= 3*w**3 + 3*w**2 + 39*w. Let b(q) = 5*q**3 + 3*q**2 + 40*q. Let a(r) = p*x(r) + 3*b(r). Factor a(c).
3*c*(c - 4)*(c + 3)
Let i be 5*1 + (24/4 - 9). Determine k, given that -5*k**4 - 45 - k**i + 9*k**2 - 60*k + 23*k**3 - 3*k**3 + 2*k**2 = 0.
-1, 3
Let t(l) = -2 - 45*l**3 - 3 + 43*l**3 - l + 4 - 3*l**2. Let p be t(-2). What is i in 25/2*i**2 - 25/2*i**4 - 5*i**3 + 0 + p*i = 0?
-1, -2/5, 0, 1
Suppose b + 4*f - 3 = -0*b, -5*b - 9 = -4*f. Let u be (8 - (b - (-2 + 5)))/2. Factor -8*y**2 - 12*y**3 + u*y**3 + 10*y**3 - 12*y.
4*y*(y - 3)*(y + 1)
Suppose 79 = -3*k + 55. Let f be ((-51)/306)/(1/k). Determine t so that 4/3*t - f - 1/3*t**2 = 0.
2
Let r be (-195)/(-1575)*21 + (-10)/(-25). Let 0*m**2 - 2/3*m**r + 2/3*m + 1/3*m**4 - 1/3 = 0. Calculate m.
-1, 1
Let b be (-6)/(-4)*(-8 + 182/21). Let w be (-1536)/864*b/(-4). What is r in 0 + w*r**2 + 8/9*r = 0?
-2, 0
Let h(o) = o**3 - 68*o**2 - 722*o - 257. Let c be h(-9). Determine y so that 2*y**c - 14/3*y**2 - 40/3 - 24*y + 26/3*y**3 - 2/3*y**5 = 0.
-2, -1, 2, 5
Let v(o) be the second derivative of o**7/14 - o**6/25 - 9*o**5/10 - 7*o**4/5 + o**3/10 + 9*o**2/5 - 217*o. Let v(q) = 0. What is q?
-1, 2/5, 3
Let o = 18 + -539/30. Let t(f) be the third derivative of o*f**6 + 0*f - 2*f**3 - 1/3*f**5 + 7/6*f**4 - 9*f**2 + 0. Factor t(p).
4*(p - 3)*(p - 1)**2
Suppose 2*f + 2*u = -6, -2*f - 3*u = 6 + 5. Factor 3*z**2 - 4 - 6*z**2 - 3*z - 2*z**f + 6*z**2.
(z - 4)*(z + 1)
Let n(t) = 1 - 4 + 4. Suppose -3*v - 50 + 47 = d, 3*v + 4*d = -3. Let y(i) = 5*i**2 - 10*i - 4. Let z(k) = v*y(k) - 4*n(k). Determine p, given that z(p) = 0.
0, 2
Let o(n) = 750*n**2 + 754*n - 5. Let s(a) = 9748*a**2 + 9798*a - 64. Let y(r) = -76*o(r) + 6*s(r). Factor y(u).
4*(u + 1)*(372*u - 1)
Let r(s) be the first derivative of -s**5/60 + s**4/4 - 22*s**2 + 15. Let y(m) be the second derivative of r(m). What is t in y(t) = 0?
0, 6
Let b(m) be the second derivative of -7/90*m**6 + 0*m**2 - 1/3*m**3 - 17/60*m**5 - 17/36*m**4 - 1/126*m**7 + 0 - 34*m. Suppose b(p) = 0. What is p?
-3, -2, -1, 0
Let t(k) be the second derivative of -7*k**6/6 + 131*k**5/4 - 575*k**4/2 + 1930*k**3/3 + 700*k**2 - 7*k + 24. Find d, given that t(d) = 0.
-2/7, 2, 7, 10
Let o be ((-126)/48)/((-28)/8). Find w, given that -15/2*w**2 + o*w**3 + 12*w + 0 = 0.
0, 2, 8
Let f be (-23)/((-759)/374) - (-2 + 5). Let x(m) be the first derivative of -5 - 15*m - 35/2*m**2 - f*m**3 - 5/4*m**4. Factor x(n).
-5*(n + 1)**2*(n + 3)
Let v(f) = -5*f - 53. Let p be v(-11). Suppose p*o + 542 - 546 = 0. Suppose -50/11 - 2/11*w**o + 20/11*w = 0. Calculate w.
5
Factor 186*f**4 + 34*f**5 + 194*f**4 + 80*f**3 - 396*f**4 - 35*f**5.
-f**3*(f - 4)*(f + 20)
Let h(x) = -47*x + 21. Let d be h(-3). Let c be d/45 - 2/(-5). Suppose o**3 + 22*o**2 + 0*o**3 - c*o**2 + 108*o - 69 + 285 = 0. Calculate o.
-6
Let z(q) be the third derivative of -1/600*q**6 + 0 - 14*q**2 + 2/75*q**5 + 0*q**3 + 0*q + 0*q**4. Factor z(b).
-b**2*(b - 8)/5
Let z(b) be the third derivative of 0 + 0*b - 1/12*b**4 - 1/420*b**7 - 152*b**2 + 1/30*b**5 + 0*b**3 + 1/240*b**6. Factor z(v).
-v*(v - 2)*(v - 1)*(v + 2)/2
Let y be 34/18 - ((-1311)/437)/(-3 - -30). Solve -2/9*o**y - 2/9*o + 4/3 = 0 for o.
-3, 2
Suppose m - 95 = -2*v, 0 = -5*v + m + m + 251. Determine g, given that -128 + v*g**3 - 48*g**3 + 13*g**2 + 32*g + g**2 = 0.
-8, 2
Let n(l) be the first derivative of -l**3/18 - 259*l**2/6 - 67081*l/6 + 372. Suppose n(y) = 0. Calculate y.
-259
Let i(j) be the first derivative of -j**6/2 - 78*j**5/5 - 54*j**4 - 70*j**3 - 69*j**2/2 + 401. Solve i(c) = 0.
-23, -1, 0
Factor 1/6*f**4 + 55/3 - 55/6*f**3 + 163/6*f - 1/2*f**2.
(f - 55)*(f - 2)*(f + 1)**2/6
Factor 270*s**2 + 2/7*s**3 + 1894/7 - 3786/7*s.
2*(s - 1)**2*(s + 947)/7
Let i be (2946/(-22095))/((1/(-3))/(-1 + 4)). Factor 1/5*q**2 + i + q.
(q + 2)*(q + 3)/5
Factor 636/5*l**2 - 67416/5*l - 2/5*l**3 + 2382032/5.
-2*(l - 106)**3/5
Find z, given that -8/13*z**2 - 8/13*z + 8/13*z**4 - 6/13*z**5 + 0 + 14/13*z**3 = 0.
-1, -2/3, 0, 1, 2
Suppose 11*s + 4*s**2 - 317 + 636 - 319 = 0. What is s?
-11/4, 0
Let n(j) = 22*j**2 - 1881*j + 5564. Let p(u) = -12*u**2 + 940*u - 2780. Let a(r) = 4*n(r) + 7*p(r). Factor a(c).
4*(c - 233)*(c - 3)
Factor 50*x**4 + 5*x**5 - 46 + x**2 + 12 - 6 - 6*x**2 - 85*x + 80*x**3 - 5*x**2.
5*(x - 1)*(x + 1)**3*(x + 8)
Find b, given that b**2 + 59536 - 114*b - 478*b + 104*b = 0.
244
Let d(y) be the second derivative of y**6/15 - 11*y**5/10 + 29*y**4/6 + 35*y**3/3 - 150*y**2 - 1598*y. Suppose d(m) = 0. What is m?
-2, 3, 5
Let f(j) be the third derivative of j**5/20 - 113*j**4/4 + 225*j**3/2 - 2*j**2 + 933*j. Factor f(b).
3*(b - 225)*(b - 1)
Factor -671394 - 1864*i - 2*i**2 + 227712 - 20*i.
-2*(i + 471)**2
Let x = -544069 - -544075. Determine k so that 1/2*k**2 - x - 1/2*k = 0.
-3, 4
Let f(v) be the third derivative of v**4/8 - 35*v**3/6 + 27*v**2. Let u be f(13). Let 2*h**4 - 6*h**4 + 3*h**3 - 7*h + 3*h**u + 3*h = 0. Calculate h.
-1, 0, 2
Let u = -7859/9 + 15853/18. Factor u*d**3 + 1/2*d**4 - 49 + 61/2*d**2 + 21/2*d.
(d - 1)*(d + 2)*(d + 7)**2/2
Let v be 2/13 - (21 + (7464/(-156) - -27)). Find a, given that -16/9 + v*a + 4/9*a**3 + 4/3*a**2 = 0.
-2, 1
Let s be (-2)/3*(29 - (20 - 0)) + 8. Solve 12/11 + 2/11*f - 46/11*f**s - 50/11*f**3 - 14/11*f**4 = 0.
-2, -1, 3/7
Suppose 34*t - 40 = -16*t + 60. Let g(m) be the third derivative of -1/330*m**5 - 26*m**t + 1/66*m**4 - 1/33*m**3 + 0*m + 0. Factor g(n).
-2*(n - 1)**2/11
Let l = 5/383032 + -157619513/141338808. Let i = -1/246 - l. Suppose -14/3*b - 8/9*b**2 - i = 0. Calculate b.
-5, -1/4
Let q(n) = -6*n**3 - n**2. Let r(t) = -2*t**4 - 753*t**3 + 2411*t**2 - 2427*t + 694. Let m(g) = 11*q(g) - r(g). Find a, given that m(a) = 0.
-347, 1/2, 1, 2
Let j(s) be the third derivative of -s**5/12 + 85*s**4/24 - 103*s**2 - 2*s. Factor j(q).
-5*q*(q - 17)
Let k(x) be the third derivative of x**7/735 - 19*x**6/70 + 109*x**5/210 + 38*x**4/7 - 452*x**3/21 - x**2 + 134*x + 5. Solve k(c) = 0 for c.
-2, 1, 2, 113
Let d = 6815 - 6812. Let x(o) be the first derivative of o - 8 + o**2 + 1/3*o**d. Let x(a) = 0. What is a?
-1
Let w(g) be the first derivative of g**6/960 - g**5/80 + g**4/16 + 74*g**3/3 + 20. Let f(y) be the third derivative of w(y). Suppose f(d) = 0. Calculate d.
2
Let y be 3*((-56)/(-12) - 4). Find u, given that 1 - 3*u**2 - 6*u - 5 + u**y = 0.
-2, -1
Let b(q) be the first derivative of q**3 - 42*q - 15/2*q**2 - 165. Suppose b(c) = 0. Calculate c.
-2, 7
Let h(p) = -p**2 + 1. Let i be (-56)/(-4 + 7 + -5). Let s(j) = 2*j**3 + 22*j**2 + 2*j - 26. Let d(v) = i*h(v) + 2*s(v). Solve d(x) = 0 for x.
-3, -2, 1
Let z(r) be the first derivative of 80*r - 102 + 5/3*r**3 + 25*r**2. Factor z(a).
5*(a + 2)*(a + 8)
Suppose 2/7*r**4 + 76/7*r + 30/7 + 20/7*r**3 + 64/7*r**2 = 0. Calculate r.
-5, -3, -1
Suppose 0 = 3*p + 3*v + 156, 5*p + 199 = v - 37. Let a be 2/(-6)*p/(-80)*-1. Find h, given that 1/5*h**4 + 3/5*h - a*h**2 - 3/5*h**3 + 0 = 0.
-1, 0, 1, 3
Let m be 22/(-40)*(13530/(-164))/11. Factor m*c + 3/4 + 27/8*c**2.
3*(c + 1)*(9*c + 2)/8
Suppose -8*x - 9 = -4*x - 5*q, -6 = 2*x - 2*q. Let o be (((-4)/x)/((-4)/(-12)))/7. Suppose 2/7*z**4 + 0*z**3 - o*z**2 + 0 + 0*z = 0. What is z?
-1, 0, 1
Let b(c) = -4*c - 31. Let v be b(-7). Let g be (v + 24/9)*-6. Factor 113*z**2 - 3*z**4 + z + 6*z**3 + z**3 - 118*z**g.
-z*(z - 1)**2*(3*z - 1)
Let n(s) = 6*s**4 + 22*s**3 - 50*s**2 - 358*s - 288. Let a(t) = 13*t**4 + 43*t**3 - 99*t**2 - 715*t - 576. Let w(b) = -2*a(b) + 5*n(b). Let w(x) = 0. What is x?
-6, -3, -1, 4
Let v(k) be the first derivative of -k**4 - 1112*k**3 - 463704*k**2 - 85939808*k + 1266. Determine r, given that v(r) = 0.
-278
Suppose -5*v + 417 = 2*z + 137, 2*v + 3*z = 112. Let w be ((-75)/(-9) + -5)/(v/24). Factor -8/7 + 2/7*t**3 - w*t**2 + 16/7*t.
2*(t - 2)**2*(t - 1)/7
Suppose 6*r = -23 + 89. Let f(d) = -5*d**3 + 97*d**2 - 321*d - 405. Let l(i) = -10*i**3 + 192*i**2 - 641*i - 810. Let m(v) = r*f(v) - 6*l(v). Factor m(b).
5*(b - 9)**2*(b + 1)
Let q(j) = -j**4 + 28*j**3 - 84*j**2 + 70*j. Let o(y) be the first derivative of -27*y**4/4 + 28*y**3 - 69*y**2/2 + 58. Let g(d) = 2*o(d) + 3*q(d). Factor g(m).
-3*m*(m - 6)*(m - 2)**2
Let o(t) be the second derivative of -6 + 1/2*t**4 - 1/15*t**6 - 4*t**2 + 4/3*t**3 + 4*t - 1/5*t**5. Factor o(d).
-2*(d - 1)**2*(d + 2)*