*y**6 - 3/10*y**5. Factor f(l).
2*(l - 2)**2*(l - 1)*(l + 2)
Let s(w) be the second derivative of -3*w**5/40 + 137*w**4/8 - 1120*w**3 - 11025*w**2 + 3172*w. Factor s(a).
-3*(a - 70)**2*(a + 3)/2
Suppose 0 = l - 1, -2*r + 0*l + 5 = 3*l. Let w be 72/(-27)*((-10)/4 + r). Let 177*o**w + 10*o**3 - 202*o**4 - 15*o**5 - 1 + 5*o - 4 + 30*o**2 = 0. What is o?
-1, 1/3, 1
Let w(v) be the second derivative of 1/45*v**6 - 1/30*v**5 + 1/9*v**3 + 0*v**2 + 2*v + 69 - 1/18*v**4. Factor w(b).
2*b*(b - 1)**2*(b + 1)/3
Let l(s) = 3*s**3 - 7*s**2 + 7*s + 4. Let x be l(4). Let g = -112 + x. Find f such that 0*f + g + 7/4*f**3 + 1/2*f**2 = 0.
-2/7, 0
Let i = 664274 + -4649917/7. Solve 6/7 + i*t**2 - 5/7*t = 0 for t.
2, 3
Let q = 420 + -417. Let d = 25723/4 - 6429. Factor 4*p + 3 + d*p**2 + 1/4*p**q.
(p + 2)**2*(p + 3)/4
Let c(y) = y**2 + 2. Let n(j) = 4*j**2 + 6168*j + 4755532. Let t(i) = 2*c(i) - n(i). Suppose t(z) = 0. What is z?
-1542
Let q be (-16)/(-9) - 4/(-18). Suppose 2*f = 0, -11 = -4*c - 4*f - 3. Factor -q*u**3 - 8*u**c - 16*u**5 - 2*u**2 + 7*u**3 + u**5 + 20*u**4.
-5*u**2*(u - 1)**2*(3*u + 2)
Solve -14/19*z**5 - 732/19*z**2 + 610/19*z**3 + 160/19*z + 0 - 24/19*z**4 = 0.
-8, 0, 2/7, 1, 5
Suppose -9*s = 30*s - 117. Factor 20*m + 733*m**4 + 3*m**2 - 8*m**3 + s*m**2 - 735*m**4 - 16.
-2*(m - 1)**2*(m + 2)*(m + 4)
Let d(p) be the first derivative of -p**5/5 + 59*p**4/4 - 838*p**3/3 - 510*p**2 + 1800*p + 1007. Factor d(q).
-(q - 30)**2*(q - 1)*(q + 2)
Factor -12*i + 12*i**3 + 3/2*i**4 - 3/2*i**2 + 0.
3*i*(i - 1)*(i + 1)*(i + 8)/2
Let p = -3264 - -3266. Let k(c) be the first derivative of 0*c + 3/8*c**4 - 2/5*c**5 + 11 + 0*c**p + 1/12*c**6 + 0*c**3. Let k(s) = 0. What is s?
0, 1, 3
Let c be (22/(-22))/((-1)/(-2)). Let h be 3/((-2)/4 - c). Factor 6*u + 0*u + 2*u - 2 + h*u**4 - 4*u**3 - 4*u.
2*(u - 1)**3*(u + 1)
Let h(a) be the second derivative of a**6/120 - 13*a**5/80 + 11*a**4/48 + 13*a**3/24 - 3*a**2/2 - 3*a - 212. Factor h(d).
(d - 12)*(d - 1)**2*(d + 1)/4
Factor 5*d**4 - 108*d**3 + 114*d**3 + 13*d**3 + 5*d - 29*d**2.
d*(d - 1)*(d + 5)*(5*d - 1)
Let i be -3 - -2 - (32/40 - 6). Let o = 4911 + -24456/5. Determine s, given that -147/5*s**3 + 27/5 + i*s**2 + o*s = 0.
-3/7, 1
Factor -6*c**2 + 126/5 - 159/5*c.
-3*(c + 6)*(10*c - 7)/5
Let i(r) = r**2 - 665*r - 12289. Let h be i(-18). Solve -6/5*k**2 + 0 + 6/5*k**4 + 14/5*k**3 - 4/5*k - 2*k**h = 0 for k.
-1, -2/5, 0, 1
Suppose -37*h + 85 = 85. Let s(c) be the first derivative of 3/20*c**4 - 8 + 3/10*c**2 - 2/5*c**3 + h*c. Factor s(b).
3*b*(b - 1)**2/5
Let a be (-69)/(-1012)*550/36. Let o(l) be the second derivative of -5/24*l**4 + 0 + a*l**3 + 1/80*l**5 - 27*l + 0*l**2. Let o(z) = 0. What is z?
0, 5
Let g(p) be the third derivative of -p**5/240 - 11*p**4/12 - 242*p**3/3 + 65*p**2 + 3. Factor g(s).
-(s + 44)**2/4
Suppose 3*n + 5*b = 485 + 1160, 3*n + 3*b = 1647. Let i be 2/11 + 1000/n. Suppose 2/7*c**i + 1/7*c**3 + 1/7*c + 0 = 0. Calculate c.
-1, 0
Let v(f) be the first derivative of -3*f**5 - 141*f**4/4 + 242*f**3 + 156*f**2 + 54. Find a, given that v(a) = 0.
-13, -2/5, 0, 4
Determine w so that -119*w - 36*w - 89*w - 98*w**2 - 59*w + 48 - 77*w = 0.
-4, 6/49
Let s(c) be the second derivative of 0*c**2 + 1 + 4/9*c**3 - 44*c - 2/45*c**5 - 2/135*c**6 + 5/27*c**4. What is a in s(a) = 0?
-3, -1, 0, 2
Let n(h) = -4*h**2 + 14*h - 8. Let j(v) = -v + 2. Suppose -2*a - 5*w = -8, -3*w = -3*a + w - 11. Let i(x) = a*n(x) + 2*j(x). Factor i(p).
4*(p - 3)*(p - 1)
Let y be (((-28)/147)/(10/(-27)))/((-117)/(-546)). Let l(d) be the first derivative of 1/5*d**3 + y*d + 16 + 6/5*d**2. Let l(r) = 0. Calculate r.
-2
Let j(c) = 3184*c + 127360. Let x be j(-40). Factor 12/11*i + 1/11*i**3 + 8/11*i**2 + x.
i*(i + 2)*(i + 6)/11
Factor -3/2*t**4 + 108*t - 24*t**3 + 0 - 165/2*t**2.
-3*t*(t - 1)*(t + 8)*(t + 9)/2
Suppose -3028 - 905 = -1311*c. Find n, given that 15/7*n**c - 3/7*n**4 - 9/7*n**2 + 0 - 3/7*n**5 + 0*n = 0.
-3, 0, 1
Let u be (-6)/135 + 139594/34515. Factor -6/5*z**3 - 2/5*z**u + 0 + 8/5*z**2 + 0*z.
-2*z**2*(z - 1)*(z + 4)/5
Let o(s) be the second derivative of s**5/16 - 665*s**4/48 + 655*s**3/12 + 1195*s. Suppose o(a) = 0. What is a?
0, 2, 131
Let q = 39663/20 + -1983. Let b(f) be the third derivative of -42*f**2 + 0 - q*f**4 + 8/15*f**3 + 0*f + 1/150*f**5. Solve b(s) = 0 for s.
1, 8
Let y(c) = -2*c**3 + 56*c**2 - 36*c - 15. Let s(r) = r**3 - 2*r**2 - 5*r + 5. Let z(w) = -3*s(w) - y(w). Factor z(l).
-l*(l - 1)*(l + 51)
Let k(x) be the third derivative of 1/150*x**5 - 45*x**2 + 0*x + 0 - 7/30*x**4 + 49/15*x**3. Find u such that k(u) = 0.
7
Let x be (-9)/189*((-3 + 1 - 336) + 1385/277). Factor 1/7*i**3 + 50653/7 + x*i**2 + 4107/7*i.
(i + 37)**3/7
Suppose 5*f = 101 - 1. Factor 42 + f*n**2 + 33 - 30*n**4 + 25*n**4 + 70*n**2 + 160*n.
-5*(n - 5)*(n + 1)**2*(n + 3)
Let g(q) be the first derivative of q**6/24 + 13*q**5/12 - 5*q**4/24 - 65*q**3/6 - 141*q**2/2 - 207. Let r(l) be the second derivative of g(l). Factor r(z).
5*(z - 1)*(z + 1)*(z + 13)
Let v(l) = 2*l**2 + 22*l + 2. Let o(s) = -7*s - 221. Let g be o(-30). Let d be v(g). Factor -3/4*p**d + p - 1/4.
-(p - 1)*(3*p - 1)/4
Let b(u) = -6*u**2 - 54*u - 25. Let g(v) = 6*v**2 + 54*v + 24. Let k(w) = -3*b(w) - 2*g(w). Let t(c) = -c - 1. Let o(i) = k(i) + 3*t(i). Factor o(q).
3*(q + 8)*(2*q + 1)
Let p = 3669 + -3669. Let s(u) be the second derivative of 26*u**3 - 7*u + 5/2*u**6 - 31/4*u**4 + p - 21/2*u**5 - 18*u**2. Suppose s(c) = 0. Calculate c.
-1, 2/5, 3
Let p(h) be the third derivative of h**7/630 + h**6/90 + h**4/8 + 4*h**3 - 42*h**2. Let u(g) be the second derivative of p(g). Determine o so that u(o) = 0.
-2, 0
Let a be ((-12)/50*225/(-180))/3. Let o(g) be the second derivative of 77/120*g**6 + 0 - 1/12*g**4 + 0*g**3 + 18*g + 0*g**2 - a*g**5. Solve o(n) = 0.
-2/11, 0, 2/7
Suppose 3*o - 3 = 0, -4*o - 5 = -g - 7. Suppose -37*d + g*d + 70 = 0. Determine q so that 4/5*q + d*q**2 + 0 = 0.
-2/5, 0
Let f(d) = -d**3 - 3*d**2 - 7*d - 18. Let u be f(-3). Determine z, given that -15*z**2 + 10*z**u + 5*z**3 - 3*z**3 = 0.
0, 5/4
Let g(a) be the second derivative of a**6/240 - 13*a**5/160 + 92*a - 26. What is p in g(p) = 0?
0, 13
Let j(u) = -u - 1. Let a be 2 - (9 - (4 - 2)). Let i be j(a). Determine f, given that -43*f**3 - 4*f**2 + 49*f**3 + f**4 - 3*f**i = 0.
0, 1, 2
Factor -3/7*u**3 + 48 - 30/7*u**2 + 309/7*u.
-3*(u - 7)*(u + 1)*(u + 16)/7
Let g(k) be the first derivative of k**8/2800 + 9*k**7/1400 + k**6/40 - k**5/8 + 31*k**3/3 - 40. Let d(r) be the third derivative of g(r). Solve d(v) = 0 for v.
-5, 0, 1
Let s(r) be the first derivative of r**3/7 - 81*r**2/14 - 480*r/7 - 1418. Factor s(h).
3*(h - 32)*(h + 5)/7
Let l(x) be the third derivative of -x**5/30 - 103*x**4/12 + 218*x**3 + 11377*x**2. Factor l(n).
-2*(n - 6)*(n + 109)
Suppose 0 = -z - 4*d + 71, -2*z + 28 = -d - 150. Suppose -179*l + 128*l - 162 + z*l - 2*l**2 = 0. What is l?
9
Let x(r) be the first derivative of -r**5 - 175*r**4/4 + 5*r**3 + 515*r**2/2 - 350*r + 5403. Find n such that x(n) = 0.
-35, -2, 1
Let v(c) = -c**2 - 46*c + 389. Let w(l) = l**2 + 66*l - 388. Let k(m) = 3*v(m) + 2*w(m). Find g, given that k(g) = 0.
-23, 17
Suppose 5*k = 4*x - 3 - 134, 2*x = 3*k + 69. Factor -1 + 5*m**4 - x*m**3 - 92*m**3 + 1 + 35*m**2 - 720*m + 805*m**2.
5*m*(m - 12)**2*(m - 1)
Let d = -13798 - -13802. Let g(z) be the third derivative of -1/4*z**3 + 1/16*z**d + 1/40*z**5 + 0*z - 18*z**2 - 1/80*z**6 + 0. Factor g(u).
-3*(u - 1)**2*(u + 1)/2
Suppose 0 = 13*x - 26 - 13. Factor -4*k + x*k**3 - 2*k**2 + k**2 + 3 - 2*k**2 + k.
3*(k - 1)**2*(k + 1)
Let b = -1024 + 1028. Let h(t) be the third derivative of -1/6*t**3 + 14*t**2 - 11/72*t**b + 0*t + 1/120*t**6 + 0 - 1/36*t**5. Let h(y) = 0. What is y?
-1, -1/3, 3
Let o = -73 - -65. Let m(l) = -15*l - 118. Let w be m(o). Find g, given that -32/11*g**w - 2/11 + 16/11*g = 0.
1/4
Let h(w) be the third derivative of -29/48*w**4 + 5*w**2 + 8/3*w**3 - 1/40*w**5 + 3 + 0*w. Let h(j) = 0. What is j?
-32/3, 1
Let h(v) = -2*v**2 + v - 1. Let y(r) = 27*r + 2*r**3 - 9*r**3 - 33*r**2 - 9 - 2*r**3 + 12*r**3. Let t(z) = 9*h(z) - y(z). What is s in t(s) = 0?
0, 2, 3
Let y(a) be the first derivative of -11 - 3/2*a + 4*a**2 - 13/6*a**3. Let y(s) = 0. What is s?
3/13, 1
Let t(v) = -19*v**5 - 16*v**4 - 48*v**3 - 8. Let z(w) = 