i + 8)**2
Suppose -22*g - 20 = 90. Let c(h) = 4*h**2 + 18*h + 98. Let o(n) = -n**2 - 9*n - 50. Let p(m) = g*o(m) - 2*c(m). Factor p(r).
-3*(r - 6)*(r + 3)
Let a(f) be the first derivative of 2*f**3/3 + 32*f**2 - 288*f + 380. Find m, given that a(m) = 0.
-36, 4
Let y be (-4)/2*1 - -2. Let t be (0 - 1)*(-68 - 3000/(-45)). Suppose y*u**2 + 0 - 4/3*u**5 + 0*u**4 - t*u + 8/3*u**3 = 0. What is u?
-1, 0, 1
Let r(w) = 54*w - 159. Let s be r(3). Let t(y) be the second derivative of 1/6*y**s + 2/3*y**4 - 10*y - y**2 + 0 + 1/4*y**5. Let t(a) = 0. Calculate a.
-1, 2/5
Let k be (-2)/18 + ((-161)/69 - 274/(-90)). Let v = -1/3 - -14/15. Factor k*i**3 + 0 + 6/5*i**2 + v*i.
3*i*(i + 1)**2/5
Suppose t - 2223 = -12*t. Solve 14 + 174*q**3 - t*q**3 - 5*q**2 - 16*q - 2 = 0.
-2, 2/3, 3
Suppose -504/11*r**2 + 162/11*r + 2/11 = 0. Calculate r.
-1/84, 1/3
Let h be (-46)/(-161) - (-26)/7. Let p be (h/(-4))/(1/(-2)). Determine k, given that 6*k**2 - p*k - 3*k - 4*k**5 + k**5 - 4*k - 6 + 12*k**3 = 0.
-1, 1, 2
Let d = -53602 - -214411/4. Factor -1/4*o**3 + 0 + 3/4*o**4 + 0*o + 1/4*o**5 - d*o**2.
o**2*(o - 1)*(o + 1)*(o + 3)/4
Suppose 1023*z - 1426 = 977*z. Let x(j) be the second derivative of 15*j**2 - 5/12*j**4 + 0 - 25/6*j**3 - z*j. Factor x(o).
-5*(o - 1)*(o + 6)
Suppose 11*w - 20 = 6*w, 0 = -z - 4*w + 300. Find d, given that 45152*d + 19563 + 3232*d + 35733 - 2*d**4 - 3359*d**2 - 3265*d**2 - 2*d**4 + z*d**3 = 0.
-1, 24
Let u be (10 - (-1512)/(-150))*10*60/(-16). Suppose 1/7*o**u - 8/7*o**2 + 1/7*o**4 + 0 - 12/7*o = 0. Calculate o.
-2, 0, 3
Suppose 0 = -9*j - 0*j + 45. Suppose 0 = -j*x + 14 + 11. Solve 3*v - 2*v**x - 6*v**2 - v**5 - 178*v**4 + 184*v**4 = 0.
-1, 0, 1
Let t(z) be the second derivative of z**4/18 - 4*z**3/3 - 13*z**2/3 + 687*z - 1. Factor t(n).
2*(n - 13)*(n + 1)/3
Factor -3254/13*t**2 - 1321938/13 + 2/13*t**3 + 1325190/13*t.
2*(t - 813)**2*(t - 1)/13
Factor 4959/8*y + 3/8*y**2 - 2481/4.
3*(y - 1)*(y + 1654)/8
Let z(t) = -10*t**2 + 534*t + 1084. Let q(w) = -29*w**2 + 1603*w + 3254. Let l(i) = -6*q(i) + 17*z(i). Factor l(y).
4*(y - 137)*(y + 2)
Let d be 1/(-6)*70/20*4095. Let o = d + 2390. Suppose 25/4*z + 15/2 + o*z**2 = 0. What is z?
-3, -2
Let n be (-2)/(10/4 - (3 - 1)). Let k(l) = 32*l + 32. Let t(w) = -w**2 + 64*w + 65. Let q(m) = n*t(m) + 9*k(m). Let q(g) = 0. What is g?
-7, -1
Suppose -3*w + 82 = 2*s, w = -4*s - 17 + 161. Let -48*n**2 + 92*n**2 + 109*n - 41*n**2 + s*n + 1728 = 0. Calculate n.
-24
Let x be (-4 + 4)/4*1. Let p = -50 - -55. Determine j, given that 4*j**2 + x*j - p*j**2 + 2*j = 0.
0, 2
Let i be -7 - 116/(-16) - (-1137)/(-4). Let v = i - -288. Factor 3/2*u**v + 3 + 3/2*u**3 - 3/2*u - 9/2*u**2.
3*(u - 1)**2*(u + 1)*(u + 2)/2
Let o(s) be the second derivative of -2401/3*s**2 - 98/9*s**3 - 1/18*s**4 + 146*s + 0. Factor o(d).
-2*(d + 49)**2/3
Let y(s) = -4*s**3 + 288*s**2 + 566*s + 294. Let z(o) = -4*o**3 + 288*o**2 + 555*o + 293. Let a(w) = -3*y(w) + 2*z(w). Factor a(b).
4*(b - 74)*(b + 1)**2
Let c(g) = g**4 - 64*g**3 + 256*g**2 - 3*g + 3. Suppose z = h + 1 - 8, 0 = 5*h - 4*z - 31. Let i(p) = p**4 + p - 1. Let r(v) = h*i(v) + c(v). Factor r(f).
4*f**2*(f - 8)**2
Suppose 64/15 + 26/15*t**2 - 92/15*t + 2/15*t**3 = 0. Calculate t.
-16, 1, 2
Let x(w) be the third derivative of w**8/84 - 254*w**7/21 + 13483*w**6/3 - 1932338*w**5/3 + 18921425*w**4/6 - 18787862*w**3/3 - 25*w**2 - 134. Factor x(p).
4*(p - 211)**3*(p - 1)**2
Let r be (1/(-3))/(12/36). Let h be 16/(-9 - r)*(-1)/4. Find o such that 2/3*o - 1/6*o**2 - h = 0.
1, 3
Let z be (-88)/(-198) - (-88)/132. Factor z*i**2 + 2/9*i**3 - 2 + 2/3*i.
2*(i - 1)*(i + 3)**2/9
Find m such that 33*m**4 + 88*m**2 - 22*m**3 - 47*m**5 - 62*m**3 - 30*m + 49*m**5 - 9*m**4 = 0.
-15, 0, 1
Let x(r) = -r**3 + 78*r + 27. Let s be x(9). Let l(k) be the first derivative of 15/16*k**4 + s*k**2 + 0*k - 1/8*k**6 + 1 + 3/4*k**3 + 3/20*k**5. Factor l(q).
-3*q**2*(q - 3)*(q + 1)**2/4
Suppose -15*f - 1/4*f**3 - 9/2*f**2 + 50 = 0. What is f?
-10, 2
Suppose 6 = -2*j + 4*j. Solve 37*l + 15 + j*l**2 - 19*l - 28*l - 8*l**2 = 0.
-3, 1
Let r(i) be the first derivative of i**6/12 + 6*i**5/5 + 27*i**4/8 - 2*i**3/3 - 9*i**2 - 1255. Find x such that r(x) = 0.
-9, -2, 0, 1
Find f, given that -529*f + 240 - 14*f**2 + 14*f**2 + 437*f + 4*f**2 = 0.
3, 20
Factor 60*x**2 - 80 + x - 83/4*x**3 + 1/4*x**4.
(x - 80)*(x - 2)**2*(x + 1)/4
Let y(u) be the first derivative of -u**5 - 410*u**4 - 6500*u**3/3 - 3240*u**2 - 5492. Determine p so that y(p) = 0.
-324, -2, 0
Let c be ((-3)/(-4))/(15/40). Factor -5*v**2 + 11*v**c - 3*v**3 + 36*v - 18*v**2.
-3*v*(v - 2)*(v + 6)
Let y(f) = -30*f**3 + 14*f**3 + 0*f**3 + 11*f**2 - 28*f**2 - 15*f + 14*f**3 - 54. Let q be y(-8). Solve -32/15 + 72/5*h**3 - 96/5*h**q - 18/5*h**4 + 32/3*h = 0.
2/3, 2
Let r = -259 - -276. Suppose v - 54 = -r*v. Let 0 - 9/8*w**4 - 3/4*w + 3/8*w**v + 9/8*w**2 + 3/8*w**5 = 0. What is w?
-1, 0, 1, 2
Suppose -25/2*z**3 - 75/2*z**2 + 369/4*z - 189/4 + 19/4*z**4 + 1/4*z**5 = 0. Calculate z.
-21, -3, 1, 3
Let m(c) be the third derivative of c**6/40 - 153*c**5/20 + 739*c**2. Factor m(b).
3*b**2*(b - 153)
Let k(r) be the second derivative of 4*r - 1/3*r**3 - 13 + 1/18*r**4 + 0*r**2. Factor k(l).
2*l*(l - 3)/3
Let o be -49*6/(-14)*83/1. Let z = -1743 + o. Factor -2/3*a**4 + z - 16/3*a**3 + 0*a - 32/3*a**2.
-2*a**2*(a + 4)**2/3
Let c(p) = 47*p**3 - 242*p**2 - 465*p - 230. Let o(k) = 1295*k**3 - 6535*k**2 - 12555*k - 6210. Let j(h) = -55*c(h) + 2*o(h). Factor j(f).
5*(f + 1)**2*(f + 46)
Let y(o) = 1615*o - 4*o**2 - 12*o**2 - 1647*o - 16. Let j(v) = v**3 - 31*v**2 - 65*v - 33. Let u(m) = -4*j(m) + 7*y(m). Factor u(k).
-4*(k - 5)*(k + 1)**2
Let y(x) be the second derivative of 0 - 38*x - 1/15*x**5 - 20/27*x**3 + 23/54*x**4 - 4/9*x**2. Factor y(u).
-2*(u - 2)**2*(6*u + 1)/9
Let m(x) be the second derivative of -8/3*x**3 + 7*x**2 + 69*x + 1/6*x**4 + 0. Factor m(q).
2*(q - 7)*(q - 1)
Let f = -1081/34 - -14121/442. Determine b so that 0*b**2 - f + 4/13*b + 2/13*b**4 - 4/13*b**3 = 0.
-1, 1
Suppose -5*w - 2*h + 257 = 0, -2*w - 2*h = -h - 103. Let q(k) = -3*k**2 + 4*k + 2. Let l(x) = 26*x**2 - 31*x - 17. Let z(o) = w*q(o) + 6*l(o). Factor z(v).
3*v*(v + 6)
Let d(h) = -45*h - 1170. Let q be d(-28). Let n be (-6)/(-10) + (8 - 738/q). Solve -8*y + n*y**2 + 40 = 0.
10
Let c(y) = 7*y + 15. Let m be c(9). Let p = 80 - m. Determine s so that 27*s - 12 + 9*s + 51*s**p + 8*s**4 - 20*s**4 - 9*s**3 = 0.
-2, -1, 1/4, 2
Suppose 14 + 91 = 5*l. Let g(o) = 2*o - 15. Let f be g(9). Let j**3 + 359*j**4 - 142*j**f - l*j**5 - 491*j**4 - 30*j**2 = 0. Calculate j.
-5, -1, -2/7, 0
Let g(d) = d**3 + d**2 - 1. Let n be g(3). Suppose -3*k + 5*c + n = -54, 0 = -4*c - 4. Let 16*b**5 - k*b**4 + 0*b**5 - 8*b**3 + 0*b**5 = 0. What is b?
-1/4, 0, 2
Let c(i) be the second derivative of -172*i - 425/12*i**4 + 9245/2*i**2 + 0 - 1/4*i**5 - 8815/6*i**3. Suppose c(h) = 0. What is h?
-43, 1
Let j(a) be the third derivative of -9/2*a**3 + 19*a**2 + 1/4*a**5 + 0 + 0*a + 1/40*a**6 + 3/8*a**4. Factor j(n).
3*(n - 1)*(n + 3)**2
Factor -18049 + 35127 - 635*i + 5*i**2 - 17718.
5*(i - 128)*(i + 1)
Let c(q) = -47*q**2 - 10*q - 13. Let t(d) = 26*d**2 + 5*d + 9. Let x(g) = 6*c(g) + 10*t(g). Solve x(y) = 0.
-1, 6/11
Let r(z) = -4980*z + 164344. Let m be r(33). Factor 3/2*q**m + 12*q**2 - 24*q + 0 + 21/2*q**3.
3*q*(q - 1)*(q + 4)**2/2
Let s(i) = -4*i + 3. Let l(d) = 2*d**2 - 56*d + 61. Let m(y) = -l(y) - 7*s(y). Suppose m(k) = 0. What is k?
1, 41
Let w(y) be the second derivative of y**4/18 + 698*y**3/9 + 121801*y**2/3 - 69*y - 7. Let w(v) = 0. What is v?
-349
Let h(w) be the third derivative of w**7/525 - w**6/60 - 2*w**5/25 + 19*w**4/15 - 16*w**3/3 + 691*w**2. Let h(z) = 0. Calculate z.
-4, 2, 5
Let q be (1415/(-566))/((-5)/(-4)) + 6. Factor 26/5*y - 8/5 - 2/5*y**q - 6*y**2 + 14/5*y**3.
-2*(y - 4)*(y - 1)**3/5
Let o = -645974 + 1937926/3. Determine k so that o*k**2 - 200/3 + 196/3*k = 0.
-50, 1
Suppose -5*k + 17 = -j - 2*j, 4*k + j - 17 = 0. Suppose 3*x - 67 = o, 0*x = 3*x + k*o - 92. Factor 9 - 6*w - 3*w - 3*w**3 - 9*w**2 - 12*w + x*w.
-3*(w - 1)*(w + 1)*(w + 3)
Suppose 55*r**2 - 81*r**2 - r**5 + 6*r**3 - 10*r**4 - 32*r - 2*r**2 + 15*r**4 - 4*r**2 = 0. Calculate r.
-2, -1, 0, 4
Let b(m) be the second derivative of -m**7/420 + m**6/20 + m**5/60 - 3*m*