t p(n) be the first derivative of 1/4*n**6 - 31 + 0*n - 3/4*n**2 + 0*n**4 + n**3 - 3/5*n**5. Solve p(t) = 0.
-1, 0, 1
Find n, given that -40*n + 25*n**3 - 5*n**5 + 23*n**4 + 23*n**4 - 41*n**4 - 5*n**2 - 20 = 0.
-1, 2
Factor -90*u**3 - 50*u + 45*u**4 - 338*u**3 + 148*u**3 + 278*u**2 + 7*u**2.
5*u*(u - 5)*(u - 1)*(9*u - 2)
Factor -2/5*k**3 + 0*k + 28/5*k**2 + 0.
-2*k**2*(k - 14)/5
Suppose 0*f = 5*f - 5. Suppose -14 = -5*y + f. Suppose -5*j - 4*j**y - 3*j + 0*j - 12*j**2 = 0. What is j?
-2, -1, 0
Let q be 3 - 0/(-1 - 12/(-4)). Factor 102*x**3 - 272*x + 4 - 37 - 504*x**2 + 1 + 222*x**q.
4*(x - 2)*(9*x + 2)**2
Let c = 17627 - 17624. Factor 1/5*m**c - 3/5*m**2 + 4/5 + 0*m.
(m - 2)**2*(m + 1)/5
Factor 16*o**2 + 13*o**5 - 2*o**5 - 11*o**4 - 5*o**4 - 4*o**3 - 7*o**5.
4*o**2*(o - 4)*(o - 1)*(o + 1)
Let a(p) be the second derivative of p**5/80 - p**4/12 - 41*p**3/24 - 9*p**2/2 - 94*p + 3. Factor a(m).
(m - 9)*(m + 1)*(m + 4)/4
Factor 96*z**3 - 10*z**5 + 144*z + 2388*z**4 - 2361*z**4 + 48 + 168*z**2 + 13*z**5.
3*(z + 1)*(z + 2)**4
Find v, given that 0*v - 7*v - 5*v**2 + 2*v**2 - 50*v - 9*v = 0.
-22, 0
Let a(s) be the first derivative of -20 + 1/12*s**3 + 1/4*s**2 - 3/4*s. Factor a(p).
(p - 1)*(p + 3)/4
Let t(w) be the third derivative of -w**6/60 - 19*w**5/30 - 35*w**4/12 - 17*w**3/3 - 545*w**2. Find z, given that t(z) = 0.
-17, -1
Let m(t) = 2*t**2 + t - 1. Let v(u) = 7*u**2 - 92*u + 93. Let a(b) = 4*m(b) - v(b). Factor a(d).
(d - 1)*(d + 97)
Let r(n) = n**2 - 8*n + 12. Let y be r(6). Let q = y - -5. Let 2/5*i + 12/5*i**3 - 8/5*i**2 + 2/5*i**q + 0 - 8/5*i**4 = 0. Calculate i.
0, 1
Factor -17*y**2 + 3*y**3 + 16*y**2 - 4*y - y**3 + 4 - y**3.
(y - 2)*(y - 1)*(y + 2)
Let f = 2088 - 2079. Suppose 15/4*g**4 - f*g**3 + 0 + 27/4*g**2 - 3/2*g = 0. Calculate g.
0, 2/5, 1
Let v(n) be the first derivative of -8/3*n**3 - 1 + 4/3*n**4 + 2*n**2 - 9*n. Let f(k) be the first derivative of v(k). Factor f(b).
4*(2*b - 1)**2
Suppose -18/7 + 12/7*s**3 - 160/7*s**2 - 108/7*s + 18/7*s**4 = 0. What is s?
-3, -1/3, 3
Let u(b) be the first derivative of 13/16*b**4 + 1/24*b**6 - b**3 + 0*b - 3/10*b**5 + 1/2*b**2 - 4. Suppose u(k) = 0. What is k?
0, 1, 2
Let q(r) be the first derivative of -r**5/40 - r**4/6 - 5*r**3/12 - r**2/2 - 4*r + 14. Let w(t) be the first derivative of q(t). Let w(h) = 0. What is h?
-2, -1
Suppose -7*h + 6*h = 11*h. Find j such that 8/5*j**3 + h + 2*j**2 + 2/5*j**4 + 4/5*j = 0.
-2, -1, 0
Let r(n) be the first derivative of -9*n**3/4 - 183*n**2/8 + 21*n/2 + 243. Find c such that r(c) = 0.
-7, 2/9
Factor -15/2*a - 3/4*a**2 - 27/4.
-3*(a + 1)*(a + 9)/4
Let r(k) be the third derivative of k**5/510 + 37*k**4/204 + 12*k**3/17 - 98*k**2 + 2*k. Factor r(z).
2*(z + 1)*(z + 36)/17
Let j(k) = k**3 - k**2 + k. Let r = -6 + 5. Let p(g) = -5*g**3 + 3*g**2 - 2*g. Let b(w) = r*p(w) - 4*j(w). Factor b(y).
y*(y - 1)*(y + 2)
Let n(t) be the first derivative of t**6/2 - 12*t**5 + 351*t**4/4 - 162*t**3 + 654. Suppose n(y) = 0. Calculate y.
0, 2, 9
Factor -1/8*u**2 - 1/8*u**3 - 15/8 + 17/8*u.
-(u - 3)*(u - 1)*(u + 5)/8
Let s(i) be the first derivative of i**6/3 + 34*i**5/5 + 39*i**4 + 64*i**3/3 - 128*i**2 - 274. Suppose s(z) = 0. Calculate z.
-8, -2, 0, 1
Suppose -5*a - j + 82 = 0, 59 = 5*a - 3*j - 15. Let c = a - 13. Factor -c*h + 2*h + h**5 + 2*h**4 - 2*h**2 + 0*h.
h*(h - 1)*(h + 1)**3
Factor -14*w**3 + 10*w**3 - w**3 - 5*w + 2 - 2 - 10*w**2.
-5*w*(w + 1)**2
Let z(g) be the first derivative of -g**7/420 + g**5/60 - g**3/12 - 6*g**2 - 7. Let t(i) be the second derivative of z(i). Factor t(h).
-(h - 1)**2*(h + 1)**2/2
Let h(w) = -2*w**5 - 12*w**4 - 18*w**3 + 12*w**2 + 15*w. Let m(t) = -9*t**5 - 60*t**4 - 90*t**3 + 60*t**2 + 75*t. Let x(b) = -24*h(b) + 5*m(b). Factor x(l).
3*l*(l - 5)*(l - 1)*(l + 1)**2
Let z(b) be the third derivative of b**5/300 - 3*b**4/20 + 3*b**3/2 + 409*b**2. Factor z(q).
(q - 15)*(q - 3)/5
Let c(q) = 2*q**4 + 28*q**3 + 26*q**2 - 4. Let b(g) = -3*g**4 - 28*g**3 - 25*g**2 + 5. Let d(v) = -4*b(v) - 5*c(v). Factor d(w).
2*w**2*(w - 15)*(w + 1)
Suppose 26*y - 8*y = 3312. Let x = y + -179. Factor 6/13*j**4 + 4/13*j**3 + 2/13*j**x - 6/13*j - 2/13 - 4/13*j**2.
2*(j - 1)*(j + 1)**4/13
Suppose 3*c + 0*u = -7*u + 5*u, -u = 0. Factor -2/9*h**4 + c + 2/9*h - 2/9*h**3 + 2/9*h**2.
-2*h*(h - 1)*(h + 1)**2/9
Let a(w) be the first derivative of 0*w**3 + 2*w**2 + 0*w + 1/160*w**5 + 7 + 1/64*w**4. Let o(y) be the second derivative of a(y). Find s such that o(s) = 0.
-1, 0
Let d(w) be the first derivative of 4*w**3/3 - 4*w**2 - 160. Determine t, given that d(t) = 0.
0, 2
Suppose -10 = -2*z, 2*z + 37 + 73 = 4*x. Let o be (2/5)/(6/x). Determine v, given that 17*v**2 - 11*v**o - 3*v**5 - 5*v**4 + 2*v - v**4 + v = 0.
-1, 0, 1
Let o(b) be the second derivative of -13*b**4/3 - 9*b**3 - b**2 - 57*b. Solve o(j) = 0 for j.
-1, -1/26
Let n(f) be the third derivative of -2*f**7/105 + f**6/6 - f**5/5 - 3*f**4/2 + 6*f**2 - f. Factor n(a).
-4*a*(a - 3)**2*(a + 1)
Let c(f) be the first derivative of -f**3/7 + 225*f**2/14 + 228*f/7 + 255. Suppose c(q) = 0. What is q?
-1, 76
Let p be (6*(-50)/45)/(6/(-99)). What is c in -5*c + 29*c + p*c**3 + 50*c**4 + 11903*c**2 - 12015*c**2 = 0?
-3, 0, 2/5
Suppose -49*g + 52*g = 6. Factor 2*i + 8*i - 3*i**2 - i**g + 6*i**2.
2*i*(i + 5)
Let b(o) be the second derivative of 0 + 1/8*o**3 - 5*o + 0*o**2 + 0*o**4 - 3/80*o**5. Factor b(p).
-3*p*(p - 1)*(p + 1)/4
Let w(u) = -12*u**3 - 16*u**2 + 4*u + 13. Let y(k) = -6 + 2 + 3*k**2 - 19*k**2 + 18 - 12*k**3 + 4*k. Let r(m) = -6*w(m) + 5*y(m). Factor r(j).
4*(j + 1)**2*(3*j - 2)
Let u(q) be the second derivative of -q**6/135 - 7*q**5/15 - 61*q**4/6 - 84*q**3 - 324*q**2 + 171*q + 1. Let u(r) = 0. What is r?
-18, -3
Let d(u) be the first derivative of u**6/180 - u**5/30 + u**4/12 + 35*u**3/3 + 3. Let o(a) be the third derivative of d(a). Factor o(j).
2*(j - 1)**2
Factor 21*k**2 - 48 + 22*k + 21*k - 3*k**3 - 9*k - 4*k.
-3*(k - 8)*(k - 1)*(k + 2)
Suppose 44*w - 92*w = 0. Determine v so that -10/21*v + w - 2/21*v**2 = 0.
-5, 0
Let o = -55 - -166/3. Let s be (-10)/(-35) + 1/21. Suppose -o*r**5 + 0*r**3 + s*r**4 + 0*r**2 + 0 + 0*r = 0. What is r?
0, 1
Let o(l) be the first derivative of 1/5*l**2 + 0*l - 1/10*l**4 + 2/25*l**5 - 5 - 2/15*l**3. Factor o(i).
2*i*(i - 1)**2*(i + 1)/5
Let k be (-3)/(-27) + 196/(-1764). Factor 0*i + 1/2*i**2 + k.
i**2/2
Factor 3*z**3 + 5*z**5 + 613*z - 613*z + 90*z**4 + 604*z**2 + 36*z**2 + 477*z**3.
5*z**2*(z + 2)*(z + 8)**2
Let l be (-4)/((-112)/18) + (-44)/(-88). Factor 4*q + l + 12/7*q**2.
4*(q + 2)*(3*q + 1)/7
Let d(w) = -9*w**2 - w + 2. Let k be d(2). Let r be k/(-27)*(-1 - -4). Factor -3 - 7*q - 5*q**3 + 3*q**r + 13*q - q**3.
3*(q - 1)**3*(q + 1)
Let m(w) be the first derivative of -w**8/336 + w**7/168 - 11*w**3/3 + 9. Let j(z) be the third derivative of m(z). Factor j(r).
-5*r**3*(r - 1)
Suppose 1461*j + 88 = 1477*j + 24. Solve -6/19*b**5 + 480/19*b**2 + 74/19*b**j - 312/19*b**3 + 0 - 128/19*b = 0 for b.
0, 1/3, 4
Let o(u) be the second derivative of -u**6/6 + 9*u**5/4 - 35*u**4/4 + 95*u**3/6 - 15*u**2 - 20*u - 1. Factor o(r).
-5*(r - 6)*(r - 1)**3
Suppose -4*h = 5*z - 0*z - 3375, 5*z - 5*h = 3330. Let l = z + -4688/7. Factor 3/7*t**4 + l*t**2 + 0 + 3/7*t + 9/7*t**3.
3*t*(t + 1)**3/7
Let n(h) = h + 9. Let q be n(6). Suppose -q = -3*g - m, -3*g - 2*m + 5*m + 3 = 0. Find z such that 2/3*z - 8/3*z**5 + 0 - 2/3*z**2 - 22/3*z**g - 6*z**3 = 0.
-1, 0, 1/4
Let s = -382 + 765/2. Let q(f) be the first derivative of -s*f**4 + 1/2*f + 7 + f**2 + 1/3*f**3 - 3/10*f**5. Solve q(x) = 0 for x.
-1, -1/3, 1
Let y(h) be the first derivative of h**4/4 - 4*h**3/3 - 51*h**2/2 - 90*h - 859. Let y(m) = 0. Calculate m.
-3, 10
Let w(t) be the third derivative of 0 + 53*t**2 + 7/3*t**3 + 1/30*t**5 + 2/3*t**4 + 0*t. Factor w(n).
2*(n + 1)*(n + 7)
Let s(x) be the second derivative of -x**4/3 + 4*x**3/3 + 6*x + 43. Factor s(y).
-4*y*(y - 2)
Let r(j) = -8*j**2 + 8*j - 5. Let g(v) = 2 - 4*v - 5*v**2 + 16*v**2 - 7*v**2 + 0. Let h(d) = 5*g(d) + 2*r(d). Suppose h(z) = 0. What is z?
0, 1
Let v(y) be the second derivative of -1/10*y**3 + 3/100*y**5 + 0 + 1/150*y**6 - 1/5*y**2 - 10*y + 1/60*y**4. Factor v(x).
(x - 1)*(x + 1)**2*(x + 2)/5
Let h be ((-3)/2)/(9/24). Let o = 8 + h. Determine d, given that -4*d + 2 + d + o*d**2 - 