. Let c(r) = -10*i(r) + 9*p(r). Let c(m) = 0. Calculate m.
4, 21
Let h(y) be the second derivative of -y**6/60 + y**5/20 - y**4/24 - 3*y - 231. Factor h(p).
-p**2*(p - 1)**2/2
Let g(q) be the second derivative of 13/6*q**6 + 55*q + 0 - 40/3*q**3 - 9/4*q**5 - 5/21*q**7 - 50/3*q**4 + 0*q**2. Find s such that g(s) = 0.
-1, -1/2, 0, 4
Let s = -903356 - -903359. Determine x so that -29/3*x + 4 + 19/3*x**2 - x**4 + 1/3*x**s = 0.
-3, 1, 4/3
Let d = 144901/330 + -24141/55. Find r, given that d*r**2 + 0 - 43/6*r = 0.
0, 43
Let -77/5*i**3 + 77/5*i + 78/5*i**2 - 1/10*i**4 - 31/2 = 0. What is i?
-155, -1, 1
Solve 0*p - 3/5*p**4 + 0 - 24/5*p**3 + 9/5*p**5 - 12/5*p**2 = 0 for p.
-1, -2/3, 0, 2
Let n(j) be the third derivative of 0*j**4 + 0*j**3 + 0*j + 0*j**5 + 2/105*j**7 + 292*j**2 + 2/75*j**6 + 0 + 1/420*j**8. Factor n(k).
4*k**3*(k + 1)*(k + 4)/5
Let x(v) be the third derivative of v**10/7560 - v**8/1680 + 41*v**4/24 + v**3/6 - 57*v**2. Let m(i) be the second derivative of x(i). Factor m(z).
4*z**3*(z - 1)*(z + 1)
Determine g, given that 7/4*g**2 - 295/2 + 2063/4*g = 0.
-295, 2/7
Let i(o) be the second derivative of 0*o**2 - 5/2*o**4 - 59*o + 3/20*o**5 + 0*o**3 + 0. Factor i(a).
3*a**2*(a - 10)
Let l be ((-6)/(-63)*-12)/((-32)/112). Suppose 3*o - 5 + 7 = -2*j, 0 = 4*j - l*o - 16. Let 1/4*t**j + 1/4 + 1/2*t = 0. Calculate t.
-1
Let l = 463 - 443. Let t be -3 + 1 + (l - 14). Factor 1/4 - 1/2*a**2 + 0*a + 1/4*a**t + 0*a**3.
(a - 1)**2*(a + 1)**2/4
Suppose -2/13*n**5 + 6/13*n**3 + 0 + 16/13*n + 28/13*n**2 - 8/13*n**4 = 0. Calculate n.
-4, -1, 0, 2
Let n(u) be the second derivative of u**5/130 + 25*u**4/78 + 127*u**3/39 - 153*u**2/13 - 1363*u. Solve n(t) = 0.
-17, -9, 1
Let c be ((-3 - -2) + -16)*-22*23/2783. What is o in 36/11*o + c + 2/11*o**2 = 0?
-17, -1
Let s(p) be the third derivative of 0 + 0*p**3 + 1/210*p**5 + 0*p - 1/42*p**4 + 56*p**2. Factor s(x).
2*x*(x - 2)/7
Let c(g) be the second derivative of -g**7/42 + 23*g**6/30 - 89*g**5/20 - 23*g**4/12 + 15*g**3 + g + 1816. Let c(u) = 0. What is u?
-1, 0, 1, 5, 18
Factor 5/6*q**3 + 265/6*q**2 + 275/6 - 545/6*q.
5*(q - 1)**2*(q + 55)/6
Let n = 47337/10880 - -107/2176. Factor -64/15 - 2/15*p**2 + n*p.
-2*(p - 32)*(p - 1)/15
Let i = -1586782 + 7933912/5. Find y such that -24/5*y**3 - 18*y**2 - i*y**4 + 0 - 20*y = 0.
-5, -2, 0
Let o(f) be the second derivative of 5*f**5/2 - 655*f**4/2 - 263*f**3 - 79*f**2 + 986*f. Factor o(d).
2*(d - 79)*(5*d + 1)**2
Factor -324/5 + 3/5*h**2 + 9/5*h.
3*(h - 9)*(h + 12)/5
Suppose 2*w - w + 7 = 2*d, 0 = -2*d - 4*w - 8. Factor -125*p**d - p**5 + 11*p - 5*p**4 + 129*p**2 - 3*p - 6*p**3.
-p*(p - 1)*(p + 2)**3
Let v(p) be the first derivative of 9*p**2 + 2*p - 14/3*p**3 - 3. Let c(j) = -j**2 + 1. Let n(y) = 12*c(y) - 2*v(y). Let n(t) = 0. What is t?
1/4, 2
Let z be ((6/(-75))/((-4)/(-10)))/((-1)/30). Factor z*q + 9/4*q**2 + 4 + 1/4*q**3.
(q + 1)*(q + 4)**2/4
Factor -27*r**2 + 1847*r + 32*r + 43659 + 3*r**3 - 6*r**3 + 284*r + 672*r.
-3*(r - 33)*(r + 21)**2
Let o be (-2)/3*(-339)/44296*28. Factor 0 - y + o*y**2.
y*(y - 7)/7
Find o such that -1110*o**3 - 1039*o**3 + 3116*o**3 - 175*o**2 - 2*o**4 - 86 - 89*o**2 - 1059*o**3 - 260*o = 0.
-43, -1
Let n(y) be the first derivative of -2/9*y**3 + 14/3*y + 2*y**2 - 87. Factor n(f).
-2*(f - 7)*(f + 1)/3
Let y be ((-23745)/(-9498))/(6/(-32)*(-21 - -1)). Factor -y*u**2 - 22/3*u - 16.
-2*(u + 3)*(u + 8)/3
Let z(v) = 8*v + 36. Let w be z(-4). Let c(d) be the third derivative of 0*d - 1/15*d**5 + 0*d**w + 0 + 0*d**3 - 11*d**2. Find r, given that c(r) = 0.
0
Let c(u) be the second derivative of 5*u**7/126 - 5*u**6/3 + 97*u**5/4 - 1825*u**4/18 - 750*u**3 + 7500*u**2 + 7774*u. Let c(g) = 0. Calculate g.
-3, 3, 10
Let i = -102 + 98. Let c(g) = -g**3 - 5*g**2 - 3*g + 8. Let q be c(i). Factor -o**5 + 6*o**3 - 3*o**3 - q*o**4 - o**5 + 3*o**4.
-o**3*(o - 1)*(2*o + 3)
Let q = 52005/2 + -26000. Let t(o) be the second derivative of q*o**4 - 7*o + 0*o**2 - 15/2*o**3 + 0 - 1/4*o**5. Factor t(s).
-5*s*(s - 3)**2
Let l(s) be the first derivative of -22/3*s**2 + 33 - 242/3*s - 2/9*s**3. Let l(o) = 0. Calculate o.
-11
Let s(b) be the first derivative of b**5/5 - 3*b**4/4 - 10*b**3 + 64*b**2 - 96*b + 9321. Factor s(g).
(g - 4)**2*(g - 1)*(g + 6)
Let r(c) be the first derivative of -55/3*c**3 + 54 - 65*c - 5/4*c**4 + 125/2*c**2. Factor r(q).
-5*(q - 1)**2*(q + 13)
Let s be (976/671)/((-28)/(-77)). Factor 0*r**2 + 6/5*r**5 - 14/5*r**3 + 0*r + 0 + 8*r**s.
2*r**3*(r + 7)*(3*r - 1)/5
Suppose 11*r - 14*r = -3. Let t = -29 - -45. Factor 13 + t*v - r + 4*v**2 + 0.
4*(v + 1)*(v + 3)
Suppose -6*o + 27 = 3. Let i(a) = 9*a**2 + 1. Let d be i(-1). Factor -c**2 + 6*c**2 + 0*c**o + 10*c - 5*c**4 - d*c**3 + 0*c.
-5*c*(c - 1)*(c + 1)*(c + 2)
Let s be ((-900)/(-8250))/(3/25). Suppose 24/11 + 34/11*i - s*i**3 - 2/11*i**2 + 2/11*i**4 = 0. Calculate i.
-1, 3, 4
Let a = -104 - -139. Let b(z) = -60*z**2 - 60*z + 155. Let q(p) = -5*p**2 - 5*p + 13. Let w(i) = a*q(i) - 3*b(i). Factor w(n).
5*(n - 1)*(n + 2)
Let m(s) = -10*s + 620. Let z be m(62). Let u(r) be the first derivative of z*r**2 - 1/18*r**4 + 9 + 0*r + 2/27*r**3. Factor u(h).
-2*h**2*(h - 1)/9
Let l(s) be the third derivative of 3*s**8/140 - s**7/14 - 16*s**6/45 - 2*s**5/5 - 19*s**3/2 + 29*s**2. Let k(r) be the first derivative of l(r). Factor k(y).
4*y*(y - 3)*(3*y + 2)**2
Suppose 3 = 5*w - 7. Factor x**4 + 119*x**w - 122*x**2 + 2*x**4.
3*x**2*(x - 1)*(x + 1)
Let a(o) be the first derivative of o**4/10 - 22*o**3/15 + 39*o**2/5 - 18*o - 2771. Determine s, given that a(s) = 0.
3, 5
Let q(u) be the first derivative of -4/3*u - 2/15*u**5 + 7/3*u**2 - 2*u**3 + 188 + 5/6*u**4. Suppose q(p) = 0. What is p?
1, 2
Let h(z) be the first derivative of 90*z**2 + 0*z - 112*z**3 - 121 + 50*z**4 - 48/5*z**5 + 2/3*z**6. Factor h(p).
4*p*(p - 5)*(p - 3)**2*(p - 1)
Suppose 254*s + 159*s = -253*s + 89*s + 1154. Let -3*p**s - 9/4*p**5 - 3/4*p**4 + 0*p + 6*p**3 + 0 = 0. Calculate p.
-2, 0, 2/3, 1
Suppose 16 = -z + 5*z. Let l be 5/((-5)/(-3)) - -4 - 2. Factor -z + 5 - l + 8 - 2*u - 2*u**2.
-2*(u - 1)*(u + 2)
Let o(i) be the third derivative of i**5/90 - i**4/4 - 18*i**3 + 2*i**2 + 802*i. Suppose o(j) = 0. What is j?
-9, 18
Let p(k) be the first derivative of 2*k**3/21 - 34*k**2/7 + 80*k - 1359. Let p(b) = 0. What is b?
14, 20
Determine y so that -622*y + 4*y**2 - 1670*y - 706*y - 6*y**2 = 0.
-1499, 0
Let o(b) be the third derivative of b**5/15 - 8*b**3/3 - 309*b**2 - 3*b. Let o(x) = 0. What is x?
-2, 2
Suppose -4*g + 23 = m - 0*g, -28 = -2*m + g. Suppose -5*i + 33 = -3*v, -2*i = -2*v - v - m. Factor 5*l**3 - 3*l**3 + 3*l**2 - i*l**2 - 3*l**3.
-l**2*(l + 3)
Let j(s) = s**5 + 9*s**4 + 83*s**3 - 84*s**2 - 144*s + 5. Let b(t) = t**5 + 13*t**4 + 123*t**3 - 126*t**2 - 216*t + 7. Let d(r) = -5*b(r) + 7*j(r). Factor d(o).
2*o*(o - 3)**2*(o + 1)*(o + 4)
Let b = -15 + 17. Suppose b*f - 3*q + 6*q = 7, q + 26 = 5*f. Factor -7*p**2 + 5*p**3 + 22*p**2 + 8*p + 7*p + f.
5*(p + 1)**3
Factor 332929/9 - 1154/9*s + 1/9*s**2.
(s - 577)**2/9
Let i(k) be the second derivative of -7*k - 11 + 0*k**2 - 13/16*k**3 - 1/32*k**4. Factor i(m).
-3*m*(m + 13)/8
Let o(p) be the first derivative of 0*p**4 - 1/6*p**6 + 0*p**2 + 0*p + 4/3*p**3 - 90 - 3/5*p**5. Factor o(w).
-w**2*(w - 1)*(w + 2)**2
Let y(s) be the first derivative of -s**4/34 - 1166*s**3/51 - 84680*s**2/17 + 170528*s/17 + 1689. Factor y(l).
-2*(l - 1)*(l + 292)**2/17
Let y(h) be the first derivative of -4*h**3 + 842*h**2 + 1128*h - 934. Factor y(a).
-4*(a - 141)*(3*a + 2)
Suppose 34*m + 290 = 5*m. Let g be (-5)/m*(3 - 3). Factor g + 2/23*n**2 + 2/23*n**3 + 0*n.
2*n**2*(n + 1)/23
Let d = -248 + 247. Let j be -4 - (-90)/24 - d. Factor j*c - 5/8*c**2 - 1/8.
-(c - 1)*(5*c - 1)/8
Suppose -109*c - 1667327 + 36*c - c**2 - 83*c + 1666572 = 0. What is c?
-151, -5
Let y(j) = -89*j + 981. Let t be y(11). Factor t*g**3 + 0*g + 4/3*g**2 + 0 - 2/3*g**5 + 0*g**4.
-2*g**2*(g - 2)*(g + 1)**2/3
Let x be ((-12)/10)/(-8 - 152/(-20)). Find h, given that 8*h + 7*h - 8*h + 3*h**x - 19*h = 0.
-2, 0, 2
Let k(v) be the second derivative of v**7/630 + 19*v**6/540 - v**5/18 + 139*v**3/6 + 7*v + 8. Let f(y) be the second derivative of k(y). Factor f(d).
2*d*(d + 10)*(2*d - 1)/3
Suppose 4103*k - 8233*k + 244 = -4069*k. Factor -8/5*s**3 - 8/5*s**2 -