e n(-6). Suppose m*l + 1/5*l**s - 1/5 = 0. What is l?
-1, 1
Factor -2*w**4 - 1082*w**2 - 257*w + 388*w**2 + 19*w - 332*w - 126*w**3.
-2*w*(w + 1)*(w + 5)*(w + 57)
Let c(b) be the first derivative of -b**6/6 + 27*b**5/5 + 15*b**4/2 - 56*b**3/3 + 1080. Solve c(k) = 0 for k.
-2, 0, 1, 28
Let j(w) be the second derivative of 0*w**2 - 91*w - 1/14*w**7 + 1/2*w**6 + 0 + 3*w**3 - 3/4*w**5 - 5/4*w**4. What is u in j(u) = 0?
-1, 0, 1, 2, 3
Let g be (0 - 3) + 0/(-2). Let n(h) = h**2 + 4*h + 5. Let a be n(g). Determine c so that 4*c**4 - a*c**4 + 2*c**4 - 4*c**2 = 0.
-1, 0, 1
Let x = -174 - 161. Let b be (x/35 - -9)/((-2)/7). Factor 0 - 4/7*z**b - 2/7*z**5 + 0*z**3 + 2/7*z + 4/7*z**4.
-2*z*(z - 1)**3*(z + 1)/7
Let q(j) be the second derivative of j**7/6720 - j**6/320 + 13*j**5/480 - j**4/8 + 13*j**3/3 - j. Let u(v) be the second derivative of q(v). Factor u(s).
(s - 4)*(s - 3)*(s - 2)/8
Let l(x) be the third derivative of x**7/2100 + x**6/48 + 47*x**5/600 + 23*x**4/240 + 9256*x**2. Suppose l(t) = 0. What is t?
-23, -1, 0
Suppose -3/5*b**4 + 216/5*b**2 + 192/5 + 372/5*b + 33/5*b**3 = 0. Calculate b.
-2, -1, 16
Let -16/3*j**3 - 64/3 + 32/3*j - 4/3*j**4 + 32/3*j**2 + 2/3*j**5 = 0. What is j?
-2, 2
Let h(k) be the second derivative of -3/7*k**3 + 2*k - 2*k**2 - 8 - 1/42*k**4. Factor h(g).
-2*(g + 2)*(g + 7)/7
Let d = -36 + 31. Let l(w) = 3*w**2 + 5*w - 5. Let r be l(d). Factor 11*q**3 - 10 - 64*q**2 - 36*q**3 - r*q + 4*q**2.
-5*(q + 1)**2*(5*q + 2)
Solve p**2 - 509 + 427 + 434*p - 2*p**2 - 351 = 0 for p.
1, 433
Let c be (7/(-2))/(245/(-210)). Let d(u) be the third derivative of 1/8*u**4 + 1/3*u**c + 0*u + 29*u**2 - 1/12*u**5 + 0. Factor d(n).
-(n - 1)*(5*n + 2)
Factor -390*h + h**2 + 495 + 210*h + 2*h**2 + 2*h**2.
5*(h - 33)*(h - 3)
Suppose -49*q - 88 = -4*g - 54*q, g - 146 = -9*q. Factor -12/5 + 14/5*s - 2/5*s**g.
-2*(s - 6)*(s - 1)/5
Suppose 5*f + 2988 = 11*f. Let 13*o + f*o**2 - 2 - 9*o - 500*o**2 = 0. What is o?
1
Let z(i) be the first derivative of i**5/20 + 11*i**4/4 - i**3/12 - 11*i**2/2 + 2335. Factor z(m).
m*(m - 1)*(m + 1)*(m + 44)/4
Find b, given that 0 + 2*b**5 - 108*b**3 + 192/7*b + 102/7*b**4 + 64*b**2 = 0.
-12, -2/7, 0, 1, 4
Suppose 3*j + 562 - 1885 = 0. Let q be ((-18)/(-44))/(3 - j/168). Factor 2/11*o**2 - q*o + 16/11.
2*(o - 4)*(o - 2)/11
Let t = -32129/14 + 2295. Let s(i) be the second derivative of 0*i**2 + 7/60*i**5 + 0*i**3 + 0 + t*i**7 + 1/6*i**6 + 1/36*i**4 + 9*i. Factor s(o).
o**2*(o + 1)*(3*o + 1)**2/3
Let a(v) be the second derivative of -v**5/20 + 59*v**4/12 - 212*v**3/3 + 408*v**2 - 4033*v. Factor a(p).
-(p - 51)*(p - 4)**2
Let s be (184 - 166)*50/99. Factor -2/11*t**4 + s*t**3 + 8092/11*t - 1632/11*t**2 + 9826/11.
-2*(t - 17)**3*(t + 1)/11
Let w(i) = -7*i**2 + 15*i + 10. Let y(q) = -15*q**2 + 30*q + 19. Let u be 7 + (-1)/2*26. Let f(l) = u*y(l) + 13*w(l). Factor f(t).
-(t - 16)*(t + 1)
Let k = -851 + 656. Let n be 20/(-260) + (-1731)/k. Find l, given that -2/5*l**5 + 6/5 + n*l**2 - 26/5*l + 14/5*l**4 - 36/5*l**3 = 0.
1, 3
Suppose 27380 - 14012 - 15216 - 3*a**2 + 255*a = 0. What is a?
8, 77
Let g be 94/170 + 2/(-10). Let v = 817/102 + -781/102. Suppose v*q**2 - 4/17 + g*q - 4/17*q**3 = 0. What is q?
-1, 1/2, 2
Let z = -219 + 223. Let a = -1 + 23. Factor 22 + 10*u**z + 4*u - a - u**3 - 3*u**3 - 10*u**2.
2*u*(u - 1)*(u + 1)*(5*u - 2)
Let r(f) be the first derivative of -2/7*f**2 + 2/21*f**3 - 6/7*f + 4. Solve r(s) = 0.
-1, 3
Suppose 0 = -21*y + 27 + 57. Factor 4*j**5 + 4 - 26*j**2 + 20*j**y + 12*j**3 + 2 - 16*j + 6*j**2 - 6.
4*j*(j - 1)*(j + 1)**2*(j + 4)
Let u(z) = z**2 + 3*z. Let h(q) = -q**2 + 103*q - 192. Let i(c) = 2*h(c) - 2*u(c). Solve i(v) = 0.
2, 48
Let r(s) be the second derivative of -s**4/78 + 3*s**3/13 + 4*s**2 + 824*s. Factor r(m).
-2*(m - 13)*(m + 4)/13
Let n(u) be the first derivative of u**6/60 - u**5/16 + u**4/12 - u**3/24 + 264*u + 103. Let h(d) be the first derivative of n(d). Find f such that h(f) = 0.
0, 1/2, 1
Let l(o) = -o + 98. Let b be l(26). Factor -93*n + n**2 + 22 + 142*n - b*n.
(n - 22)*(n - 1)
Suppose 25/4*h**2 + 85*h - 195 = 0. What is h?
-78/5, 2
Let b = -1605804 - -24087076/15. Factor -b*z**2 + 14/15*z + 2.
-2*(z + 1)*(8*z - 15)/15
Let -1/11*h**4 - 61/11*h**2 - 3*h + 3*h**3 + 62/11 = 0. What is h?
-1, 1, 2, 31
Let m(k) = -7*k**2 + 91*k + 855. Let w(l) = 11*l**2 - 136*l - 1368. Let q(i) = 8*m(i) + 5*w(i). Factor q(x).
-x*(x - 48)
Let u(a) be the second derivative of -50/3*a**2 + 4*a + 11/6*a**5 - 130/9*a**3 - 7/6*a**6 + 7 + 355/36*a**4. Suppose u(r) = 0. Calculate r.
-5/3, -2/7, 1, 2
Let 12/7*z**4 - 274/7*z - 16/7*z**3 - 120/7 + 2/7*z**5 - 180/7*z**2 = 0. What is z?
-5, -3, -1, 4
Solve 2/5*f**2 - 874/5*f - 876/5 = 0.
-1, 438
Let t(f) be the second derivative of 0*f**2 + 1/40*f**6 - 20 + 9/8*f**5 + 0*f**3 + 225/16*f**4 - 3*f. Factor t(b).
3*b**2*(b + 15)**2/4
Let n = -13 - -15. Let t(p) = 3*p**2 - 1. Let v be t(-1). Factor -3*z**2 + 4 + 0*z**v + 4*z**2 - 3*z**n + 2*z.
-2*(z - 2)*(z + 1)
Factor 9*v - 9*v - 5367*v**2 + 5370*v**2.
3*v**2
Let y(p) be the second derivative of 10/3*p**4 - 125*p**2 - 2 + 10*p - 1/4*p**5 - 25/6*p**3. Determine m so that y(m) = 0.
-2, 5
Suppose p - 91 = -3*p - 91. Let m(c) be the third derivative of p + 26*c**2 + 0*c**3 + 2/5*c**6 + 1/3*c**4 + 0*c - 2/21*c**7 - 3/5*c**5. Factor m(t).
-4*t*(t - 1)**2*(5*t - 2)
Let c(h) be the third derivative of -h**5/150 + h**4/20 + 2*h**3/3 - 1672*h**2. Find d, given that c(d) = 0.
-2, 5
Suppose 62*p - 65*p + 87 = 0. Suppose 0 = -4*f + 217 - p. Factor f*g - 97 + 23*g + 5*g**2 + 342.
5*(g + 7)**2
Let g(p) = 177*p**2 + 4570*p - 1737363. Let o(j) = 45*j**2 + j. Let y(w) = -g(w) + 4*o(w). Suppose y(k) = 0. What is k?
761
Let g(l) be the first derivative of l**4/10 + 44*l**3/15 + 79*l**2/5 - 204*l/5 - 1173. Let g(q) = 0. Calculate q.
-17, -6, 1
Let t be (-2 + 146/70)*(980/(-42))/(-7). Factor t*w**2 + 4*w + 14.
2*(w + 7)**2/7
Let b = 19/24904 - -12433/24904. Suppose -5*d + 4*s + 3 = -4, 4*d + s - 14 = 0. Factor -9/2*k + 2 + 3*k**2 - b*k**d.
-(k - 4)*(k - 1)**2/2
Suppose -6*p = 15 - 45. Factor 3*u - 2*u**5 - 8*u**3 + 3*u**5 + 2*u**p + 2*u**3.
3*u*(u - 1)**2*(u + 1)**2
Let y(s) be the first derivative of 5*s**3/3 + 135*s**2/2 + 630*s + 2392. Factor y(o).
5*(o + 6)*(o + 21)
Let w = -228 + 240. Let m be (-1)/3 - (76/w + -8). Factor -26/3*s - m*s**3 + 5/3 + 25/3*s**2.
-(s - 5)*(s - 1)*(4*s - 1)/3
Let n(j) be the second derivative of 54*j - 140/3*j**3 - 245/12*j**4 + 0 - 40*j**2. Factor n(a).
-5*(7*a + 4)**2
Let s(y) be the first derivative of -y**7/210 - 2*y**6/15 - 6*y**5/5 - 16*y**4/3 + 158*y**3/3 + 47. Let d(f) be the third derivative of s(f). Factor d(m).
-4*(m + 2)**2*(m + 8)
Let g(n) = -n**4 + 4*n**3 - 27*n**2 + 28*n - 10. Let u(c) = c**4 - 28220 + 28220 + c**2. Let v(h) = -g(h) - 3*u(h). Suppose v(j) = 0. What is j?
-5, 1
Factor -33 - 1/4*x**2 - 133/4*x.
-(x + 1)*(x + 132)/4
Let 567/2*i + 1131/4*i**2 + 0 - 3/4*i**3 = 0. What is i?
-1, 0, 378
Let i = 120367/80250 - -4/40125. Determine r, given that 2 - 1/2*r**4 + 2*r**3 - i*r**2 - 2*r = 0.
-1, 1, 2
Find o, given that 6*o + 9/2*o**4 + 0 + 3/2*o**5 - 9/2*o**2 - 15/2*o**3 = 0.
-4, -1, 0, 1
Let c be 5 + (230/(-120) - 3) + (-10)/(-15). Suppose -c*n**5 + 0 - 18*n**3 + 6*n**4 - 12*n + 24*n**2 = 0. Calculate n.
0, 2
Let a(i) be the second derivative of i**5/10 - 27*i**4/2 + 104*i**3 - 308*i**2 - 31*i + 11. Factor a(b).
2*(b - 77)*(b - 2)**2
Let n be 4/141*(-189)/(-336). Let h = 331/2820 + n. Find g, given that -h*g + 0 + 8/15*g**2 = 0.
0, 1/4
Let n be ((-39)/(-12))/((2 + 2)/160). Factor 8*m + 130 + 2*m**2 - n.
2*m*(m + 4)
Let p(a) = -2*a**3 + 351*a**2 + 1990*a + 183. Let r be p(181). Factor -6/5*u + 4/5*u**r + 2/5 + 4/5*u**3 - 6/5*u**4 + 2/5*u**5.
2*(u - 1)**4*(u + 1)/5
Let c(m) be the second derivative of -m**6/150 - 54*m**5/5 - 4860*m**4 - 2*m + 1898. Solve c(f) = 0 for f.
-540, 0
Let x be (2/(-6))/((-8)/48). Solve -2*i**5 - 40*i - 8*i**4 + x*i**3 + 16 + 45*i**2 - 17*i**2 + 4*i**5 = 0 for i.
-2, 1, 2
Factor 1660 + 133*f**2 - 3048*f - 98*f**2 - 2772*f.
5*(f - 166)*(7*f - 2)
Let a be ((-86)/(-18))/1 - (-1030)/4635. Let r(l) be the second derivative of -2*l**3 + 28*l + a*l**2 + 0 + 1/6*l**4. Solve r(b) = 0.
1, 5
Let r(h) be the second derivative of -5*h**4/12 + 55*h**3 - 31*h - 7. Find q, given that r