r**2 + 10*r**2 - 2*r**2.
3*r*(r - 4)
Let f be 904/20 - 16920/376. Factor 4/5*q + 9/5*q**3 - 36/5*q**2 + 48/5 + f*q**4.
(q - 2)**2*(q + 1)*(q + 12)/5
Let i(p) be the third derivative of -p**7/4200 + p**6/1800 + p**5/100 + 8*p**3 - 25*p**2. Let x(y) be the first derivative of i(y). Factor x(t).
-t*(t - 3)*(t + 2)/5
Suppose -2654/5*y**2 + 881792/5 - 879136/5*y - 2/5*y**3 = 0. What is y?
-664, 1
Let a(f) = -2*f**4 - 3*f**3 + f - 1. Let d(o) be the second derivative of o**6/30 + o**3/6 - o**2/2 + 26*o. Let b(l) = a(l) - d(l). Find k such that b(k) = 0.
-1, 0
Let v = 200572462231/2420 + -82881176. Let j = 6/605 + v. Suppose -33/2*r**2 - j - 6*r**3 - 3/4*r**4 - 18*r = 0. What is r?
-3, -1
Suppose 4*d = 4, 3*n + 0*d - 3*d = 345. Suppose 0 = l - 3*v + 2*v - 34, n = 4*l + v. Solve -240*m**4 + l*m**2 + 66*m**2 + 16*m + 180*m**3 + 340*m**4 = 0.
-1, -2/5, 0
Solve 12*q**4 - 3*q**5 - 780*q**2 - 11907*q - 12608544*q**3 + 12608910*q**3 + 24*q**2 = 0 for q.
-7, 0, 9
Let u(y) be the first derivative of 5/3*y**3 + 3/2*y**2 - 2*y + 83. Factor u(q).
(q + 1)*(5*q - 2)
Factor -12800/3*u**3 - 322/3*u - 2/3 - 13120/3*u**2.
-2*(u + 1)*(80*u + 1)**2/3
Let j(y) = 15*y**3 + 108*y**2 + 306*y - 429. Let s(l) = -8*l**3 - 55*l**2 - 151*l + 214. Let r(d) = -11*j(d) - 21*s(d). Find n, given that r(n) = 0.
-5, 1, 15
Let w(c) be the third derivative of -19*c**6/24 + 815*c**5/6 - 173935*c**4/24 - 18490*c**3/3 - 6216*c**2. Let w(y) = 0. Calculate y.
-4/19, 43
Let f(d) be the second derivative of -d**6/30 - 17*d**5/10 - 199*d**4/12 - 45*d**3 - 279*d + 7. Factor f(g).
-g*(g + 2)*(g + 5)*(g + 27)
Let -1504*w**3 + 4504/3*w**2 + 0*w - 2/3*w**5 + 378*w**4 + 0 = 0. Calculate w.
0, 2, 563
Let -171*x**2 - 77*x**2 - 2*x**3 + 4060*x - 5196 - 9700 + 0*x**3 - 2*x**3 = 0. Calculate x.
-76, 7
Let z(j) be the second derivative of -5/16*j**4 - 1/16*j**5 - 1 - 25/8*j**2 + 21*j + 15/8*j**3. Let z(m) = 0. Calculate m.
-5, 1
Factor -225352 - 5*t**2 + 91537 - 3650*t - 171932 - 360378.
-5*(t + 365)**2
Let w = 15165 + -15165. Let a(l) be the first derivative of w*l + 1/12*l**4 + 13 - 2/3*l**3 + 4/3*l**2. Determine s, given that a(s) = 0.
0, 2, 4
Let r(m) = 75*m**3 - 44225*m**2 + 58825*m - 19600. Let f(v) = 39*v**3 - 22112*v**2 + 29414*v - 9800. Let h(i) = 5*f(i) - 2*r(i). Factor h(q).
5*(q - 490)*(3*q - 2)**2
Factor -h**3 + 5*h**2 - 6*h + 2029*h**4 - 2030*h**4 + 6*h**3 - 3*h**3.
-h*(h - 3)*(h - 1)*(h + 2)
Let t(z) = -3*z**2 - 6774*z - 3905651. Let u(s) = 2*s**2 + 4519*s + 2603767. Let w(h) = 5*t(h) + 8*u(h). Factor w(g).
(g + 1141)**2
Let r(b) = b**3 - 26*b**2 + 26*b - 23. Let d be r(25). Determine l, given that -41*l**3 + 307*l - 973 + 58*l**d + 901 - 31*l + 4*l**4 = 0.
-2, 1/4, 6
Let o(z) be the third derivative of 0*z**3 - 1/2415*z**7 + 0*z - 33*z**2 + 1/690*z**5 - 1/138*z**6 + 0 + 5/138*z**4. Let o(b) = 0. What is b?
-10, -1, 0, 1
Suppose -15*k**4 + 0 + 3/4*k**5 + 153/4*k**3 + 0*k + 0*k**2 = 0. Calculate k.
0, 3, 17
Let y(m) be the first derivative of 50 + 3/5*m**4 - 18/25*m**5 + 0*m**2 + 1/5*m**6 + 0*m + 0*m**3. Suppose y(q) = 0. What is q?
0, 1, 2
Factor 110*m - 25/2 + 45/2*m**2.
5*(m + 5)*(9*m - 1)/2
Let a = 28191 + -28187. Suppose -3/2*y**a + 0 - 6*y**3 + 6*y**5 + 0*y + 3/2*y**2 = 0. Calculate y.
-1, 0, 1/4, 1
Let o(k) be the third derivative of -k**8/84 + 8*k**7/105 - k**6/30 - 2*k**5/3 + 2*k**4/3 + 16*k**3/3 + 6*k**2 + 34. Factor o(b).
-4*(b - 2)**3*(b + 1)**2
Let v(r) = -19*r**3 + 35*r**2 - 136*r + 90. Let i(f) = 30*f**3 - 52*f**2 + 206*f - 136. Let u(x) = 5*i(x) + 8*v(x). Factor u(a).
-2*(a - 5)*(a - 4)*(a - 1)
Factor -2/9 + 101/9*h**2 + 11*h.
(h + 1)*(101*h - 2)/9
Let b(v) be the second derivative of 2*v**7/21 + 14*v**6/15 - 14*v**5 + 110*v**4/3 + 46*v**3 - 234*v**2 + 6645*v. What is y in b(y) = 0?
-13, -1, 1, 3
Let h(o) be the third derivative of -5*o**8/336 + 23*o**7/42 - 19*o**6/4 + 107*o**5/6 - 865*o**4/24 + 85*o**3/2 + 436*o**2. Factor h(i).
-5*(i - 17)*(i - 3)*(i - 1)**3
Let o(n) be the first derivative of 5*n**5/3 + 255*n**4/2 - 2612*n**3/3 + 2764*n**2/3 - 352*n - 4242. Solve o(s) = 0.
-66, 2/5, 4
Let g = 134 - 134. Let j be 21 - 18 - (g + 0). Factor 15*a + 2*a**2 - j*a**2 + 9*a**2 + 10 - 3*a**2.
5*(a + 1)*(a + 2)
Let m(r) be the second derivative of -31*r - 1/3*r**3 - 1/6*r**4 - 1/30*r**5 - 12*r**2 + 0. Let q(j) be the first derivative of m(j). Factor q(b).
-2*(b + 1)**2
Let k(n) be the third derivative of 5*n**8/336 - 32*n**7/21 + 61*n**6/8 + n**5/3 - 305*n**4/6 + 19*n**2 + 21*n. Suppose k(u) = 0. Calculate u.
-1, 0, 2, 61
Factor 92 - 200 + 108 + 3570*r**2 + 801969*r + 5*r**3 - 164724*r.
5*r*(r + 357)**2
Let r = 480123 + -480121. Find f such that 0 + 1/11*f**3 - 1/11*f**r - 2/11*f = 0.
-1, 0, 2
Let c be 1/(1/((-10)/(-5))). Suppose -3*n + 0*n**c - 59*n + 8*n - 30*n + 184 - 4*n**2 = 0. Calculate n.
-23, 2
Let f(c) be the second derivative of 8*c + 146/3*c**3 - 4*c**2 - 3 + 324/5*c**5 - 228*c**4. Factor f(a).
4*(a - 2)*(18*a - 1)**2
Let a = -477 - -484. Let g be (100/105)/(a/49). Find r such that -5/3*r**2 - 20/3*r - g = 0.
-2
Let i be (81/(-14) + 6)/(2/35). Let t(k) be the second derivative of 18*k + 0 - 9/4*k**3 - 3/8*k**4 - i*k**2 + 3/40*k**5. Factor t(m).
3*(m - 5)*(m + 1)**2/2
Solve -32*i**3 + i**3 - 266*i**5 + 2*i**3 - 31*i**3 + 167*i**5 - 237*i**4 + 36*i**2 = 0 for i.
-2, -2/3, 0, 3/11
Let j(i) = 5*i**3 + 192*i**2 + 378*i + 179. Let s = 769 - 766. Let c(m) = -m**2 + m - 2. Let o(w) = s*c(w) - j(w). Factor o(t).
-5*(t + 1)**2*(t + 37)
Suppose -201*w + 83 + 161 = -140*w. Suppose 0 + 0*r**2 + 2/15*r**3 - 2/15*r**w + 0*r = 0. Calculate r.
0, 1
Let r(b) = -b**5 - b**4 - b. Suppose -12*z + 20*z + 8 = 0. Let s(m) = -6*m**5 - 15*m**4 + 6*m**2 - 12*m. Let x(w) = z*s(w) + 9*r(w). Factor x(u).
-3*u*(u - 1)**3*(u + 1)
Let y(b) be the third derivative of b**7/140 + 11*b**6/120 + 7*b**5/30 - 19*b**4/24 - 5*b**3/4 + 51*b**2 - 25. Suppose y(f) = 0. Calculate f.
-5, -3, -1/3, 1
Let s(v) be the second derivative of v**7/21 + 8*v**6/5 + 33*v**5/5 + 32*v**4/3 + 7*v**3 - 105*v + 2. Factor s(p).
2*p*(p + 1)**3*(p + 21)
Let k be (((-214)/535)/(-1 + 3))/(2/(-4)). Factor 2560 + k*b**2 - 64*b.
2*(b - 80)**2/5
Factor 2/9*f**5 - 636*f**3 + 0 - 208/3*f**4 - 1920*f**2 - 1926*f.
2*f*(f - 321)*(f + 3)**3/9
Factor -84/5*t**2 - 297*t - 1/5*t**3 + 2430.
-(t - 6)*(t + 45)**2/5
Let c = -234 + 264. Suppose c = 63*o - 53*o. Solve -n**2 - 2/3*n + 0 - 1/3*n**o = 0.
-2, -1, 0
Let c(s) be the first derivative of -2*s**5/65 + s**4/13 + 2*s**3/39 - 2*s**2/13 - 1076. Suppose c(q) = 0. Calculate q.
-1, 0, 1, 2
Let b(h) = 68*h**3 + 32*h**2 - 167*h - 197. Let g(d) = 385*d**3 + 191*d**2 - 1003*d - 1183. Let w(x) = 34*b(x) - 6*g(x). Suppose w(a) = 0. What is a?
-1, 10, 20
Suppose 17 + 53 = 35*b. Factor 12*t**5 - 25*t**4 + 0*t**b - 44*t**2 + 5*t**2 + 9*t - 20*t**4 + 63*t**3.
3*t*(t - 1)**3*(4*t - 3)
Let d(n) be the first derivative of 1/5*n**5 + 1/4*n**4 - 2*n**2 + 0*n - 4/3*n**3 - 21. Let d(h) = 0. Calculate h.
-2, -1, 0, 2
Suppose -2*j - 5*j = -140. Let -4*m**4 + 0*m - 12*m**3 - 4*m**2 - j*m + 32*m + 8 = 0. What is m?
-2, -1, 1
Suppose 0 = -11*b + 21*b - 20. Suppose -161*h**3 + 192 - 80*h + 173*h**3 - 12*h**b - 36*h**2 + 4*h**4 = 0. What is h?
-4, -3, 2
Let t(w) be the first derivative of -2*w**5/5 + 508*w**4 - 516128*w**3/3 - 9950. Suppose t(d) = 0. Calculate d.
0, 508
Let u(n) be the first derivative of 2/15*n**5 + 251 - 2/9*n**3 + 0*n**4 + 0*n + 0*n**2. Factor u(w).
2*w**2*(w - 1)*(w + 1)/3
Let r = 348 - 343. Factor 2*u**5 - 6*u**3 + 27*u**4 + 11*u**5 - 25*u**r.
-3*u**3*(u - 2)*(4*u - 1)
Let m(i) be the first derivative of -2*i**5/15 - 8*i**4/3 - 16*i**3 - 128*i**2/3 - 160*i/3 + 1904. Factor m(x).
-2*(x + 2)**3*(x + 10)/3
Let q(t) be the first derivative of -245*t**3/3 - 385*t**2 - 605*t - 9870. Factor q(b).
-5*(7*b + 11)**2
Let v(p) be the first derivative of -p**5/5 + 915*p**4 - 1674450*p**3 + 1532121750*p**2 - 700945700625*p + 3120. Suppose v(j) = 0. What is j?
915
Suppose 2*c = 5*l - 37, 2*l + 3*c = -780 + 753. Let a(k) = k - 1. Let w be a(3). Factor 1/2*s**l + 0 + 5/2*s**w + 3*s.
s*(s + 2)*(s + 3)/2
Let g(x) = 13*x**3 + 47*x**2 - 10*x - 5. Let y(z) = -5*z**3 - 24*z**2 + 9*z + 2. Let m(v) = 2*g(v) + 5*y(v). Factor m(i).
i*(i - 25)*(i - 1)
Let p be ((-2)/(-306))/(-11 - 134/(-12)). Let h(x) be the second derivative of 1