 Factor p(y).
-5*(y - 4)*(y + 3)
Suppose -2*z - 170 = -2*b, 5*b + 2*z = 29 + 424. Let c = -53 + b. What is y in -24*y**5 + c*y**3 - 2*y**2 - 7*y**2 - 20*y**3 - 7*y**2 + 44*y**4 = 0?
-2/3, 0, 1/2, 2
Let u(n) be the first derivative of -n**5/80 + 11*n**4/48 - 35*n**3/24 + 25*n**2/8 - 33*n - 71. Let y(h) be the first derivative of u(h). Factor y(m).
-(m - 5)**2*(m - 1)/4
Let y(f) be the first derivative of f**4/10 + 172*f**3/5 + 3276*f**2 - 13520*f + 7275. Let y(d) = 0. Calculate d.
-130, 2
Let z(g) be the second derivative of -58 + 2*g - 1/170*g**5 - 216/17*g**2 + 12/17*g**3 + 1/17*g**4. Factor z(i).
-2*(i - 6)**2*(i + 6)/17
Let b(n) be the second derivative of -16/5*n**5 + 0 + 4*n**3 + 2/5*n**6 - 16*n**2 - 33*n + 5*n**4. Suppose b(t) = 0. Calculate t.
-2/3, 1, 4
Let b(i) be the first derivative of -17/7*i**2 - 1/21*i**6 + 104/21*i**3 - 27/7*i**4 + 8/7*i**5 + 0*i - 216. Factor b(l).
-2*l*(l - 17)*(l - 1)**3/7
Let f(i) be the first derivative of -14*i**2 + 45 + 6*i**3 + 0*i - 1/2*i**4. Factor f(j).
-2*j*(j - 7)*(j - 2)
Suppose 2*x + 170 = 156, t - 4*x = 30. Let z(c) be the first derivative of 0*c + 0*c**t - 25 + 3/7*c**4 - 4/7*c**3 - 3/35*c**5. Factor z(y).
-3*y**2*(y - 2)**2/7
Let -372003 - 47515 - 2148*o - 3*o**2 + 35026 = 0. Calculate o.
-358
Let d(k) = -3*k + 21*k - 38*k + 210 - 15*k. Let i be d(6). Suppose -1/2*q**3 - 5/2*q**2 + 0*q + i = 0. Calculate q.
-5, 0
Let i(q) be the first derivative of -q**5 + 0*q**2 + 0*q + 0*q**4 + 0*q**3 - 5/6*q**6 - 54. Factor i(x).
-5*x**4*(x + 1)
Let p be (-5)/(-1) + 2 + -5. Suppose -4*a + 12 + 7 + 2 + 2 - 7 - 2*a**p = 0. What is a?
-4, 2
Let q be 4*6130/24 - -1*3. Let j = 1030 - q. Factor -64/9*z**2 - j*z - 1.
-(8*z + 3)**2/9
Let r(j) be the third derivative of 1/30*j**5 + 0 + 0*j - 1/540*j**6 + 3/2*j**3 + 14*j**2 - 1/4*j**4. Let x(z) be the first derivative of r(z). Solve x(b) = 0.
3
Let w be 124/1302 + 30/63. Let v(a) be the second derivative of 0*a**3 + 0 - 1/70*a**5 - 1/14*a**4 - 11*a + w*a**2. Factor v(o).
-2*(o - 1)*(o + 2)**2/7
Suppose -4*c + 3*b = 314, 4*b - 2 = 5*b. Let i be 12/40*-1 + (-64)/c. Solve 3/4*s**2 + 7/4*s + i = 0 for s.
-2, -1/3
Let w be 85/(-17)*(27/(-15) - -1). Let q(x) = 145*x**2 + 320*x + 265. Let s(z) = 13*z**2 + 29*z + 24. Let h(c) = w*q(c) - 45*s(c). Factor h(g).
-5*(g + 1)*(g + 4)
Suppose -2*d = 4*n - 138, -6*n + 236 = 4*d - 8*n. Let d*k**3 + 22*k - 64*k**3 + 36*k - 15*k**2 - 21 - 11*k - 8*k = 0. Calculate k.
-7, 1
What is z in -13/4*z**2 + 0 + 1/4*z**4 - 15/4*z + 3/4*z**3 = 0?
-5, -1, 0, 3
Let w be (-72)/(-4)*6/15*5. Let b be ((-2)/(-6))/((-212)/w + 6). Determine p, given that p**b + 3*p**3 - 6*p**3 - 8*p**2 - 4*p**3 + p**5 - 3*p = 0.
-1, 0, 3
Let r(k) be the third derivative of -7*k**5/270 + 3421*k**4/108 + 326*k**3/9 - 848*k**2 + 5*k + 2. Factor r(w).
-2*(w - 489)*(7*w + 2)/9
Let i(a) = -7*a**2 + 6*a + 6. Let y(u) = 3*u**2 - 3*u - 2. Suppose -3*m = x - 10 + 9, -x - 5 = 0. Let o(w) = m*i(w) + 5*y(w). Factor o(p).
(p - 2)*(p - 1)
Suppose h + 11*c - 8*c = 27, -7*h - 2*c = -18. Factor 2/9*l**2 + 4/9*l + h.
2*l*(l + 2)/9
Let o(b) be the first derivative of -b**4 - 80*b**3/3 + 278*b**2 + 1400*b + 8730. Factor o(t).
-4*(t - 7)*(t + 2)*(t + 25)
Factor 25*m**3 + 160 - 60*m**2 + 5*m**4 + 30*m - 60*m**2 - 56*m + 46*m.
5*(m - 2)**2*(m + 1)*(m + 8)
Let p(r) = 14*r**5 - 726*r**4 + 794*r**3 + 1578*r**2 + 22. Let d(h) = -5*h**5 + 240*h**4 - 265*h**3 - 526*h**2 - 8. Let b(u) = 11*d(u) + 4*p(u). Factor b(q).
q**2*(q - 263)*(q - 2)*(q + 1)
Suppose -2*p = -l + 6, 5*l - 140 = 7*p - 77. Factor -l*c + 0 + 18/7*c**4 - 256/7*c**3 + 134*c**2.
2*c*(c - 7)**2*(9*c - 2)/7
Let i be ((-12)/3600)/(77/(-22)). Let c(m) be the third derivative of -1/60*m**5 + 0*m - 1/150*m**6 - 6*m**2 - i*m**7 + 0*m**3 - 1/60*m**4 + 0. Factor c(n).
-n*(n + 1)**2*(n + 2)/5
Let -3/7*f**4 + 0 + 0*f**3 + 9/7*f**2 - 6/7*f = 0. Calculate f.
-2, 0, 1
Suppose 3*k = 129 + 51. Let w be (-172)/(-43) + 0 + (-1 - -1). Factor k*c**3 + 44*c**2 + c**4 + w*c**4 - 10*c**2 + 21*c**2.
5*c**2*(c + 1)*(c + 11)
Determine h so that 675684 - 3*h**2 - 70*h + 4*h**2 - 1507*h - 67*h = 0.
822
Let v(p) be the first derivative of -p**4/2 + 148*p**3/3 + 561*p**2 + 972*p - 1003. Factor v(w).
-2*(w - 81)*(w + 1)*(w + 6)
Let y = -842 + 817. Let d be 0/(4 - 1) - y/5. Suppose 0*r**4 + 0 + 4/7*r**3 - 2/7*r + 0*r**2 - 2/7*r**d = 0. What is r?
-1, 0, 1
Let g(n) = n**3 - n. Suppose -8 = 33*m - 140. Let c(a) = -5*a**3 - a**2 + 6*a. Suppose h = -1 + 2. Let l(s) = h*c(s) + m*g(s). Factor l(f).
-f*(f - 1)*(f + 2)
Let v(u) = 39*u + 28. Let x be v(7). Let d = x - 601/2. Determine m, given that d*m - 1/2 + 1/2*m**2 - 1/2*m**3 = 0.
-1, 1
Let u(y) = -8*y - 174. Let j be -11 - -20 - (31 - 0). Let c be u(j). Factor 0 + 16/3*t**4 + 4/3*t**5 + 4/3*t + 8*t**3 + 16/3*t**c.
4*t*(t + 1)**4/3
Let j(k) = 3*k**2 - 55*k + 24. Let a be j(18). Suppose -a*q = -37 + 19. Factor 15/4*n**2 - 12*n + 21/4*n**q + 3.
3*(n - 1)*(n + 2)*(7*n - 2)/4
Factor -y - 5 + 283440*y**2 - 283439*y**2 - 3*y.
(y - 5)*(y + 1)
Suppose -5*i = 10*p - 7*p - 303, 3*p = -i + 291. Let t be p/144*(-6)/(-10). Factor -4/5 - 8/5*j + t*j**3 + 1/5*j**4 - 3/5*j**2.
(j - 2)*(j + 1)**2*(j + 2)/5
Let i(k) be the first derivative of -82 - 4/3*k**3 + 92*k**2 - 2116*k. Solve i(m) = 0.
23
Let a(t) be the first derivative of 2/21*t**3 - 1/7*t**2 + 0*t - 76. Solve a(v) = 0 for v.
0, 1
Let v(h) be the second derivative of -16/3*h**4 - 35*h - 3/20*h**5 + 131/18*h**3 - 1 - 11/3*h**2. Factor v(a).
-(a + 22)*(3*a - 1)**2/3
Factor -1751*h**2 + 3066001*h - 5368567751/3 + 1/3*h**3.
(h - 1751)**3/3
Let t(z) be the second derivative of 13*z**6/30 + 67*z**5/20 - z**4/4 - 67*z**3/6 - 5*z**2 + 439*z - 14. Let t(n) = 0. What is n?
-5, -1, -2/13, 1
Factor 23*r**2 - 35*r**2 - 4*r**4 + 40 + 72*r**2 - 4*r**3 - 92*r.
-4*(r - 2)*(r - 1)**2*(r + 5)
Suppose -15*u + 50 = 10*u. What is x in -31*x**u - 2567 + 13*x**2 - 132*x + 6923 + 19*x**2 = 0?
66
Let n(r) = r**3 + r**2 - 4*r. Let c be n(-2). Suppose 11*i**2 - 85*i - 8*i**2 - 4*i**2 - c*i**2 = 0. What is i?
-17, 0
Let k(s) be the second derivative of -1/24*s**4 + 1/3*s**2 + 6*s + 0*s**3 + 16 - 1/120*s**5. Factor k(h).
-(h - 1)*(h + 2)**2/6
Let w(j) = -13*j**2 - 10*j + 27. Suppose 3*c + 0*v + 5*v = -2, 2*v + 8 = -3*c. Let z(i) = -6*i**2 - 5*i + 12. Let l(a) = c*w(a) + 9*z(a). Factor l(x).
-x*(2*x + 5)
Find m, given that -50*m**3 - 54*m**2 + 0 - 63/8*m**4 + 112*m - 1/8*m**5 = 0.
-56, -4, 0, 1
Let a(s) = 44*s**2 - 160*s - 764. Let j = 427 + -399. Let t(n) = -8*n**2 + 29*n + 139. Let p(w) = j*t(w) + 5*a(w). Find v such that p(v) = 0.
-3, 6
Let g be (-286)/(-9) + (4/27)/((-65)/195). Let c(r) be the first derivative of 8 + 63/4*r**4 + 8*r - 30*r**2 + g*r**3. Factor c(s).
(s + 2)*(7*s - 2)*(9*s - 2)
Let b(w) be the first derivative of -w**6/90 - 3*w**5/5 - 27*w**4/2 - 2*w**3 - 7*w**2/2 + 107. Let h(c) be the third derivative of b(c). Factor h(g).
-4*(g + 9)**2
Let o(v) be the first derivative of v**6/24 - v**5/5 + 5*v**3/6 - v**2/8 - 3*v/2 + 453. Determine s, given that o(s) = 0.
-1, 1, 2, 3
Factor -40*o + 35/2*o**4 - 95/2*o**3 + 10 + 125/2*o**2 - 5/2*o**5.
-5*(o - 2)**2*(o - 1)**3/2
Let o be ((-20)/(-50))/(2/10). Let m be o + (-5)/4 + (-20)/(-16). Factor -8*a - 5*a**2 - 3*a**3 + 7*a**3 + 8*a**4 - 7*a**m + 4*a**5 + 4*a**4.
4*a*(a - 1)*(a + 1)**2*(a + 2)
Let c(w) be the third derivative of -7*w**5/60 - 2245*w**4/24 + 107*w**3 + 3*w**2 - 193*w. Suppose c(i) = 0. What is i?
-321, 2/7
Let r(c) = 4*c**3 - c. Let t(u) = -85*u**3 - 35*u**2 - 55*u - 45. Let m(a) = -20*r(a) - t(a). Factor m(g).
5*(g + 1)*(g + 3)**2
Let d(x) be the second derivative of 11 + 0*x**2 + 1/9*x**4 - 2*x + 32/9*x**3. Suppose d(g) = 0. Calculate g.
-16, 0
Factor 124/9*j + 4/9*j**3 - 62/9*j**2 + 26/3.
2*(j - 13)*(j - 3)*(2*j + 1)/9
Let t be (-14 - (-9506)/665)*110/77. Determine n so that t*n + 2/19*n**4 + 0 - 8/19*n**2 - 2/19*n**3 = 0.
-2, 0, 1, 2
Let i = -56 - -61. Suppose -i*n - 3*s + 28 = 0, 35 = 3*n + 5*s + 15. Let -16*d**3 + d - d**5 - 8 + 8*d**2 + 5*d**n + 11*d = 0. Calculate d.
-2, -1, 1
Let n(q) = -q**4 - 23*q**3 - 60*q**2 + 35*q + 67. Let c(d) = d**4 + 3*d**3 + d + 1. Suppose 3*s + 10 = 13*s. Let b(o) = s*n(o) - 3*c(o). Factor b(m).
-4*(m - 1)*(m + 1)*(m + 4)**2
Let w(f) be the first derivative of -1620*f - 5/3*f**3 - 289 - 90*f**2. Let w