ve of b**6/300 - b**5/75 - b**4/4 + 12*b**3/5 - 423*b**2. Factor y(h).
2*(h - 3)**2*(h + 4)/5
Let m(s) be the first derivative of 155*s**3/12 + 39*s**2 + s + 10741. Factor m(k).
(k + 2)*(155*k + 2)/4
Let r = -629772 + 629774. Factor -4/3*q**r - 115/3*q + 29/3.
-(q + 29)*(4*q - 1)/3
Let y be (-9)/(-11)*((-7293)/(-153) - 47). Factor -6/11*r**2 + y - 1/11*r**3 + 1/11*r.
-(r - 1)*(r + 1)*(r + 6)/11
Let t be (-2)/8 - (2392/32)/(-23). Let s(b) = b**3 - 2*b. Let u(k) = 6*k**3 - 14*k**2 - 5*k. Let v(p) = t*s(p) - 3*u(p). Factor v(o).
-3*o*(o - 3)*(5*o + 1)
Let i(v) be the first derivative of 18*v**6 + 372*v**5/5 + 32*v**4 - 160*v**3 - 96*v**2 + 64*v - 2696. Determine w, given that i(w) = 0.
-2, -2/3, 2/9, 1
Let w(r) be the first derivative of -41 + 0*r**3 + 0*r + 2/25*r**5 + 3/5*r**4 - 1/15*r**6 + 0*r**2. Factor w(v).
-2*v**3*(v - 3)*(v + 2)/5
Let p(c) = -c**2 + 171*c + 546. Let t(n) = 2*n**2 - 170*n - 544. Let v(w) = 2*p(w) + 3*t(w). Suppose v(q) = 0. Calculate q.
-3, 45
Let t = 18572 + -18567. Let m(h) be the third derivative of -1/108*h**6 - 1/108*h**4 + 0 - 2/27*h**3 + 0*h - 15*h**2 + 4/135*h**t. Factor m(i).
-2*(i - 1)**2*(5*i + 2)/9
Let c(b) be the second derivative of 0*b**3 - 67*b - 1/4*b**5 + 5/4*b**4 + 0 - 10*b**2. Solve c(u) = 0.
-1, 2
Let m(w) be the first derivative of -3*w**4/4 + 233*w**3 - 1389*w**2/2 + 693*w + 945. Determine n, given that m(n) = 0.
1, 231
Let y(s) be the second derivative of -s**7/1960 + s**6/840 + s**5/56 + 3*s**4/56 + 109*s**3/6 + 193*s. Let m(f) be the second derivative of y(f). Factor m(a).
-3*(a - 3)*(a + 1)**2/7
Suppose -2*p + 2 = -2*s, -11*s + p = -15*s + 11. Let d(c) be the second derivative of 24*c + 0 + 6*c**3 + 1/5*c**5 - s*c**4 - 8*c**2. Factor d(q).
4*(q - 4)*(q - 1)**2
Let s(h) be the first derivative of 7*h**4/18 - 160*h**3/27 + 103*h**2/9 - 20*h/3 + 1554. Let s(k) = 0. What is k?
3/7, 1, 10
Let r(c) be the first derivative of c**6/27 + 12*c**5/5 - 55*c**4/18 + 804. Solve r(l) = 0 for l.
-55, 0, 1
Let a(k) be the third derivative of -43*k**2 + 1/40*k**5 + 0*k**4 + 0 + 0*k**3 + 1/80*k**6 + 0*k. Factor a(t).
3*t**2*(t + 1)/2
Let k(o) = -4*o**3 + 366*o**2 - 756*o + 5. Let h(g) = -7*g**3 + 549*g**2 - 1134*g + 8. Let i(l) = 5*h(l) - 8*k(l). Determine b so that i(b) = 0.
-63, 0, 2
Let o(a) = a**3 + 19*a**2 - 17*a - 10. Let k be o(-20). Let r = -70 - k. Determine s so that -243*s**2 + 0 + 4*s + 221*s**2 + r = 0.
0, 2/11
Let l(n) be the second derivative of n**4/66 - 146*n**3/33 - 2072*n. Let l(a) = 0. What is a?
0, 146
Let t be (-21)/(-35) - (-2178)/70. Let h = -148 - -150. Determine s, given that -402/7*s**h - t*s**4 - 438/7*s**3 - 24/7 - 24*s - 6*s**5 = 0.
-2, -1, -2/7
Let u(y) be the second derivative of 32/3*y**3 - 30*y + 26/3*y**4 + 0 + 0*y**2 + 2/15*y**6 + 11/5*y**5. Factor u(p).
4*p*(p + 1)*(p + 2)*(p + 8)
Let s = -423 - -425. Factor 3*c**2 + c**3 + 6080*c**5 - 3*c**4 - 6083*c**5 + 4*c**3 - s*c**3.
-3*c**2*(c - 1)*(c + 1)**2
Suppose 603*t - 605*t = -20*s - 12, -s = 5*t - 30. Factor 0 + 1024/15*h**2 + s*h - 128/5*h**3 - 4*h**4 - 2/15*h**5.
-2*h**2*(h - 2)*(h + 16)**2/15
Let t = 36 - -17. Factor -26*u + u**4 + t*u + u**5 - 29*u - 5*u**2 - 3*u**3.
u*(u - 2)*(u + 1)**3
Factor 603*a + 3/2*a**2 + 1203/2.
3*(a + 1)*(a + 401)/2
Let h(x) = 24*x**2 - 598*x + 1221. Let u(r) = -13*r**2 + 298*r - 610. Let b(y) = -6*h(y) - 11*u(y). Factor b(a).
-(a - 308)*(a - 2)
Let y(z) = 180*z**3 + 1552*z**2 + 57592*z + 431992. Let j(u) = -67*u**3 - 517*u**2 - 19197*u - 143997. Let w(h) = 8*j(h) + 3*y(h). Factor w(n).
4*(n + 10)*(n + 60)**2
Let o be (-20)/4 + 2 + 3 + 4/8. Factor 9/2*y**3 + o*y + 2 - 7*y**2.
(y - 1)**2*(9*y + 4)/2
Let t(s) be the first derivative of -2/21*s**3 + 11/7*s**2 + 69 + 0*s. Let t(v) = 0. Calculate v.
0, 11
Let q(w) be the third derivative of -w**7/105 - 17*w**6/20 - 73*w**5/15 - 8*w**4 - 4*w**2 - 47*w - 1. Factor q(s).
-2*s*(s + 1)*(s + 2)*(s + 48)
Let n(a) be the second derivative of a**6/40 - 9*a**5/20 + a**4 + 3*a**2/2 - 4*a - 9. Let y(q) be the first derivative of n(q). Suppose y(v) = 0. What is v?
0, 1, 8
Let k(p) be the second derivative of 0*p**2 - 11/10*p**6 + 0*p**3 - 19/30*p**5 - 9/28*p**7 - 1/9*p**4 - 36*p + 0. Let k(r) = 0. Calculate r.
-2, -2/9, 0
Let q(z) be the second derivative of -178*z + 0*z**2 + 1/22*z**4 + 3/110*z**5 + 0 + 1/33*z**3 + 1/165*z**6. Find s, given that q(s) = 0.
-1, 0
Let g(n) be the third derivative of -n**5/12 - 35*n**4/2 - 4615*n**3/6 + 11*n**2 + 57. Factor g(b).
-5*(b + 13)*(b + 71)
Factor -692221/3*c**3 + 463148*c**2 - 231852*c - 1666/3*c**4 + 0 - 1/3*c**5.
-c*(c - 1)**2*(c + 834)**2/3
Let f(k) be the first derivative of k**3/3 - 242*k**2 + 791. Let f(g) = 0. What is g?
0, 484
Let y(r) = -r**2 - 14*r + 27. Let d be y(-17). Let x = d + 24. Determine s, given that 7/3*s**2 + 11/3*s**4 + 20/3*s**3 - 2/3*s + x = 0.
-1, 0, 2/11
Let z(w) be the first derivative of w**5/4 - 10*w**4/3 + 35*w**3/6 - 80*w + 9. Let j(k) be the first derivative of z(k). Suppose j(t) = 0. Calculate t.
0, 1, 7
Let s be (30/(-2))/3*36/(-20). Suppose 9*d - 27 + s = 0. Solve 8*a**d - 156*a**5 + 80*a**4 - 121*a + 68*a**3 + 121*a = 0.
-1/3, -2/13, 0, 1
Let x(z) be the second derivative of -1/21*z**4 - 2/105*z**6 - 1/147*z**7 + 4/7*z**2 + 4/35*z**5 - 1/3*z**3 - 2*z - 7. Let x(a) = 0. What is a?
-4, -1, 1
Let h(w) be the second derivative of -w**8/3360 - w**7/1680 + w**6/360 - 5*w**3/6 - 2*w**2 + 33*w. Let v(k) be the second derivative of h(k). Solve v(y) = 0.
-2, 0, 1
Let g(c) = 40*c + 1924. Let d be g(-48). Let r(s) be the first derivative of -20*s - 55/3*s**3 + 30*s**2 + 15/4*s**d + 4. Factor r(y).
5*(y - 2)*(y - 1)*(3*y - 2)
Let j(g) = 13*g**5 - 19*g**4 - 17*g**3 + 345*g**2 - 775*g + 425. Let s(z) = -2*z**5 + 3*z**3 + z**2 + z + 1. Let t(u) = -j(u) - 7*s(u). Solve t(c) = 0 for c.
-18, -6, 1, 2
Let t(g) = 7*g**2 - 48*g - 108. Let w(v) = -v**2 + 9*v. Let a(j) = -t(j) - 8*w(j). Factor a(k).
(k - 18)*(k - 6)
Let l = -1037 - -1034. Let i be -1 - (10 + -13)*(-1)/l. Factor -12/17*x**3 + 2/17*x**4 + 18/17*x**2 - 8/17*x + i.
2*x*(x - 4)*(x - 1)**2/17
Let h(f) be the second derivative of -3/5*f**3 + 1/5*f**4 + 151*f + 0*f**2 - 1/50*f**5 + 0. Factor h(k).
-2*k*(k - 3)**2/5
Let j(p) be the first derivative of -p**6/6 - 13*p**5/5 - 21*p**4/4 + 85*p**3/3 - 25*p**2 - 153. Let j(l) = 0. What is l?
-10, -5, 0, 1
Find q, given that 1600/7*q - 2/7*q**4 - 1536/7 + 68/7*q**3 - 544/7*q**2 = 0.
2, 4, 24
Suppose 113*f - 229*f = -149*f + 132. Factor 1/3*s**5 - 3*s**3 + f - 5/3*s**4 + 28/3*s + 13/3*s**2.
(s - 6)*(s - 2)*(s + 1)**3/3
Let y be 49/(-2)*((-109)/(-55) + -2). Let s = y - 1/22. Factor 6/5 - s*n**2 + 4/5*n.
-2*(n - 3)*(n + 1)/5
Suppose -5*a + j - 55 + 74 = 0, 154 = -4*a - 18*j. Factor 7/4*s**a + 0 - 3/2*s.
s*(7*s - 6)/4
Let b be 13 + 108/(204/(-17)). Let k(q) be the second derivative of -29*q + 40/3*q**3 - 5/12*q**b - 160*q**2 + 0. Factor k(v).
-5*(v - 8)**2
Let l(y) be the second derivative of -y**5/5 + 104*y**4/3 - 998*y**3/3 + 792*y**2 - 132*y + 1. Factor l(u).
-4*(u - 99)*(u - 4)*(u - 1)
Find g, given that 576/5 + 4/5*g**2 - 296/5*g = 0.
2, 72
Let l(o) be the first derivative of o**5 + 425*o**4/4 - 295*o**3 - 1305*o**2/2 - 4611. Factor l(g).
5*g*(g - 3)*(g + 1)*(g + 87)
Let q = 82 - -550. Let g = -630 + q. Factor 2/5*h - 1/5*h**g + 0 - 1/5*h**3.
-h*(h - 1)*(h + 2)/5
Let x(k) = -k. Let j(p) = 2*p + 56*p**2 + p**3 - 51*p**2 - 3*p. Let r(q) = -j(q) - 5*x(q). Suppose r(u) = 0. Calculate u.
-6, 0, 1
Suppose -1163*n + 888 + 662 + 1392 = -1710. Factor 9 - 51/2*b + 3/2*b**5 + 0*b**3 + 21*b**2 - 6*b**n.
3*(b - 3)*(b - 1)**3*(b + 2)/2
Suppose 121*y - 7746 = 2055. Let t be (-93)/(-310) - (y/(-30) + 3). Factor -3/7*r - 3/7*r**2 + t.
-3*r*(r + 1)/7
Let g be (2296/(-112) + (-6)/(-4))/1. Let d be (-144)/96 - g/10. Factor -d*t**2 + 0 + 0*t.
-2*t**2/5
Let x(r) be the second derivative of r**5/100 - r**4/6 + 4*r**3/15 + 32*r**2/5 - 11*r - 28. Find g such that x(g) = 0.
-2, 4, 8
Find a such that 2/13*a**2 - 414/13 - 28/13*a = 0.
-9, 23
Factor 398*r**4 + 872439*r + 452022 - 4000*r**5 + 189471*r**2 + 78915*r**2 + 16614*r**3 + 168267 - 17*r**4 + 4003*r**5.
3*(r + 1)*(r + 3)*(r + 41)**3
Suppose 172 = 3*i + 154. Suppose i + 4*v + 12 - 12*v**2 - v**3 - 6 - 3*v**3 = 0. What is v?
-3, -1, 1
Let s(o) = -3*o**4 + 2*o**3 + o**2 + o + 1. Le