2/3*p**4 - 1/15*p**5 + 0*p**3. Factor t(c).
-4*c*(c - 4)
Let f(n) = n**2 + 1. Let r(m) = -15*m**2 - 70*m + 65. Suppose 0 = -12*b - 22 + 34. Let t(h) = b*r(h) + 10*f(h). Let t(v) = 0. Calculate v.
-15, 1
Suppose 19 = -5*k - 2*i, 3*i = 3*k - k. Let o be -9*2*k/18. Factor -48*v - o*v**3 - 10 + 28 + 18 + 11*v**2 + 10*v**2.
-3*(v - 3)*(v - 2)**2
Let r be 130/(-25) - ((29 - 14) + -25). Factor 3/5*t**2 + 0 - r*t.
3*t*(t - 8)/5
Let k be 11 + 27/(1944/4262208). Factor -k*o**3 - 11550*o**2 - 40/3 + 214375/3*o**4 - 2060/3*o.
5*(o - 1)*(35*o + 2)**3/3
Let b(x) be the first derivative of x**6/120 - 7*x**5/40 + 5*x**4/4 - x**3/3 - 45*x**2/2 - 82. Let f(p) be the third derivative of b(p). Factor f(k).
3*(k - 5)*(k - 2)
Let i(y) = -y**2 + 2269*y - 181435. Let k be i(83). Solve -247/5*h**2 - 9/5 - 361/5*h**k + 21*h = 0.
-1, 3/19
Let i = 23535 - 23535. Let f(d) be the second derivative of 1/4*d**5 + 0 - 5/6*d**3 - 36*d + 0*d**2 + i*d**4. Determine x so that f(x) = 0.
-1, 0, 1
Let v(c) be the third derivative of c**6/40 - 11*c**5/10 + 91*c**4/8 - 51*c**3 - 1662*c**2. Solve v(z) = 0 for z.
2, 3, 17
Let r be 1/54*(-164)/(-820). Let c(d) be the second derivative of 0 - 5/108*d**4 + 1/180*d**5 - 17*d + r*d**6 + 0*d**2 + 1/18*d**3. Factor c(g).
g*(g - 1)**2*(g + 3)/9
Let j(d) be the second derivative of -d**7/189 + 2*d**6/15 + d**5/30 - 28*d**4/27 + 4*d**3/3 + 1476*d. Solve j(l) = 0.
-2, 0, 1, 18
Let r(a) be the first derivative of -58 + 1/6*a**3 - 2*a - 3/4*a**2. Factor r(p).
(p - 4)*(p + 1)/2
Let l(r) be the second derivative of r + 1/40*r**5 + 17 + 1/12*r**4 + r**2 - 7/12*r**3. What is u in l(u) = 0?
-4, 1
Suppose -3*s + 12 = 2*w, 59 - 55 = -2*w + s. Let b be ((-7)/21)/(w - 1)*6. Factor -9 - 3*k - 1/4*k**b.
-(k + 6)**2/4
Factor 14/9*d**3 + 22/9*d**2 - 116/9*d + 80/9.
2*(d - 1)*(d + 4)*(7*d - 10)/9
Let x(g) be the third derivative of -3*g**7/175 + 136*g**6/25 + 3043*g**5/75 + 878*g**4/15 + 37*g**3 + 1087*g**2. Suppose x(s) = 0. What is s?
-3, -1/3, 185
Factor -147/2*t**2 + 3/2*t**4 + 0 - 90*t + 18*t**3.
3*t*(t - 4)*(t + 1)*(t + 15)/2
Let m(g) be the second derivative of 8/105*g**6 + 1/7*g**5 + 4*g + 0*g**2 - 1/147*g**7 - 3/7*g**3 - 23 - 4/21*g**4. Find u such that m(u) = 0.
-1, 0, 1, 9
Let m(g) = 25*g**2 + 150*g + 755. Let c(a) = a**2 + 29*a + 1. Let r(u) = 30*c(u) - m(u). Factor r(z).
5*(z - 1)*(z + 145)
Let d = -1733 - -8737/5. Let v = d + -561/40. Factor -3/8*g**2 + v*g + 3/4.
-3*(g - 2)*(g + 1)/8
Let o(f) be the first derivative of -19*f**2/2 + 461*f - 94. Let h be o(24). Factor 2/7*d**h + 0 + 4/7*d + 18/7*d**3 + 2*d**2 + 10/7*d**4.
2*d*(d + 1)**3*(d + 2)/7
Suppose 1108 + 92 = 3*r. Suppose -14 = -7*s + 14. Let -4*k**s + r*k**2 + k**4 - 3*k**4 - 2 - k**5 - 14*k**3 - 9*k - 416*k**2 = 0. What is k?
-2, -1
Suppose 6*l = 13*l - 6*l. Factor l*h**2 - 13*h**4 + 9*h**3 - 9*h - h**2 + 7*h**4 + 7*h**4.
h*(h - 1)*(h + 1)*(h + 9)
Let d(z) be the third derivative of z**7/42 - z**6/6 - z**5/4 + 15*z**4/4 + 946*z**2. Factor d(h).
5*h*(h - 3)**2*(h + 2)
Let z(h) be the first derivative of -h**5 - 210*h**2 - 110/3*h**3 + 35 + 15*h**4 - 245*h. Factor z(c).
-5*(c - 7)**2*(c + 1)**2
Let r(o) be the first derivative of o**3/6 - 357*o**2/4 - 179*o - 3306. Factor r(y).
(y - 358)*(y + 1)/2
Let s = -520056 + 520061. Let 0 + 0*v - 14/19*v**4 - 8/19*v**3 - 2/19*v**s + 24/19*v**2 = 0. What is v?
-6, -2, 0, 1
Suppose 19*f + 8*f = 270. Factor 12 - f*j + 13*j + 6*j + 7*j + 4*j**2.
4*(j + 1)*(j + 3)
Let k be 71418/(4 + 2) - -3. Factor -108*w + k*w**2 - 3*w**5 - 13*w**4 - 17*w**4 - 111*w**3 - 12086*w**2.
-3*w*(w + 2)**2*(w + 3)**2
Let b = -29401 - -29404. Suppose -4/13*i**b - 2/13*i**2 + 0 + 4/13*i + 2/13*i**4 = 0. What is i?
-1, 0, 1, 2
Let -8 + 68/3*t + 0*t**4 - 22*t**2 + 23/3*t**3 - 1/3*t**5 = 0. Calculate t.
-6, 1, 2
Let o = 7100/21 - 338. Let x(k) be the first derivative of -1 - o*k**3 + 1/7*k**2 + 0*k. Factor x(d).
-2*d*(d - 1)/7
Let g be (-1602)/30*1110/(-296). Suppose -g*p**2 - 75/2 - 21/4*p**4 - 735/4*p - 237/4*p**3 = 0. Calculate p.
-5, -1, -2/7
Let -186/7*a**3 + 2/7*a**4 - 54*a**2 + 0 - 190/7*a = 0. Calculate a.
-1, 0, 95
Let m(i) be the third derivative of -i**6/300 + 6*i**5/25 - 32*i**4/5 + 1024*i**3/15 + 578*i**2. Factor m(h).
-2*(h - 16)**2*(h - 4)/5
Let h(j) = 5*j**4 + 2*j**3 + 86*j**2 + 2*j - 2. Let l(b) = 28*b**4 + 10*b**3 + 433*b**2 + 11*b - 11. Let a(n) = -11*h(n) + 2*l(n). Let a(s) = 0. What is s?
-8, 0, 10
Let t be 7 + -11 + (-130)/(-14) - 6/21. Let s(b) be the second derivative of 0 + 1/60*b**4 - 1/15*b**3 - 4*b + 1/100*b**t + 0*b**2. Factor s(p).
p*(p - 1)*(p + 2)/5
Let o be ((-19)/(2945/62))/(18/(-10)). Find k such that 8/3*k - o*k**2 + 26/9 = 0.
-1, 13
Let x = 4580612/21 + -662996/3. Let y = x - -2885. Find k such that 15/7*k**2 + 125/7 - y*k - 1/7*k**3 = 0.
5
Determine s so that 133/3 - 131/6*s - 1/6*s**2 = 0.
-133, 2
Let x(c) be the second derivative of 2*c**6/15 - 57*c**5/5 + 215*c**4 + 10354*c**3/3 - 11532*c**2 - 562*c. Factor x(k).
4*(k - 31)**2*(k - 1)*(k + 6)
Let p = 6149 - 276703/45. Let o(a) be the third derivative of -1/15*a**5 + 0 - 2/9*a**4 - 22*a**2 - 2/315*a**7 + 0*a + p*a**6 + 8/9*a**3. What is i in o(i) = 0?
-1, 1, 2
Let t(m) = 17*m**2 + 878*m + 879. Let j(u) = -2*u**2 + u + 1. Let p(f) = -18*j(f) - 2*t(f). Factor p(s).
2*(s - 888)*(s + 1)
Suppose 3*s - d - 1 = 0, -2*s - d + 9 = -0. Factor 45*n**2 - 49*n**s - 68*n + 92*n - 4*n**3.
-4*n*(n - 2)*(n + 3)
Let w(b) = -b**3 + 7*b**2 - 19*b + 47. Let o be w(5). Find s, given that 2*s**5 - 112/9*s**4 - 76/3*s**o - 4/3 + 94/9*s + 80/3*s**3 = 0.
2/9, 1, 3
Let z(b) be the first derivative of b**8/840 + b**7/140 + b**6/90 + 109*b**3/3 - b**2 - 66. Let t(i) be the third derivative of z(i). Factor t(m).
2*m**2*(m + 1)*(m + 2)
Factor -132*u**2 - u**3 + 3 - 343*u**2 + 9 - 12.
-u**2*(u + 475)
Let u(w) be the third derivative of w**5/690 - 479*w**4/138 + 229441*w**3/69 + 2*w**2 - 167. Factor u(r).
2*(r - 479)**2/23
Let a(m) be the second derivative of -51*m**4/10 - 2*m**3/15 - m + 2243. Factor a(n).
-2*n*(153*n + 2)/5
Let h(l) be the third derivative of 0*l**3 - 1/525*l**7 + 0*l + 3/50*l**5 - 27*l**2 + 1/100*l**6 + 0 - 9/20*l**4. Suppose h(q) = 0. Calculate q.
-3, 0, 3
Let h(k) = -10*k**2 + 1640*k + 1640. Let a(u) = -11*u**2 + 1640*u + 1639. Let s(t) = 5*a(t) - 6*h(t). Determine w, given that s(w) = 0.
-1, 329
Let w(j) = 2*j**3 + 158*j**2 + 625*j - 1786. Let a(p) = -3*p**3 - 237*p**2 - 934*p + 2680. Let r(t) = -7*a(t) - 10*w(t). Factor r(i).
(i - 2)*(i + 6)*(i + 75)
Let d(j) be the first derivative of 3*j**5/50 - j**4 + 208*j - 108. Let o(w) be the first derivative of d(w). Factor o(t).
6*t**2*(t - 10)/5
Let y = -81 + 83. Let 37*k - 19*k - 20*k - k**y + 3 = 0. What is k?
-3, 1
Suppose -4*u = -3*w - 26 + 6, -14 = 4*w + u. Let b be (w/1)/(15/(-6)). Factor -b*f**3 + 3/5*f**4 - 4/5*f**2 + 9/5*f**5 + 0 + 0*f.
f**2*(f - 1)*(3*f + 2)**2/5
Let i(b) be the third derivative of -b**8/168 - 23*b**7/525 + b**6/20 + 23*b**5/150 - b**4/6 - 3645*b**2 + b. Determine m, given that i(m) = 0.
-5, -1, 0, 2/5, 1
Let h be (-1 + 3)/(-2) - 119. Let k be h/(-55) + 6/(-33). Factor 8*s**2 - 4*s + 2*s**k - 6*s**2.
4*s*(s - 1)
Let s(n) be the first derivative of -n**4/10 - 182*n**3/15 + 377*n**2/5 - 114*n + 2055. Find z such that s(z) = 0.
-95, 1, 3
Suppose 0 = 25*s - 115 + 40. Suppose -11 = -4*g - 5*h, -20 + 3 = -s*g + 5*h. Factor -2/11*x**g + 6/11*x**2 + 4/11*x**3 - 8/11 - 8/11*x.
-2*(x - 2)**2*(x + 1)**2/11
Let y(q) be the third derivative of -20*q**2 - 1/40*q**6 - 3/10*q**5 + 0 + 0*q + 2*q**4 + 0*q**3. Determine b, given that y(b) = 0.
-8, 0, 2
Let l(a) = 8*a**2 - 48*a + 229. Let q be l(5). Let g be 8/12*-3 + 594/q. Let -2/7*r**2 + 10/7 + g*r = 0. What is r?
-1, 5
Let w = -988581 - -988583. What is n in 1/4*n + 0*n**3 + n**4 - 5/2*n**w + 3/2 - 1/4*n**5 = 0?
-1, 1, 2, 3
Suppose -27*u + 30*u - 177 = -56*u. Let y(l) be the third derivative of 0*l**u + 1/42*l**7 + 0*l - 27*l**2 + 1/24*l**6 + 5/8*l**4 + 0 - 5/12*l**5. Factor y(q).
5*q*(q - 1)**2*(q + 3)
Let f be 16/(-20)*(-225)/(-10). Let p be ((-9)/(-15))/(f/(-24)). Factor -2/5*u**2 - p + 6/5*u.
-2*(u - 2)*(u - 1)/5
Let q(c) = -28*c - 31. Let y be q(-3). Suppose 3*d + y - 65 = 0. Factor 2/3*p**2 + 2/3*p**d + 0 + p**3 + 1/6*p**5 + 1/6*p.
p*(p + 1)**4/6
Let c(v) be the second derivative of v**6/75