*a**2 + 11/95*a**5 - 2*a**3 - 3/19*a**4 - 17 - 121/3420*a**6 + 0*a. Let g(f) be the third derivative of r(f). Factor g(y).
-2*(11*y - 6)**2/19
Suppose 497*r - 1160 = -227 + 61. Factor 49/9 + 1/9*l**r - 14/9*l.
(l - 7)**2/9
Let p(f) be the third derivative of f**7/42 - 13*f**6/12 + 11*f**5/3 + 65*f**4/3 - 160*f**3 - f**2 - 1102. Solve p(b) = 0.
-2, 2, 24
Factor 49 - 853*b + 350*b + 119 + 339*b - 4*b**2.
-4*(b - 1)*(b + 42)
Suppose 3 = 3*u - 0*u - z, -4 = 4*u - 4*z. Let y = 135 - 133. Factor 37*d**u + d - 38*d**y + 5*d.
-d*(d - 6)
Suppose -3*f = 5*s + 15, -493*f = -s - 490*f + 51. Find p, given that 3/2*p**4 - 6*p + s*p**3 + 9/2*p**2 - 6 = 0.
-2, -1, 1
Let f(u) be the first derivative of -u**4/4 - 17*u**3/3 + 39*u**2/2 + 21*u + 13. Let w be f(-19). Solve 5/3*n**w + 10/3*n - 5 = 0.
-3, 1
Let m(w) be the third derivative of -1/60*w**6 + w**4 + 86*w**2 + 0 + 0*w**5 + 16/3*w**3 + 0*w. Factor m(h).
-2*(h - 4)*(h + 2)**2
Suppose 0 = -9*x - 16*x + 50. Let b(r) be the second derivative of -1/4*r**5 - x*r + 0 - 15*r**2 + 5/2*r**4 + 5/6*r**3. Factor b(t).
-5*(t - 6)*(t - 1)*(t + 1)
Let i be (-165 - -207) + (-16)/7 + 24/84. Solve -i*y**3 + 50*y**2 - 1/2*y**5 - 19/2*y**4 + 0*y + 0 = 0 for y.
-10, 0, 1
Let u(w) be the third derivative of -2*w**2 + 43 + 5/36*w**3 + 0*w + 0*w**4 - 1/72*w**5. Factor u(i).
-5*(i - 1)*(i + 1)/6
Find f such that -21/4*f**3 - 9*f**2 + 3*f + 12 - 3/4*f**4 = 0.
-4, -2, 1
Let w(f) be the third derivative of -5*f**7/21 - 71*f**6/24 - 59*f**5/4 - 110*f**4/3 - 130*f**3/3 - f**2 + 2*f + 366. Solve w(u) = 0 for u.
-13/5, -2, -1/2
Suppose u - 7*l + 12*l + 29 = 0, 25 = -5*l. Let q be (-1344)/210*1/u. Suppose 4/5*f**5 - 4/5*f**4 + 0 - 12/5*f**3 - q*f + 4*f**2 = 0. Calculate f.
-2, 0, 1
Suppose 65 = -59*r + 72*r. Factor -247*s + 221*s - r - 77 - 87 - s**2.
-(s + 13)**2
Factor -80 - 1/3*t**2 - 46/3*t.
-(t + 6)*(t + 40)/3
Suppose 6*a - 3*a = -5*g + 127, 0 = 5*a - 4*g - 224. Find v such that 39*v**2 + 80*v - 7 - a*v**2 - 68 = 0.
1, 15
Let p(t) be the first derivative of -42 - 3/5*t**6 - 12/5*t**2 + 164/15*t**3 - 16/5*t + 104/25*t**5 - 21/2*t**4. Solve p(g) = 0.
-2/9, 1, 2
Let d(t) = 8*t + 243. Let u be d(-30). Suppose w - 6 = y - 7, u = -2*w + 3*y. Determine h so that w + 6/5*h**2 + 4/5*h + 2/5*h**3 = 0.
-2, -1, 0
Factor 27201*l**3 + 175*l**4 + 314*l**4 - 61224*l + 1786524 + 1948872*l + 585248*l**2 + 158*l**5 - 35585*l**2 - 155*l**5.
3*(l + 2)**2*(l + 53)**3
Let b(c) be the second derivative of c**6/6 + 27*c**5/4 + 125*c**4/6 - 3*c + 207. Factor b(k).
5*k**2*(k + 2)*(k + 25)
Suppose -99*i + 44*i + 38*i + 34*i = 0. Let b(l) be the third derivative of -1/12*l**4 + i - 2/9*l**3 + 0*l + 5*l**2 - 1/90*l**5. Let b(j) = 0. What is j?
-2, -1
Let v(p) = 11*p**2 - 119*p - 868. Let f(r) = 135*r**2 - 1430*r - 10415. Let w(t) = -2*f(t) + 25*v(t). Factor w(n).
5*(n - 29)*(n + 6)
Let z(o) = 66*o + 161. Let m(t) = -23*t - 54. Let d(a) = 7*m(a) + 2*z(a). Let j be d(-2). Determine s, given that 8/5 - 8/5*s**j - 4/5*s + 4/5*s**3 = 0.
-1, 1, 2
Suppose -k + 87 = 2*k + 5*c, 0 = -4*k - 2*c + 102. Determine v, given that 32*v**3 - 25*v**4 + 16*v**3 - 124*v**2 + 32 + 25*v**4 + k*v + 20*v**4 = 0.
-4, -2/5, 1
Determine z, given that 61*z + 1213898 + z**2 - 1213898 = 0.
-61, 0
Let w(u) be the third derivative of u**5/30 - 13*u**4/2 + 497*u**3/3 - u**2 + 20*u + 6. Solve w(m) = 0.
7, 71
Factor 0 - 1/8*i**3 + 61/8*i**2 + 31/4*i.
-i*(i - 62)*(i + 1)/8
Let l(m) = -9*m**3 + 631*m**2 + 1477*m - 1987. Let d(w) = -3*w**3 + 210*w**2 + 498*w - 663. Let z(q) = 8*d(q) - 3*l(q). Factor z(t).
3*(t - 73)*(t - 1)*(t + 3)
Let j = -749438 + 749440. Suppose 2*r = -0 + 6. Suppose 2/17*m**4 + 0*m**r - 6/17*m**j + 0 - 4/17*m = 0. Calculate m.
-1, 0, 2
Let b(d) = d**3 + 32*d**2 - 3*d - 77. Let j be b(-32). Suppose 276 = 65*z - j*z. Determine l, given that -3/2*l**3 - 3 - 15/2*l - z*l**2 = 0.
-2, -1
Let p(u) be the third derivative of u**8/1512 + u**7/135 + u**6/90 - 11*u**5/135 - 7*u**4/108 + 5*u**3/9 + 1080*u**2. Determine n so that p(n) = 0.
-5, -3, -1, 1
Let p be (-4 - 0)/((-6)/51). Let y = p - 31. Let -y*u**3 + 0*u**2 + 3*u**2 + 0*u**2 = 0. What is u?
0, 1
Let t(r) be the third derivative of 17/140*r**7 + 0*r + 2*r**2 + 27 - 37/80*r**6 + 19/40*r**5 + 0*r**3 + 0*r**4 + 1/224*r**8. Factor t(j).
3*j**2*(j - 1)**2*(j + 19)/2
Let k(d) be the first derivative of d**3/5 + 801*d**2/5 - 3216*d/5 - 4298. Find a, given that k(a) = 0.
-536, 2
Let z(p) = p**2 + p - 1. Let b(y) = 25*y**2 - 140*y - 1475. Let l = -60 - -61. Let g(w) = l*b(w) - 30*z(w). Factor g(c).
-5*(c + 17)**2
Let l(a) = -212*a**3 + 464*a**2 + 12*a - 24. Let v(u) = 18*u**3 - u + 2. Let r(c) = -l(c) - 12*v(c). Factor r(w).
-4*w**2*(w + 116)
Let o be 37/((-666)/(-27))*18 - 23. Factor 2/7*d**3 - 2/7*d + 0 - 2/7*d**2 + 2/7*d**o.
2*d*(d - 1)*(d + 1)**2/7
Let w(v) be the second derivative of 2 - 1/5*v**3 - 17/60*v**4 - 1/50*v**6 - 3*v - 7/50*v**5 + 0*v**2. What is n in w(n) = 0?
-3, -1, -2/3, 0
Suppose 0 = -205*d + 228*d + 92. Let m be (-75)/60 - d/(24/9). Suppose 0*k + 0*k**2 - 3/4*k**5 + 1/2*k**3 + 0 + m*k**4 = 0. What is k?
-2/3, 0, 1
Suppose -4503*f - 24 = -4508*f - h, -4*f + 5*h = 62. Factor -8 + 5/3*o + 1/3*o**f.
(o - 3)*(o + 8)/3
Let q(z) be the first derivative of 14*z**5/5 + 107*z**4/2 + 256*z**3/3 + 28*z**2 + 3592. Determine t so that q(t) = 0.
-14, -1, -2/7, 0
Let y = 1687/10235 + 72/2047. Factor -y*l**2 - 9/5 - 6/5*l.
-(l + 3)**2/5
Let z be 2 + (-18)/(-432)*0. Let u(x) be the first derivative of 0*x + 2/5*x**5 - 4*x**4 - 18*x**z + 14*x**3 + 28. Find s, given that u(s) = 0.
0, 2, 3
Let o be ((-8)/80*0)/(-1). Let m(s) be the third derivative of -8*s**2 + 1/180*s**6 + 1/180*s**5 + o*s**3 + 0*s + 0 - 1/630*s**7 - 1/36*s**4. Factor m(v).
-v*(v - 2)*(v - 1)*(v + 1)/3
Let v(r) be the third derivative of -172*r**2 + 11/15*r**5 + 0*r**3 + 3/70*r**7 + 0 + r**4 + 1/4*r**6 + 0*r + 1/336*r**8. Suppose v(u) = 0. What is u?
-3, -2, 0
Let h = 3234 - 2165. Suppose h*a - 1075*a = -12. Solve -4/5*d**3 - 2/15*d**5 + 14/15*d - 2/5 - 4/15*d**a + 2/3*d**4 = 0.
-1, 1, 3
Let p(s) = -130*s**3 + 2*s**2 + 3*s + 2. Let u be p(-1). Let d = -130 + u. Let 15 + 1 - 6*r - d + 3*r**4 - 12*r**2 - 6 + 6*r**3 = 0. Calculate r.
-3, -1, 1
Let t(y) be the third derivative of y**6/480 + 7*y**5/80 - 17*y**4/8 - 28*y**3/3 + 822*y**2 + 2*y. Solve t(d) = 0 for d.
-28, -1, 8
Let v(a) be the first derivative of 85*a**4/4 + 1625*a**3/3 + 95*a**2 + 2182. Factor v(g).
5*g*(g + 19)*(17*g + 2)
Let c be (135/315)/((-5)/(-35)). Let v(u) be the first derivative of 0*u + 0*u**2 + 0*u**c - 13 - 12/5*u**5 - 3*u**6 - 1/2*u**4. Solve v(i) = 0 for i.
-1/3, 0
Let n(o) = 7*o**3 + 7*o**2 + 3*o. Let u(c) = 8*c**2 + 9*c**2 + 36*c**3 + 19*c**2 + 16*c. Let x(l) = 16*n(l) - 3*u(l). Find w such that x(w) = 0.
-1, 0
Let a(q) = 7*q**3 - 355*q**2 - 731*q - 357. Let v(m) = 120*m**3 - 6033*m**2 - 12426*m - 6066. Let o(u) = 69*a(u) - 4*v(u). Let o(c) = 0. Calculate c.
-1, 123
Suppose 5*j = 5*d + 310, 2*d = -2*j - 3*d + 89. Let n be 190/j*6/5. Suppose 0*k**3 + 0 + 3/4*k**2 - 1/2*k - 1/4*k**n = 0. Calculate k.
-2, 0, 1
Let h be (-795)/(-33) + 6*(-4)/264. Solve 3/4*j**3 - h - 9*j**2 + 27*j = 0.
2, 8
Factor -764/7*y - 1/7*y**2 - 145924/7.
-(y + 382)**2/7
Let v(l) be the second derivative of -l**6/2 - 57*l**5/20 + 15*l**4/2 - 358*l - 1. Solve v(d) = 0.
-5, 0, 6/5
Let u = 31215/62606 + 44/31303. What is j in 5 - u*j**2 + 3/2*j = 0?
-2, 5
Factor 355 - 370/3*w + 5/3*w**2.
5*(w - 71)*(w - 3)/3
Let y(z) be the third derivative of z**6/360 - 65*z**5/36 + 369*z**4 - 1458*z**3 + 3586*z**2. Suppose y(r) = 0. What is r?
1, 162
Let g be (4 - (0 - 1)) + -10*(-2)/(-4). Let r(z) be the third derivative of z**2 + 0*z - 1/60*z**5 + g - 1/12*z**4 - 1/6*z**3. Factor r(t).
-(t + 1)**2
Let p(k) be the first derivative of k**4/10 - 724*k**3/15 - 705. Factor p(b).
2*b**2*(b - 362)/5
Let d(p) be the third derivative of 5/336*p**8 + 0 - 1/3*p**6 - 4*p**2 + 1/6*p**5 - 16*p + 1/21*p**7 + 35/24*p**4 - 10/3*p**3. Factor d(t).
5*(t - 1)**3*(t + 1)*(t + 4)
Let j be (-11)/(-2) - (9/(-18) - -1). Let k(s) = s**3 - 6*s**2 + 23*s - 87. Let z be k(j). Factor -l**2 - 1/2*l**z + 0 + 3/2*l.
-l*(l - 1)*(l + 3)/2
Let k(t) be the first derivative of t**5/15 + 7*t**4/6 + 20*t**3/9 - 175*t**2/3 - 375*t - 3356. Factor k(y).
(y - 5)*(y + 5)**2*(y + 9)/3
