
Let x(r) be the first derivative of 729*r**3/4 + 81*r**2 + 12*r - 564. Solve x(s) = 0.
-4/27
Let z(b) = 84*b**2 + 1638*b - 471. Let h(n) = -21*n**2 - 410*n + 118. Let p(o) = 9*h(o) + 2*z(o). What is r in p(r) = 0?
-20, 2/7
Let a be (-4 - (-830)/(-8))/((-7)/12). Let h = 185 - a. Find f, given that 8/7*f**3 - 8/7*f**4 + 4/7*f**2 - 10/7*f + h*f**5 + 4/7 = 0.
-1, 1, 2
Let m be 5 + ((-21)/15 - (-8)/(-20)). Let j(f) be the first derivative of f**4 + m*f**3 + 0*f + 2 + 8/5*f**2. Factor j(z).
4*z*(z + 2)*(5*z + 2)/5
Suppose -35 + 49/4*o**3 + 246*o - 1743/4*o**2 = 0. Calculate o.
2/7, 35
Let n(c) = 4*c**4 + 3*c**3 - 32*c**2 - 57*c + 64. Let i(j) = 2*j**4 + 2*j**3 - 16*j**2 - 28*j + 32. Let d(r) = -9*i(r) + 4*n(r). Suppose d(f) = 0. Calculate f.
-4, -2, 1, 2
Let c be (-52)/(-20) + (16/(-10))/(-4). Suppose -72 = c*h - 81. Factor 3/7*f**h - 3/7*f**2 + 0*f + 0.
3*f**2*(f - 1)/7
Let m be (-101)/(-9) + 2/(-9). Suppose -5*t = -m + 1. Solve r - 2*r**t + 5*r + 5*r**2 = 0.
-2, 0
Let p(v) be the first derivative of -2*v**3/57 + 60*v**2/19 - 1800*v/19 + 379. Solve p(y) = 0 for y.
30
Let i(k) = -5*k**3 - 13*k**2 + 61*k - 69. Let a(p) = -4*p**3 - 12*p**2 + 62*p - 70. Let g(t) = -3*a(t) + 2*i(t). Factor g(r).
2*(r - 2)**2*(r + 9)
Let u(t) be the second derivative of -27*t**2 + 3*t**3 + 16*t - 1/8*t**4 + 0. Suppose u(q) = 0. What is q?
6
Let y be (8 - (-20)/(-5))*2*5. Let i(p) = 2*p**3 + 18*p**2 + 3*p. Let f(c) = 25*c**3 + 235*c**2 + 40*c. Let d(b) = y*i(b) - 3*f(b). Factor d(g).
5*g**2*(g + 3)
Let k = -116 + 268. Let q = k - 911/6. Suppose 1/3*u + q + 0*u**2 - 1/6*u**4 - 1/3*u**3 = 0. Calculate u.
-1, 1
Let r = 118927/60 - 1982. Let l(q) be the third derivative of -1/40*q**6 + 3*q**2 + 0*q - 1/6*q**3 - r*q**5 + 0 - 5/24*q**4. Factor l(w).
-(w + 1)**2*(3*w + 1)
Let j(q) be the first derivative of 11 - 12*q + 9/2*q**2 + q**3. Let j(h) = 0. Calculate h.
-4, 1
Let n = -5483/4 - -1371. Factor 1/4*t**4 - 1/4*t**3 + 0 + n*t**5 + 0*t - 1/4*t**2.
t**2*(t - 1)*(t + 1)**2/4
Suppose 0 = 5*y - 2*y + w - 14, -2*w + 20 = 4*y. Find f, given that y*f**3 - 4*f + 6*f**2 + 2*f**3 + 5*f**4 + 6*f - 3*f**4 = 0.
-1, 0
Let o(g) be the second derivative of -1/6*g**3 + 13*g - 1/48*g**4 + 0 + 0*g**2. What is p in o(p) = 0?
-4, 0
Factor -10 + 16*h**3 + 3*h**4 + 38 - 180*h + 39*h**2 + 6 + 74 + 14*h**3.
3*(h - 1)**2*(h + 6)**2
Let j(v) be the second derivative of 0*v**3 - 1/5*v**4 + 1/25*v**5 + 2*v + 8/5*v**2 + 0. Let j(d) = 0. Calculate d.
-1, 2
Suppose 37*a - 245 = -12*a. Let t(h) be the second derivative of 0 - 1/3*h**3 + h + 1/10*h**a + 0*h**2 + 1/4*h**4. Factor t(g).
g*(g + 2)*(2*g - 1)
Let z(f) be the third derivative of f**3 - 13*f**2 - 1/40*f**6 + 0*f**5 + 3/8*f**4 + 0 + 0*f. Factor z(o).
-3*(o - 2)*(o + 1)**2
Let u(c) be the first derivative of -1/2*c**3 + 9/4*c**2 - 3*c - 6. Factor u(t).
-3*(t - 2)*(t - 1)/2
Let v be ((-1 - -6) + 5)/(16 + -10). Let 3*x - 1/3*x**3 + x**2 + v = 0. What is x?
-1, 5
Let l(x) be the second derivative of x**6/10 + 6*x**5/5 + 13*x**4/4 + 3*x**3 + 171*x. Factor l(j).
3*j*(j + 1)**2*(j + 6)
Let v(u) be the second derivative of -u**7/126 - u**6/45 + u**5/20 + 2*u**4/9 + 2*u**3/9 + 13*u - 1. Suppose v(a) = 0. What is a?
-2, -1, 0, 2
Let d(m) be the third derivative of -m**8/12096 + m**7/756 - m**6/108 + m**5/6 - 9*m**2. Let h(n) be the third derivative of d(n). Factor h(u).
-5*(u - 2)**2/3
Let i(k) be the third derivative of k**5/20 - k**4/24 + k**3/6 - 3*k**2. Let m be i(1). Factor 2*f**2 + 16*f**m - 17*f**3 - f**2.
-f**2*(f - 1)
Let w be (-18)/4 - (22 - 106/4). Factor -18*m**3 - 9*m**4 + 0 + w*m - 3/2*m**5 - 12*m**2.
-3*m**2*(m + 2)**3/2
Let j(q) = 2*q**2 + 47*q - 634. Let p(l) = l**2 + 48*l - 631. Let h(x) = -4*j(x) + 6*p(x). Let h(n) = 0. Calculate n.
25
Let c(x) be the third derivative of -x**6/390 - 11*x**5/390 - 5*x**4/39 - 4*x**3/13 - 2*x**2 - 2*x. Factor c(d).
-2*(d + 2)**2*(2*d + 3)/13
Let d(h) be the third derivative of h**8/168 - h**7/21 + h**6/20 + h**5/6 - h**4/3 - 14*h**2 + 4. Factor d(p).
2*p*(p - 4)*(p - 1)**2*(p + 1)
Solve -3/5*t**4 - 3/5*t**2 + 6/5 + 9/5*t**3 - 9/5*t = 0.
-1, 1, 2
Let m be (-1)/(-7) + 20/7. Suppose 0 = r - m*r + 2. Find b, given that 2*b**2 - 3*b + 0 + r + b - b**2 = 0.
1
Let f(n) be the third derivative of n**5/135 + 5*n**4/108 - 4*n**3/9 - 45*n**2 - 4. Find k such that f(k) = 0.
-4, 3/2
Let y be 4/(-6)*(2 + -5). Factor 108*i**2 - 2*i**3 + 95*i**y - 213*i**2.
-2*i**2*(i + 5)
Suppose 0 = -3*f - 2*f, 15 = 3*o - 4*f. Suppose -2*m - 8 = 0, 2*m + 37 = o*r + 4*m. Determine y, given that -8*y - 2*y**3 + 3*y**4 + y**5 - 3*y**4 + r*y = 0.
-1, 0, 1
Suppose g - 2*g = 2*w - 5, -4*w = 4*g - 16. Let x be w*(-63)/(-15) - 3. Factor 4/5*r**3 + 0*r**2 - x*r**5 + 0 + 2/5*r**4 + 0*r.
-2*r**3*(r - 1)*(3*r + 2)/5
Suppose 10*z - z = 216. Let p be ((-16)/(-14))/(48/z). What is b in p*b**2 + 8/7*b + 4/7 = 0?
-1
Let n be ((-11)/2)/((-42)/9 + 5). Let b = 17 + n. Factor -1/2 - 1/2*r**4 + r**3 - 1/2*r + r**2 - b*r**5.
-(r - 1)**2*(r + 1)**3/2
Let a(p) = 8*p**2 + 5*p - 93. Let d(j) = 6*j**2 + 6*j - 92. Let b(h) = 2*a(h) - 3*d(h). Factor b(q).
-2*(q - 5)*(q + 9)
Factor 22/5*a**2 - 8/5*a + 0.
2*a*(11*a - 4)/5
Factor 29 + 5*w**2 + 3*w**2 - 12*w**2 - 30*w + 3*w**2 + 2*w**2.
(w - 29)*(w - 1)
Let q = -3166 - -28504/9. Determine o so that 4/3 + 2/9*o**2 + q*o = 0.
-3, -2
Let 62/19*h + 116/19 + 2/19*h**2 = 0. Calculate h.
-29, -2
Let r = 8644/3273 - -28/1091. Factor 2/9*x**5 - r*x**2 - 4/3*x**4 + 26/9*x**3 + 0 + 8/9*x.
2*x*(x - 2)**2*(x - 1)**2/9
Let b = 7/18 + -11/63. Let t(q) be the first derivative of -1 - b*q**2 - 1/7*q**3 + 3/28*q**4 + 3/7*q. Solve t(i) = 0.
-1, 1
Let q be 4/14 - 26/(-7). Let g = 13514/10131 + -2/3377. Factor -2/3 + 2*r**q + 2*r - g*r**3 - 2/3*r**5 - 4/3*r**2.
-2*(r - 1)**4*(r + 1)/3
Let a(u) be the first derivative of 5/6*u**2 - 5 - 1/9*u**3 + 2*u. Factor a(t).
-(t - 6)*(t + 1)/3
Let o be (-3)/(-4) + (-19)/38. Factor 1/4*n + o*n**2 - 1/2.
(n - 1)*(n + 2)/4
Suppose -29 = -5*p + 2*c, 3*c = -3*p + c + 27. Factor -14*t**2 - 2 + 0 - p*t + 7*t**5 + 0*t - 4*t + 4*t**3 + 16*t**4.
(t - 1)*(t + 1)**3*(7*t + 2)
Let m be (2 + (-66)/24)/(203/(-28) - -7). Suppose -4/7*r**2 - 2/7*r - 2/7*r**m + 0 = 0. What is r?
-1, 0
Let p = 159/11 - 455/33. Solve -2/3*n + 4/3 - p*n**2 = 0.
-2, 1
Suppose -64*q = 58*q - 244. Factor -17/4*t**3 + 3/4*t**4 + 5/2 + 35/4*t**q - 31/4*t.
(t - 2)*(t - 1)**2*(3*t - 5)/4
Let m(z) = z**2 + 9*z - 7. Let d be m(-10). Factor 2*l**2 + 2 + 10*l**4 - 11*l**4 - d.
-(l - 1)**2*(l + 1)**2
Factor 5/3*r**4 - 4/3 + 6*r**3 + 17/3*r**2 + 0*r.
(r + 1)**2*(r + 2)*(5*r - 2)/3
Factor 3*h**5 - 2*h**5 - 2*h**4 - h**2 - 3*h**2 + 6*h + 11*h**2 - h**4 - 3*h**3.
h*(h - 3)*(h - 2)*(h + 1)**2
Let h(d) = 11*d**2 - 13*d + 34. Let k be h(6). Solve -1 - 1 - k*p**2 + 354*p**2 = 0 for p.
-1, 1
Suppose 9 = -3*t - 5*l, -2*l - 10 = -0*t - 2*t. Suppose -g - 4*i = -t*g + 2, -4*g = 2*i - 26. Factor -g + 7/3*q**3 - 44/3*q**2 + 25*q.
(q - 3)**2*(7*q - 2)/3
Let d(x) = -x**3 - 54*x**2 - 35*x + 74. Let p(l) = 4*l**3 + 161*l**2 + 105*l - 226. Let c(z) = -11*d(z) - 4*p(z). Factor c(y).
-5*(y - 1)*(y + 2)*(y + 9)
Let v(m) be the first derivative of m**6/72 + m**5/30 - m**3/18 - m**2/24 - 79. Let v(c) = 0. What is c?
-1, 0, 1
Factor 5*q**3 + 4*q**4 - 77*q**3 + 72*q + 108*q**2 - 72 + 4 - 44*q**2.
4*(q - 17)*(q - 1)**2*(q + 1)
Let z(k) be the first derivative of 4*k**3/3 + 108*k**2 - 711. Let z(j) = 0. What is j?
-54, 0
Let t(u) be the second derivative of -u**4/6 + 106*u**3/3 - 2809*u**2 + 3*u - 21. Factor t(i).
-2*(i - 53)**2
Let w(r) be the first derivative of -2*r**5/5 + 7*r**4 - 48*r**3 + 160*r**2 - 256*r - 13. Determine s, given that w(s) = 0.
2, 4
Solve -126/11*h + 2/11*h**2 + 124/11 = 0.
1, 62
Suppose -10*b + 479 = 439. Let d(z) be the second derivative of 3/80*z**5 + 3/4*z**2 + 0 - 1/40*z**6 + 3/16*z**b - 5/8*z**3 + 10*z. Factor d(v).
-3*(v - 1)**3*(v + 2)/4
Suppose -19*b = 167 - 205. Let x be 3 + (0/2 - 0). Factor 2*n**4 + 2*n + 5*n**x - b*n - n**3 + 2*n**2.
2*n**2*(n + 1)**2
Let v(y) be the first derivative of -2 - 5/2*y**2 - 4/9*y**3 - 5/36*y**4 + 0*y - 1/90*y**5. Let k(n) be the second derivative of v(n). Factor k(b).
-2*(b + 1)*(b + 4)/3
Let k be 2 + 1/1*12. Let j be (-2 + 4)*21/k. Factor -5*a**j + 4*a - 4 + 0*a**2 + 4*a**2 - a**3 + 2*a**3.
-4*(a - 1)**2*(a + 1)
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