 n**2 - n + 197. Let k(r) = -a(r) - c(r). Let k(v) = 0. Calculate v.
-13/2, 0
Let y = 17998 - 12277. Factor -y*s**2 + 6*s + 5725*s**2 - 15*s - 15*s + 36.
4*(s - 3)**2
Let w(q) be the second derivative of -q**5/80 + q**4/6 + 19*q**3/24 + 5*q**2/4 + 3727*q. Factor w(k).
-(k - 10)*(k + 1)**2/4
Factor 22025*g - 75948 - 836*g**2 - 1745*g**3 + 1749*g**3 + 304928 + 19491*g.
4*(g - 107)**2*(g + 5)
Let z be -15*19/(-1525 + -14). Let v(s) be the first derivative of -1/36*s**4 + 8 - 2/9*s**2 + z*s**3 + 0*s. Factor v(n).
-n*(n - 4)*(n - 1)/9
Let t = -27320 - -27324. Let g(m) be the third derivative of 0 - 3*m**2 - 3/80*m**5 + 0*m**t + 1/32*m**6 + 0*m - 1/448*m**8 + 0*m**3 - 1/280*m**7. Factor g(b).
-3*b**2*(b - 1)**2*(b + 3)/4
Let z be 152 - 10*11/(55/(-4)). Factor -190*m - z*m**2 - 75/2*m**3 - 40.
-5*(m + 2)**2*(15*m + 4)/2
Let z(g) = -3*g**3 - 36*g**2 - 47*g + 88. Let s(r) = 7*r**3 + 67*r**2 + 96*r - 175. Let k(q) = -4*s(q) - 10*z(q). Suppose k(t) = 0. What is t?
-45, -2, 1
Suppose -27*n = -39*n + 72. Let v(d) be the second derivative of -2*d + 1/16*d**4 + 1/40*d**n + 0*d**3 + 0 + 0*d**2 - 3/40*d**5. Factor v(o).
3*o**2*(o - 1)**2/4
Let t be (2610/(-2523))/((-38)/551). Determine i, given that 21/2*i**4 + 0 - 9/4*i**5 + 6*i**2 + 0*i - t*i**3 = 0.
0, 2/3, 2
Let w(v) be the first derivative of 1/300*v**5 + 19/2*v**2 + 5 + 0*v + 1/30*v**4 + 1/10*v**3. Let x(c) be the second derivative of w(c). Factor x(m).
(m + 1)*(m + 3)/5
Let o(v) be the third derivative of -4/27*v**3 + 1/135*v**7 + 1/90*v**5 + 7/27*v**4 - 11/270*v**6 + 0*v - 71*v**2 + 0. Suppose o(j) = 0. Calculate j.
-1, 1/7, 2
Let b(y) = -9*y**2 - 1542*y. Let x(w) = -4*w**2 - 759*w. Let m(u) = 3*b(u) - 7*x(u). Factor m(r).
r*(r + 687)
Let s(l) be the third derivative of 0*l - 5*l**2 + 1/6*l**4 - 7 - 1/60*l**5 + 0*l**3. Suppose s(r) = 0. Calculate r.
0, 4
Let v(m) be the first derivative of 2/5*m**5 - 7/2*m**4 + 0*m + 16/3*m**3 + 42 + 16*m**2. Factor v(p).
2*p*(p - 4)**2*(p + 1)
Suppose -3*a + 2 = -1, y - 2*a + 2 = 0. Suppose -2*u = -c - 10, -c = -15*u + 8*u + 35. Factor 9/4*s**5 - 15/4*s**4 + 0*s**2 + y*s + 3/2*s**3 + c.
3*s**3*(s - 1)*(3*s - 2)/4
Let o(c) = 2*c**4 - 93*c**3 + 468*c**2 + 7100*c - 59316. Let f(x) = x**4 + 3*x**3 - 2*x - 3. Let p(v) = f(v) + o(v). Factor p(r).
3*(r - 13)**3*(r + 9)
Let b(k) be the first derivative of -2*k**3/21 - 212*k**2/7 + 426*k/7 - 9279. Solve b(o) = 0 for o.
-213, 1
Let z(r) = 55*r**2 - 479*r + 3090. Let f(i) = 735*i**2 - 6225*i + 40170. Let s(a) = -3*f(a) + 40*z(a). Suppose s(g) = 0. Calculate g.
-103, 6
Suppose -78*v + 76*v - 160 = 0. Let i be -3*(3/2)/(1260/v). Factor -i*a**4 + 6/7*a**2 + 0 + 0*a**3 - 4/7*a.
-2*a*(a - 1)**2*(a + 2)/7
Let p be 2/((-2)/(-9)) + 1. Let u be 1/((3/(-8))/(8/(160/(-15)))). Let 320*j + 1579*j**2 + 30 + 1125*j**3 - 154*j**u - p = 0. Calculate j.
-1, -2/15
Let y(a) be the third derivative of a**7/1890 + 7*a**6/1080 - 23*a**5/180 + 113*a**4/216 - 26*a**3/27 + 1250*a**2. Factor y(z).
(z - 4)*(z - 1)**2*(z + 13)/9
Factor -20*u**3 + 25 + 96*u**2 - 22*u - 126*u**2 + 49*u - 7*u + 5*u**4.
5*(u - 5)*(u - 1)*(u + 1)**2
Let f(h) be the third derivative of -h**7/560 + h**6/80 + h**5/40 - h**4/4 - 378*h**2. What is n in f(n) = 0?
-2, 0, 2, 4
Let c(i) = 62*i - 57. Let g be c(1). Let o(x) be the third derivative of 16/15*x**6 + 9*x**3 + 9*x**4 + 10*x**2 + 24/5*x**g + 0*x + 0. Factor o(y).
2*(4*y + 3)**3
Let j(z) be the first derivative of -891*z**5/10 - 5391*z**4/4 - 3709*z**3/2 - 933*z**2 - 198*z + 5022. What is f in j(f) = 0?
-11, -6/11, -1/3, -2/9
Factor -4*s**3 + 790*s + 1094*s + 2880 + 255*s**2 + 41*s**2.
-4*(s - 80)*(s + 3)**2
Suppose 8*w - 12 = 4*w. Suppose -w*j = -8 - 13. Suppose 48 - 6*i**2 + j*i**4 - 4*i**4 - 12*i**2 - 6*i**2 = 0. Calculate i.
-2, 2
Let v(c) be the first derivative of c**3/15 + 781*c**2/5 + 609961*c/5 + 2315. Factor v(d).
(d + 781)**2/5
Let f(y) be the third derivative of -9/4*y**4 + 0 - 51*y**2 + y - 1/7*y**7 + 89/40*y**6 + 0*y**3 + 11/20*y**5. Suppose f(h) = 0. What is h?
-1/2, 0, 2/5, 9
Let l = 1615 + -1612. Suppose -8 = 4*m - 8*h + 12*h, -l*h - 4 = 4*m. Factor 2/3*c**m + 0 + 6*c.
2*c*(c + 9)/3
Let d(w) be the second derivative of -w**6/135 + 29*w**5/90 - 89*w**4/54 - 269*w**3/27 - 50*w**2/3 + w + 5042. What is x in d(x) = 0?
-1, 6, 25
Let l(y) = -6*y**2 + 5*y. Let k(i) = -3*i**3 + 795*i**2 + 33*i - 831. Let b(z) = -k(z) + 6*l(z). Factor b(q).
3*(q - 277)*(q - 1)*(q + 1)
Let u be 22/((-792)/30) - ((-137)/24 + 3). Let s(g) be the first derivative of g - u*g**4 + 15/4*g**2 + 6 + 13/3*g**3 - 14/5*g**5. Let s(j) = 0. What is j?
-1, -2/7, -1/4, 1
Let c(x) = -2*x**2 + 3*x. Let y(g) = -9*g**4 + 84*g**3 - 199*g**2 - 66*g + 196. Let d(s) = 6*c(s) - y(s). Solve d(z) = 0.
-1, 1, 14/3
Let k(l) be the first derivative of l**4/14 - 6*l**3/7 - 22*l**2/7 - 1743. Factor k(x).
2*x*(x - 11)*(x + 2)/7
Let i(h) be the second derivative of 0*h**4 - 4*h + 1/120*h**6 - 1/40*h**5 - 1/8*h**2 + 1/12*h**3 - 1. Find k such that i(k) = 0.
-1, 1
Let o(y) be the first derivative of -35*y**4/12 + 100*y**3/3 + 30*y**2 - 47*y - 58. Let q(d) be the first derivative of o(d). Suppose q(g) = 0. What is g?
-2/7, 6
Let g(x) be the second derivative of x**6/150 + 9*x**5/100 - x**4/5 - 2*x**3/3 + 568*x - 2. Factor g(q).
q*(q - 2)*(q + 1)*(q + 10)/5
Suppose -24*n - 837 = 4*m - 19*n, -2*n = -2*m - 414. Let q be ((-144)/(-576))/((-10)/m). Factor -6*y + 4/5 + q*y**2.
2*(y - 1)*(13*y - 2)/5
Let 171/7*t**3 + 90/7 + 9/7*t**4 + 63*t + 569/7*t**2 = 0. What is t?
-15, -3, -2/3, -1/3
Let t(a) be the first derivative of a**3 - 717*a**2/2 + 714*a + 473. Determine r, given that t(r) = 0.
1, 238
Let n = 181 - 177. Suppose -n*s = g - 27, -3*s + 16 + 10 = -5*g. Factor -2*r - s - 1/7*r**2.
-(r + 7)**2/7
Suppose -542 = -8*d - 502. Let l(y) be the first derivative of 5/2*y**4 - 3*y**d - 7 + 35/3*y**3 + 5*y**2 + 0*y. Let l(m) = 0. What is m?
-1, -1/3, 0, 2
Let z be 2/30*5 - 2314/(-6). Let p = z - 382. What is u in 1/5*u**2 + 23/5*u - 7/5*u**p + 6/5 - 23/5*u**3 = 0?
-3, -1, -2/7, 1
Let s(t) be the third derivative of t**7/168 + 17*t**6/72 - t**5/24 - 85*t**4/24 + 26*t**3 - 2*t**2 + 8. Let v(c) be the first derivative of s(c). Factor v(w).
5*(w - 1)*(w + 1)*(w + 17)
Let h(q) = 5*q**2 + 1. Let i(b) = -6*b**2 + 56*b - 130. Let t(x) = 2*h(x) + i(x). Find j, given that t(j) = 0.
-16, 2
Let c(t) = t**5 - t**4 - 1. Let h(n) = -n - 2 - 5*n**4 - 16*n**4 + n**5 + 2*n**3 + 19*n**4. Let f(b) = 2*c(b) - h(b). Find g, given that f(g) = 0.
-1, 0, 1
Factor -234/7*m + 0 - 6/7*m**4 - 222/7*m**3 + 66*m**2.
-6*m*(m - 1)**2*(m + 39)/7
Let u(l) be the first derivative of -l**3/3 - 12*l**2 - 135*l + 11705. Factor u(x).
-(x + 9)*(x + 15)
Let -224*g**2 + 4*g**5 - 18811*g**4 + 1408*g - 18817*g**4 + 37632*g**4 - 152*g**3 + 2560 = 0. What is g?
-4, -2, 4, 5
Let s = 9530 - 5662. Determine r so that -7732*r + s*r + r**3 + 3872*r - 6*r**2 = 0.
0, 2, 4
Let v(x) = -812*x**2 - 5685*x + 3. Let u be v(-7). Solve 14/3*q**2 - u - 2/3*q**3 - 14/3*q = 0 for q.
-1, 3, 5
Factor -144/5 - 16/5*y**2 - 36/5*y**3 - 1/5*y**5 + 13/5*y**4 + 32*y.
-(y - 9)*(y - 2)**3*(y + 2)/5
Let w = 674 - 679. Let u be 0/w + -3 + 54/15. Determine y so that -24/5 + u*y**4 + 18/5*y**2 + 12/5*y - 3*y**3 = 0.
-1, 2
Let c(d) be the third derivative of -20/9*d**3 + 1/525*d**7 + 31/450*d**5 - 1 - 44*d**2 + 7/9*d**4 - 13/450*d**6 + 0*d. What is j in c(j) = 0?
-2, 2/3, 5
Let w(q) be the first derivative of 3*q**4/4 + 3*q**3 - 108*q**2 - 972*q + 414. Suppose w(u) = 0. Calculate u.
-6, 9
Let a(n) be the first derivative of 2/27*n**6 + 44 - 8/15*n**5 + 11/9*n**4 - 8/9*n**3 + 0*n**2 + 0*n. Let a(b) = 0. Calculate b.
0, 1, 2, 3
Suppose -3730 - 1506 = 34*l. Let u = l - -154. Find n, given that 3/2*n**4 + u*n**3 + 3*n + 0 - 9/2*n**2 = 0.
-2, 0, 1
Let f = 448675/2467652 - 1/224332. Let 6/11*u**2 + f*u**3 + 6/11*u + 2/11 = 0. What is u?
-1
Let v(b) = 3*b**2 - b + 1. Let n(t) = -14*t**2 + 132*t - 484. Let p(l) = n(l) + 4*v(l). Factor p(a).
-2*(a - 60)*(a - 4)
Solve -2/11*v**2 - 322/11*v + 0 = 0.
-161, 0
Let j(r) be the first derivative of 41*r**6/840 + 39*r**5/280 - r**4/28 + 2*r**3/3 - 60*r - 13. Let b(c) be the third derivative of j(c). Factor b(z).
3*(z + 1)*(41*z - 2)/7
Find a such that 5584/3*a - 3897632/3 - 2/3*a**2 = 0.
1396
Let j = 51 + -47. Factor -h**5 + 6