.
1, 7
Let x = -248 + 250. Let b(c) be the first derivative of -7 + 2/45*c**3 + 4/15*c**x + 2/5*c. Suppose b(r) = 0. Calculate r.
-3, -1
Suppose -362*y = -278 - 1170. Factor 2*s**3 + 0*s**2 + 0 + 0*s + 14/3*s**y.
2*s**3*(7*s + 3)/3
Let i = -216742909/143475 - -3/47825. Let k = i - -1527. Factor -20/3*r - r**2 + 70/3*r**3 + k*r**4 + 4/3.
(r + 1)**2*(7*r - 2)**2/3
Let a be 2678/52 - 43 - 3. Let -2*y**4 + 1 - 41/4*y**2 + 65/8*y**5 - 199/8*y**3 + a*y = 0. What is y?
-1, -2/13, 2/5, 2
Let b = 194410/291543 - 16/97181. Factor 5/6*r - b - 1/6*r**2.
-(r - 4)*(r - 1)/6
Factor -128/3 - 106/9*m**2 + 2/9*m**3 + 488/9*m.
2*(m - 48)*(m - 4)*(m - 1)/9
Let r(a) = -a**3 + 7*a**2 - 8*a + 7. Let q be r(5). Let k = -14 + q. Factor -13*z**3 - 3*z**4 + z**4 - 2*z**5 + 19*z**3 + 2*z**2 - 4*z**k.
-2*z**2*(z - 1)*(z + 1)**2
Suppose -5*g + 2 = q, g + 10 = 4*q + 2. Let -2*d - d**3 + 21808 - 21808 - 3*d**2 + g*d**3 = 0. Calculate d.
-2, -1, 0
Let l be 3 + 3 - ((7 - 3) + 3). Let o(q) = -q**2. Suppose 0 = -s + 17 + 3. Let k(z) = -15*z**2 + 5*z - 10. Let g(x) = l*k(x) + s*o(x). Factor g(c).
-5*(c - 1)*(c + 2)
Let k be ((-32)/56)/(10/(-35)). Factor -12*b**2 + 7*b**k + 9*b**2 + b**2 - 26 - 3*b**2 + 24*b.
2*(b - 1)*(b + 13)
Suppose 13 + 7 = 4*o. Suppose -2*n - o*v + v = 4, -5*n - 4*v + 8 = 0. Factor -n*m**2 - 24*m + 58*m - 4 - 26*m.
-4*(m - 1)**2
Let k be (112/32)/((-5)/(-640)). Suppose k*z - 1274 = 435*z. Find c such that -32/7*c - 144*c**3 - 320/7*c**2 + 0 + z*c**5 - 112*c**4 = 0.
-2/7, 0, 2
Let d = 7290 + -4373999/600. Let q(k) be the third derivative of 0*k**4 - d*k**6 + 29*k**2 + 0*k**3 + 1/100*k**5 + 0*k + 0. Suppose q(g) = 0. What is g?
0, 3
Let i(l) be the third derivative of 3/20*l**4 + 0*l + 1/300*l**5 + 0 - 78*l**2 + 0*l**3. Factor i(j).
j*(j + 18)/5
Suppose 3*b = -2*s + b + 834, s - b - 413 = 0. Let q = s - 411. Factor 18*m**2 - 8*m**3 - 11/2*m - 32*m**q + 1/2.
-(m + 1)*(4*m - 1)**3/2
Let c = -101808/5 + 407327/20. Factor 1 - 4*u + 25/4*u**2 - c*u**3 + 7/4*u**4 - 1/4*u**5.
-(u - 2)**2*(u - 1)**3/4
Let s(l) be the first derivative of 5*l**3 + 110 + 12*l + 12*l**2 + 3/4*l**4. Factor s(i).
3*(i + 1)*(i + 2)**2
Let q(z) be the first derivative of -29/6*z**2 - 841/6*z - 1/18*z**3 - 18. Suppose q(u) = 0. What is u?
-29
Let t(j) = -2*j**4 + 1. Let m(d) = -9*d - 3*d**3 - 4 - 17*d**4 - 19*d**4 - 16*d**4 + 63*d**4 - 15*d**2. Let a(w) = m(w) + 4*t(w). Let a(r) = 0. Calculate r.
-1, 0, 3
Suppose -20 = -4*v - n - 3*n, -4*v - 2*n + 18 = 0. Suppose 5*w = v*q + 3, -6*w + 15 = q - 2*w. Factor -t - 4*t + 3*t**2 + 5*t**q + 2*t**2 - 5*t**4.
-5*t*(t - 1)**2*(t + 1)
Let m(k) be the third derivative of k**7/105 + k**6/6 - 16*k**5/15 - 8*k**4 + 9*k**2 + 151. Factor m(b).
2*b*(b - 4)*(b + 2)*(b + 12)
Let g(v) be the first derivative of 121/21*v**6 + 128/7*v**2 - 614/21*v**3 + 226 - 24/7*v - 249/14*v**4 + 638/35*v**5. Determine c, given that g(c) = 0.
-3, -1, 2/11, 1
Let x be (11 + 5)/16*0. Suppose -9/5 + x*h + 1/5*h**2 = 0. What is h?
-3, 3
Factor -268/7*b - 9*b**3 + 264/7*b**2 + 0 - 1/7*b**4.
-b*(b - 2)**2*(b + 67)/7
Determine x so that 0 - 1/2*x + 1/6*x**2 = 0.
0, 3
Let i(k) be the third derivative of -k**8/168 - 4*k**7/15 + 47*k**6/30 + 14*k**5/15 - 31*k**4/4 - 173*k**2. Determine n, given that i(n) = 0.
-31, -1, 0, 1, 3
Suppose -26 + 10 = -8*m + 16. Let q(o) be the first derivative of 1/8*o**6 - 5/4*o**3 + 0*o - 3/4*o**2 - 3 + 3/20*o**5 - 9/16*o**m. Factor q(r).
3*r*(r - 2)*(r + 1)**3/4
Let s(x) be the third derivative of -1/90*x**5 + 7/3*x**4 + 0 + 0*x + 190*x**2 - 196*x**3. Suppose s(d) = 0. Calculate d.
42
Let k be (-23 + 979/44)*24/(-9). What is n in 2*n**k - 24 - 2/9*n**3 + 0*n = 0?
-3, 6
Let q(b) be the second derivative of -20*b - 1/36*b**3 + 13/72*b**4 + 0*b**2 - 49/180*b**6 - 7/24*b**5 + 0. Suppose q(j) = 0. Calculate j.
-1, 0, 1/7
Suppose 3111 = 2*l - 11*t + 16*t, 0 = 5*l + 3*t - 7768. Let c = l - 4658/3. Factor -1/3*z**2 - c*z**4 + 2/3 - z + z**3.
-(z - 2)*(z - 1)**2*(z + 1)/3
Let c(o) be the first derivative of 1225*o**4/18 + 9380*o**3/27 - 277*o**2/3 + 8*o - 7465. Factor c(x).
2*(x + 4)*(35*x - 3)**2/9
Solve -3200/7 - 2/7*s**3 - 928/7*s - 82/7*s**2 = 0 for s.
-25, -8
Factor -1/7*a**3 + 0 + 26/7*a**2 - 24*a.
-a*(a - 14)*(a - 12)/7
Let u be 14/2 + 70/(-18 - -8). Suppose u = -8*a - 16*a + 72. Suppose 0*o + 0 - 2/7*o**5 - 8/7*o**4 - 10/7*o**a - 4/7*o**2 = 0. Calculate o.
-2, -1, 0
Let d = 24104 - 506144/21. Suppose -8/21 - 2/21*v**4 + 10/7*v**2 - d*v**3 + 4/7*v**5 + 8/21*v = 0. Calculate v.
-2, -1/2, 2/3, 1
Let n(x) be the second derivative of x**7/168 + 7*x**6/40 + 137*x**5/80 + 93*x**4/16 + 27*x**3/4 + 79*x. Factor n(v).
v*(v + 1)*(v + 2)*(v + 9)**2/4
Let a(y) be the second derivative of y**4/6 - 296*y**3/3 - 297*y**2 + 1031*y. Find i such that a(i) = 0.
-1, 297
Suppose 8693 = 2663*u - 1959. Factor -26*k**2 - 186/5*k**3 + 18/5*k**u + 0 - 22/5*k.
2*k*(k - 11)*(3*k + 1)**2/5
Let r(h) be the second derivative of 31/4*h**3 + 1/8*h**4 - 24*h**2 - 18*h + 2. Factor r(g).
3*(g - 1)*(g + 32)/2
Suppose -4*r + 3*b = -39, 0 = 2410*b - 2415*b - 65. Let 10/11*s**4 + 0 - 2/11*s**5 - 16/11*s**3 + r*s + 8/11*s**2 = 0. Calculate s.
0, 1, 2
Find m, given that -208/3*m + 2/3*m**3 - 46/3*m**2 - 72 = 0.
-2, 27
Let a = 164 - 154. Factor 21*o**2 - a*o**3 + 4583*o + 5*o**2 + 40 - 4471*o.
-2*(o - 5)*(o + 2)*(5*o + 2)
Let o(t) be the second derivative of -t**6/60 - 3*t**5/20 - 11*t**4/24 - t**3/2 - 1826*t + 1. What is a in o(a) = 0?
-3, -2, -1, 0
Let y(a) = -55*a**2 - 2045*a + 3085. Let k(l) = 9*l**2 + 337*l - 514. Let w(m) = -25*k(m) - 4*y(m). What is u in w(u) = 0?
-51, 2
Let p(v) be the first derivative of 2 - 13*v**2 + 2/3*v**3 + 60*v. Factor p(s).
2*(s - 10)*(s - 3)
Let g(a) be the first derivative of -1/14*a**6 + 0*a**2 + 42 - 6/35*a**5 + 57/28*a**4 + 0*a + 20/7*a**3. Suppose g(v) = 0. Calculate v.
-5, -1, 0, 4
Solve 72*y**2 + 6*y**3 - 96 + 0*y**3 - 4*y**4 + 6*y**3 + 896*y + 871*y - 1751*y = 0.
-2, 1, 6
Let t(m) = m**3 + 4*m**2 - 20. Let p be t(2). Let s(w) be the first derivative of 5/2*w**2 - 26 + 4/5*w**5 - 8*w**3 + 0*w + 15/4*w**p. Factor s(k).
k*(k - 1)*(k + 5)*(4*k - 1)
Let n be -253 - (-5 - 0 - (-30)/6). Let x be 17/33 - (-46)/n - 0. Factor 1/3*t**2 + 2/3*t + x.
(t + 1)**2/3
Let a(y) = -9*y + 41. Let b(m) = 9*m - 40. Let t(s) = 5*a(s) + 6*b(s). Let k be t(5). Factor -2*d**5 - d**5 - 18*d**4 + k*d**4 - 7*d**3 - 2*d**2.
-d**2*(d + 1)**2*(3*d + 2)
Let c = 62/2607 + 4904/13035. Factor c*g**3 + 34/5*g**2 - 162/5 + 126/5*g.
2*(g - 1)*(g + 9)**2/5
Let q = -285 - -289. Determine i, given that 23*i**4 - 2 + 5 - 3 + 16*i**q + 108*i**2 - 144*i**3 - 3*i**5 = 0.
0, 1, 6
Let q(t) = 1588*t - 96866. Let x be q(61). Determine n, given that 32/9*n**3 - 16/9 + 10*n**x + 28/9*n - 14/9*n**4 = 0.
-1, 2/7, 4
Let p(x) be the second derivative of 15/2*x**4 + 225*x**3 + 3*x + 1/10*x**5 - 10 + 3375*x**2. Determine i so that p(i) = 0.
-15
Let u be (44/(-6))/(24/(-36)). Suppose 3*o - u = -v, 3*o + 5 - 1 = 2*v. Factor 563*w + 0 + 0 - 562*w + w**o.
w*(w + 1)
Let q(z) be the second derivative of z**5/45 + 32*z**4/27 - 1034*z**3/27 + 968*z**2/9 + 11*z + 11. Let q(r) = 0. Calculate r.
-44, 1, 11
Let x(t) = 9*t**2 + 2815*t - 802. Let f(u) = 125*u**2 + 39410*u - 11205. Let r(m) = 6*f(m) - 85*x(m). Let r(g) = 0. What is g?
-188, 1/3
Factor 1434787 - 602*p**2 - 7788*p + 605*p**2 + 2840543 - 710404 + 1489486.
3*(p - 1298)**2
Factor 884/3 - 1/3*h**3 + 829/3*h - 56/3*h**2.
-(h - 13)*(h + 1)*(h + 68)/3
Let x be (184/2300)/((-2364)/2855 - 0). Let u = 2/591 - x. Factor -28/5 - 27/5*t**2 + 46/5*t - u*t**4 + 13/10*t**3.
-(t - 7)*(t - 2)**3/10
Factor -148/9*u + 80/9 + 14/9*u**2.
2*(u - 10)*(7*u - 4)/9
Let i = 104 + -102. Let h(p) = p**2 - p**i - 1 + p**2 + 0*p**2 - p. Let j(f) = 5*f**2 - 9*f - 6. Let c(a) = -6*h(a) + j(a). Factor c(y).
-y*(y + 3)
Let t(m) be the first derivative of 0*m**2 - 3 + 1/4*m - 1/12*m**3. Factor t(j).
-(j - 1)*(j + 1)/4
Factor 74*o**2 + 63*o**2 - 125*o**2 - 640*o**2 - 4116 - 4128*o - 413*o**2 - 3*o**3.
-3*(o + 2)**2*(o + 343)
Let h(y) be the second derivative of y**4/54 - 1892*y**3/27 + 894916*y**2/9 - 3410*y. Factor h(b).
2*(b - 946)**2/9
Let a(i) = -i**2 - 3*i + 64. Let k be a(0). Factor -130*q - k*q + 66*q + 4*q**2 + 1024.
4*(q - 16)**2
Let l = 3/54176 - -108307/812640. Let -24/5*v**3 - 32/15*v**2 - l*