r(x).
(x - 2)*(23*x - 2)/4
Find q, given that 98*q - 132 + 1/4*q**4 - 81/4*q**2 + 0*q**3 = 0.
-11, 3, 4
Let n be -7*72/84 - 40/(-6). Let d(k) be the first derivative of 0*k + 2*k**2 + n*k**3 - 3/2*k**4 - 7. Factor d(t).
-2*t*(t - 1)*(3*t + 2)
Let b = 6461233/4 - 1615307. Suppose b*s**2 + 125/2*s - 255/4 = 0. Calculate s.
-51, 1
Suppose -411*q + 410*q - 6 = 0. Let c be q - (-399)/49 - 1. Factor 0*j - 6/7*j**2 + 0 - c*j**3 - 2/7*j**4.
-2*j**2*(j + 1)*(j + 3)/7
Let i(w) be the first derivative of -31 - 35/24*w**4 + 27*w - 35/12*w**3 - 1/4*w**5 - 5/2*w**2. Let y(x) be the first derivative of i(x). Factor y(r).
-5*(r + 1)*(r + 2)*(2*r + 1)/2
Let w = -163 + 166. What is o in 27*o**4 + 90*o**3 + w*o**5 - 68 + 31*o + 68*o + 138*o**2 + 95 = 0?
-3, -1
Let q = 577/1151 - 3/2302. Let l(v) be the second derivative of 0*v**2 + 0 - 6*v - 1/2*v**3 - 3/20*v**5 - q*v**4. Suppose l(f) = 0. What is f?
-1, 0
Let w = 99043/22 - 98963/22. Factor -18/11*o**2 - 2/11*o**3 - 48/11*o - w.
-2*(o + 2)**2*(o + 5)/11
Let z = -26 - -29. Suppose -z*t = 2*m - 15, -4*m - 3*t + 5*t + 6 = 0. Factor -22 - 7*w**3 - 2*w**2 + m*w**3 + 10*w + 18.
-2*(w - 1)*(w + 2)*(2*w - 1)
Suppose -2*g - 72 = 2*g. Let r(i) = i**2 + 17*i - 14. Let b be r(g). Let j**5 + 3*j**b + 3*j**4 + 2*j**3 - 2*j**5 - 7*j**4 = 0. Calculate j.
-2, 0, 1
Let c(q) be the first derivative of 28*q**5/5 + 26*q**4 + 116*q**3/3 + 20*q**2 - 1918. Factor c(v).
4*v*(v + 1)*(v + 2)*(7*v + 5)
Let t(p) be the second derivative of 3*p**5/10 + 13*p**4/2 + 40*p**3/3 + 6*p**2 - 32*p. Let x(j) = j**3 - j**2 + 3. Let u(f) = -t(f) + 4*x(f). Factor u(l).
-2*l*(l + 1)*(l + 40)
Solve 133*n - 25/3*n**4 - 30 - 589/3*n**2 + 305/3*n**3 = 0 for n.
3/5, 1, 10
Let s be 10*-1*(-5)/10. Let m = -176609 + 529828/3. Factor 0*r + 2/3*r**3 + 0*r**2 - r**4 + 0 + m*r**s.
r**3*(r - 2)*(r - 1)/3
Let v be 88 + -92 - -50*1. Suppose 5*g + 13 = w, -5*g + v = -2*w + 62. Factor 4/9*k**2 + 0*k + 0 - 2/9*k**4 + 2/9*k**w.
-2*k**2*(k - 2)*(k + 1)/9
Suppose 195*m + 18 = -3*n + 193*m, 0 = -3*n - 5*m - 54. Determine l, given that -1/2*l**n - 338 + 26*l = 0.
26
Let z(c) be the third derivative of c**6/240 - 61*c**5/60 - 21*c**4/2 - 2*c**2 - 53*c - 47. Factor z(o).
o*(o - 126)*(o + 4)/2
Let c = -33668 - -33671. Let z(q) be the second derivative of -3/4*q**5 + 29*q + 0*q**2 - 1/10*q**6 + 0 - 2*q**c - 2*q**4. Factor z(l).
-3*l*(l + 1)*(l + 2)**2
Let i(t) be the third derivative of t**5/75 - 22*t**4/3 - 442*t**3/15 + 31*t**2 + 5. Let i(g) = 0. Calculate g.
-1, 221
Let s(d) be the third derivative of -d**7/252 - 5*d**6/72 - 29*d**5/72 - 25*d**4/36 + d**2 + 1665. Factor s(l).
-5*l*(l + 1)*(l + 4)*(l + 5)/6
Let r be ((-483)/(-2))/(69/92). Let k = 324 - r. Determine c so that 346/5*c**k - 112*c**3 - 88/5*c + 8/5 + 294/5*c**4 = 0.
2/7, 1/3, 1
Factor n**5 - 55*n + 12*n**2 + 455 - 217 - 15*n**3 - 35*n**3 + 10*n**4 + 68*n**2 - 224.
(n - 1)**4*(n + 14)
Let f(k) be the third derivative of k**6/660 - 25*k**5/66 - 32*k**4/11 - 3667*k**2. Suppose f(r) = 0. What is r?
-3, 0, 128
Let k = 325 - 305. Factor 3*o**3 - 15*o**2 + 3*o**4 + 6*o + 4*o**3 + k*o**5 - 13*o**5 - 10*o**5 + 2*o**3.
-3*o*(o - 1)**3*(o + 2)
Suppose -2*p - i + 1384 = -4*i, 0 = -5*i - 10. Find m, given that -15*m**4 + 704*m**2 - p*m**2 - 2*m + 25*m**3 + 2*m - 25*m**5 = 0.
-1, -3/5, 0, 1
Suppose 0*n + 0 + 120*n**2 - 2/5*n**3 = 0. What is n?
0, 300
Let f(x) be the second derivative of x**5/80 - 257*x**4/48 + 5461*x**3/8 + 16641*x**2/8 + 1694*x. Suppose f(o) = 0. Calculate o.
-1, 129
Solve -46/3*d**3 - 22/3*d**4 - 2/3*d**5 + 22/3*d**2 + 0 + 16*d = 0 for d.
-8, -3, -1, 0, 1
Let t = -264 - -266. Factor -50*i + 995 - 4*i**2 - 1043 + 3*i**2 - i**t.
-2*(i + 1)*(i + 24)
Suppose -17*m + 541 = 592. Let s be 0 + 78/(-168) - m/4. Solve -s*j**3 - 96/7*j - 30/7*j**2 + 128/7 = 0 for j.
-8, 1
Determine r, given that -224 + 147*r**2 - 191*r - 221*r - 20*r**3 + 154*r**2 - 664*r**2 + 155*r**2 = 0.
-8, -7/5, -1
Let z = 149131/3 + -49710. Let z*m**3 - 23/3*m**2 - 121/3 + 143/3*m = 0. Calculate m.
1, 11
Let o(y) = 65*y**2 - 20915*y + 110. Let j(m) = 7*m**2 - 2324*m + 12. Let i(a) = -55*j(a) + 6*o(a). Factor i(z).
5*z*(z + 466)
Let g = 1676/27 + -44389/378. Let i = -384/7 - g. Factor i + 3/2*m**2 - 3/2*m - 1/2*m**3.
-(m - 1)**3/2
Let k(j) = 151*j - 602. Let g be k(4). Let u be 30/8 - 1/(-4). Solve 27*r**4 - g*r**3 + 2*r**3 - 5*r**2 - 22*r**u = 0.
-1, 0, 1
Let c(z) be the second derivative of -z**6/72 + 7*z**5/24 + 25*z**4/4 + 131*z**3/6 - 100*z. Let x(n) be the second derivative of c(n). Factor x(t).
-5*(t - 10)*(t + 3)
Suppose 0 = 2*o + 14*c - 11*c - 74, -5*o = 3*c - 176. Factor 28 + 32 + 10 - 4*w**2 - o.
-4*(w - 3)*(w + 3)
Let o be ((-6)/8)/((-23 + -7)/300). Let c(k) be the second derivative of -3/20*k**5 + 9/2*k**3 + o*k**2 + 3/4*k**4 - 29*k + 0. Let c(s) = 0. Calculate s.
-1, 5
Let l(r) be the second derivative of r**5/15 - 18*r**4 - 896*r**3/3 - 5440*r**2/3 + 548*r - 4. Factor l(g).
4*(g - 170)*(g + 4)**2/3
Factor 1/7*t**2 + 11/7 - 12/7*t.
(t - 11)*(t - 1)/7
Let q(u) be the third derivative of 2 + 0*u + 7/2*u**3 + 5/16*u**4 - 16*u**2 - 1/40*u**5. Suppose q(g) = 0. What is g?
-2, 7
Let k be 2 - -20*34/1020. Factor 2/3*m**2 - 2*m - k.
2*(m - 4)*(m + 1)/3
Let 30*r**3 + 2*r**3 - 4*r**4 + 7*r**4 + 99*r**2 - 345*r + 198 + 22*r**3 - 9*r**3 = 0. Calculate r.
-11, -6, 1
Suppose 3*d + 5*n - 17 = 0, -d + 6*d - 17 = 3*n. Let m(j) be the first derivative of 0*j + 1/16*j**d + 1/12*j**3 - 10 + 0*j**2. Factor m(f).
f**2*(f + 1)/4
Let k(l) = -l. Let p be k(-4). Suppose 0 = j - 4*r - 8, -3*j + 10*r - p = 12*r. Factor -4/5*n**3 + j*n**2 + 2/5 + 4/5*n - 2/5*n**4.
-2*(n - 1)*(n + 1)**3/5
Suppose -2*h - 2*h + 4*r = 0, 3*h - 7 = -4*r. Let w be (h - 165/(-42)) + 21/(-49). Factor 3/4*o**2 - w*o**3 + 27/4*o**4 + 0*o + 0.
3*o**2*(3*o - 1)**2/4
Let a be (78/(-24) - -4)/((-21)/(-28)). Let l be (a*(-2)/10)/((-1323)/1890). Solve -8/7 + l*q**3 - 2/7*q + 8/7*q**2 = 0.
-4, -1, 1
Let f = -81579 + 81579. Factor -3/2*z**5 + 0*z**2 - 3/2*z**4 + 3*z**3 + f*z + 0.
-3*z**3*(z - 1)*(z + 2)/2
Suppose -1 = -2*v + 3. Suppose -3*q = 7*j - 45, 3*j - 3020*q - 25 = -3022*q. Find z such that 12/5*z**v + 3*z**j + 0 - 3/5*z = 0.
-1, 0, 1/5
Let -2244*q**2 + 4480*q**2 - 2101*q**2 - 356 + 26*q**3 - 394 + 13*q**3 - 75*q + 3*q**4 = 0. What is q?
-5, 2
Suppose r + 2*z + 529 - 4203 = 0, 5*z = -5*r + 18395. Factor -n**2 + r*n + n**2 + 4*n**2 + n**2 - 3829*n.
5*n*(n - 29)
Solve -120*k**3 - 2157*k - 216*k**2 + 4078*k - 21*k**4 - 2017*k + 48 = 0 for k.
-2, 2/7
Let o be (-489)/(-21) - 2/7. Suppose o - 3 = 4*i. Determine x, given that 4*x**2 + x**3 - x**i - 2*x**3 - 5*x**3 + 3*x**5 = 0.
-2, 0, 1
Let s(v) be the second derivative of v**6/15 + 17*v**5/10 + 15*v**4 + 36*v**3 - 216*v**2 - 1034*v. Factor s(y).
2*(y - 1)*(y + 6)**3
Let f(o) be the first derivative of 1/2*o**6 - 81 + 0*o - 42/5*o**5 + 96*o**2 + 112*o**3 + 99/4*o**4. Factor f(r).
3*r*(r - 8)**2*(r + 1)**2
Let m(u) be the third derivative of u**7/1470 + 101*u**6/168 - 169*u**5/140 - 505*u**4/168 + 253*u**3/21 + 6465*u**2. Factor m(q).
(q - 1)**2*(q + 1)*(q + 506)/7
Let a(i) be the first derivative of i**6/120 - 37*i**5/180 + 2*i**4/9 + 110*i**3/3 - 34. Let d(l) be the third derivative of a(l). Solve d(n) = 0.
2/9, 8
Let x(a) = -2*a**3 - 203*a**2 + 2372*a - 6223. Let n(s) = 7*s**3 + 608*s**2 - 7117*s + 18678. Let v(q) = -3*n(q) - 8*x(q). Suppose v(w) = 0. What is w?
-50, 5
Let a(c) be the first derivative of c**5/20 + c**4/4 + 5*c**3/12 + c**2/4 - 482. Determine o so that a(o) = 0.
-2, -1, 0
Let s be -2 + 3 + (37 - -3). Factor 18*q + 3*q - 87*q**2 + 43*q**2 + 24 + s*q**2.
-3*(q - 8)*(q + 1)
Let u be (-57*(-288)/(-172368))/((1/(-1))/154). Factor 16/3 - 4/3*y**3 + 12*y**2 - u*y - 4/3*y**4.
-4*(y - 1)**3*(y + 4)/3
Factor 889350 + 3/2*o**2 - 2310*o.
3*(o - 770)**2/2
Let o(w) = -3*w**2 + 6894*w - 3953718. Let t(m) = 3*m**2 - 6895*m + 3953719. Let v(c) = 7*o(c) + 6*t(c). Factor v(z).
-3*(z - 1148)**2
Let w = 219 - 230. Let c(s) = 4*s**2 - 14*s - 40. Let z(t) = 21*t**2 - 69*t - 200. Let o(n) = w*c(n) + 2*z(n). What is h in o(h) = 0?
-2, 10
Let w(s) be the first derivative of -s**4/12 - 392*s**3/3 - 783*s**2/2 - 1174*s/3 + 5135. Factor w(u).
-(u + 1)**2*(u + 1174)/3
Let w = 923990617/8 + -5129071458241/44408. Let c = w + 3/3172. Suppose -c*m + 8/7 + 162