**5 + 545*b**3 - 37*b**3 - 48 - 5*b**5 - 524*b**2 + m*b = 0. What is b?
2/3, 1, 3
Let x(w) be the third derivative of -w**8/84 + 11*w**7/105 - w**6/5 - w**5/30 + w**4/3 + 40*w**2. Find f such that x(f) = 0.
-1/2, 0, 1, 4
Let d(f) = 7*f**4 + 10*f**3 - 11*f**2 + 6*f. Let x(t) = -75*t**4 + 282*t**2 - 65*t - 94*t**2 - 68*t**2 - 110*t**3. Let b(c) = -65*d(c) - 6*x(c). Factor b(u).
-5*u**2*(u - 1)**2
Suppose -31*z = -29*z. Factor -3*b - b + z*b + 3*b**3 + b**3.
4*b*(b - 1)*(b + 1)
Suppose -4*i - 3*o = -26, 5*o = -i + o + 26. Find j, given that 6/11*j**i + 18/11 + 24/11*j = 0.
-3, -1
Solve 65*d**3 + 40/3 + 60*d + 290/3*d**2 + 15*d**4 = 0.
-2, -1, -2/3
Let v(z) = -z**2 + 13*z + 12. Let l be v(13). Let m be 0*(-4)/l - -34. Factor 25*u**2 + 8 - 15*u - 21*u - 20*u**3 - 11*u**2 + m*u**2.
-4*(u - 1)**2*(5*u - 2)
Suppose 68*j - 29*j = 17*j + 44. Factor -5/2*r - 2*r**3 + 1 - 11/2*r**j.
-(r + 1)*(r + 2)*(4*r - 1)/2
Let w(k) be the 