0*a + 1/168*a**6 + 0. Find f, given that i(f) = 0.
-1, 2/5
Let y(d) be the first derivative of 50/3*d**3 + 24 + d - 5/12*d**4 - 250*d**2. Let l(g) be the first derivative of y(g). Factor l(a).
-5*(a - 10)**2
Let t(k) be the first derivative of k**3 + 177*k**2 + 10443*k + 1099. Find o, given that t(o) = 0.
-59
Determine a, given that -745*a**2 - 5940*a - 605 - 21600*a**3 - 2518*a**2 - 1620*a**2 - 8000*a**4 - 14097*a**2 = 0.
-11/10, -1/4
Let c(k) be the first derivative of -21/2*k**2 - 36*k - 1/2*k**3 + 109. Factor c(l).
-3*(l + 2)*(l + 12)/2
Let p(k) be the third derivative of -1/42*k**4 - 55*k**2 + 0 + 0*k**3 + 0*k + 1/84*k**5 - 1/840*k**6. Factor p(r).
-r*(r - 4)*(r - 1)/7
Let l(u) = -7*u - 82. Let t be l(-12). Factor -34*x + 1429*x**t - 2*x - 1433*x**2.
-4*x*(x + 9)
Let h = -4 + 4. Let f be h + 0 - (23 + -25). Factor 5*t**2 - 7 - 5*t - 5 + f.
5*(t - 2)*(t + 1)
Let f = -159677 - -159681. Suppose f*p**2 - 8 + 10/3*p + 2/3*p**3 = 0. Calculate p.
-4, -3, 1
Let w(g) be the first derivative of -g**4/2 + 52*g**3/27 - 5*g**2/3 - 4*g/9 - 284. Find x, given that w(x) = 0.
-1/9, 1, 2
Let n = 513 + -58. Let h = n + -450. Suppose 0 + 4/5*j**h - 16/5*j**2 + 24/5*j**3 - 16/5*j**4 + 4/5*j = 0. What is j?
0, 1
Let m(x) be the second derivative of -1/4*x**5 + 7 - 5/3*x**4 + 5/2*x**3 + 45*x**2 + x. Factor m(w).
-5*(w - 2)*(w + 3)**2
Let -4/9*m**2 + 0 + 340/9*m = 0. Calculate m.
0, 85
Let n(d) = 3*d**4 - 114*d**3 - 636*d**2 - 554*d + 14. Let l(j) = 2*j**4 - 112*j**3 - 636*j**2 - 552*j + 12. Let r(k) = -7*l(k) + 6*n(k). Factor r(h).
4*h*(h + 1)*(h + 9)*(h + 15)
Let i = 2363/2065 - 169/295. What is g in 0 - 4/7*g + 0*g**2 + i*g**3 = 0?
-1, 0, 1
Let v = 7442/35 - 4838/35. Solve -498/5*j**2 + v*j - 72/5 + 3*j**3 + 15*j**4 = 0 for j.
-3, 2/5, 2
Let u(n) be the first derivative of -61 - 158/3*n**3 + 67/2*n**2 - 72/5*n**5 + 3/2*n**6 + 41*n**4 - 10*n. Let u(x) = 0. What is x?
1/3, 2/3, 1, 5
Let t be -2*((-6)/11 + 527/1309). Suppose 4/7 - 2/7*c**2 - t*c = 0. Calculate c.
-2, 1
Let c(r) be the second derivative of 18*r - 7/4*r**3 + 11/2*r**2 + 2 + 1/160*r**5 + 3/16*r**4. Determine x, given that c(x) = 0.
-22, 2
Suppose 4*n + 4*y - 52 = 0, -58*y + 55*y + 21 = -3*n. Solve 30/7*x - 9/7*x**2 - n = 0.
1, 7/3
Suppose 0 = -11*c + 53 + 2. Let 3*r**2 + 6*r + r**2 - 7*r - 2*r**4 - 2 + 0*r**4 - r**c + 2*r**3 = 0. What is r?
-2, -1, 1
Let n(a) = -20*a**3 + 915*a**2 + 3660*a + 3690. Let z(v) = -17*v**3 + 912*v**2 + 3660*v + 3688. Let x(o) = -4*n(o) + 5*z(o). Factor x(q).
-5*(q - 184)*(q + 2)**2
Factor 320*x + 369*x**2 + 324 + 375*x**2 - 1126*x**2 + 378*x**2.
-4*(x - 81)*(x + 1)
Suppose 1/3*x**3 - 16/3*x + 1/3*x**2 + 20/3 = 0. What is x?
-5, 2
Suppose s = -5*i, -7*i - s = -8*i + 12. Factor -2*j + 1/3*j**i + 5/3.
(j - 5)*(j - 1)/3
Let o(w) be the second derivative of 7/4*w**3 + 25/48*w**4 + 1/20*w**5 - 2 + 27*w + 9/8*w**2. Factor o(l).
(l + 3)**2*(4*l + 1)/4
Suppose 8*k**3 - 5126*k**2 - 5*k**3 - 783 + 4877*k**2 - 1035*k = 0. Calculate k.
-3, -1, 87
Let -2/7*f**5 - 8/7*f + 10/7*f**3 - 6/7*f**4 + 30/7*f**2 - 24/7 = 0. What is f?
-3, -2, -1, 1, 2
Suppose -4*j - 4 + 114 = 2*l, -l = -j + 35. Solve -29*w**3 - j*w**4 + 2*w**5 - 295 - 8*w**3 + 5*w**3 + 295 = 0.
-1, 0, 16
Let v(g) be the first derivative of g**6/120 + 3*g**5/80 + g**4/24 + 59*g + 23. Let y(c) be the first derivative of v(c). Factor y(p).
p**2*(p + 1)*(p + 2)/4
Let b(t) be the second derivative of t**3 + 4 + 2*t**2 + 11*t + 1/6*t**4. Factor b(r).
2*(r + 1)*(r + 2)
Let k(j) be the first derivative of 0*j + 1/6*j**6 + 171 - 5/6*j**3 + 0*j**4 + 1/2*j**5 - 1/2*j**2. Let k(v) = 0. Calculate v.
-2, -1, -1/2, 0, 1
Let h be (-25)/20*(-48096)/8350. Suppose -h*y - 2/5*y**2 - 162/5 = 0. What is y?
-9
Let k(g) be the first derivative of 10*g**6/9 + 116*g**5/15 + 15*g**4 - 20*g**3/9 - 100*g**2/3 - 32*g + 2849. Find q, given that k(q) = 0.
-3, -2, -1, -4/5, 1
Let o(k) be the first derivative of -24*k**2 - 5 + 4/3*k**3 + 80*k. Factor o(x).
4*(x - 10)*(x - 2)
Let g(n) = 3*n**2 - 3184*n + 849048. Let x(a) = a**2 - 1061*a + 283015. Let o(q) = 3*g(q) - 8*x(q). Factor o(m).
(m - 532)**2
Let v(g) be the first derivative of -64 - 6/7*g**2 - 3/14*g**4 + 11/7*g**3 - 15/7*g. Find o, given that v(o) = 0.
-1/2, 1, 5
Determine p so that 105/2*p - 5/4*p**2 + 110 = 0.
-2, 44
Factor 3993971 + 3330840 + 11004*i + 3*i**2 + 2765857.
3*(i + 1834)**2
Let y be (25 - 24)/((9/6 + -2)*166/(-249)). Find q, given that 1/6*q**3 - 100/3 + y*q**2 + 10*q = 0.
-10, 2
Let q be (4/(160/(-45)))/((-18)/(-96)*-4). Factor 3/2*g + q + 3/8*g**2.
3*(g + 2)**2/8
Let f(q) be the second derivative of q**6/120 + 3*q**5/160 - 11*q**4/32 + 13*q**3/48 + 15*q**2/16 + 3206*q. Solve f(t) = 0.
-5, -1/2, 1, 3
Let x be 3808/2720 - ((-4)/10)/(2/3). Let 0 + 1/6*j**3 - j**x + 3/2*j = 0. Calculate j.
0, 3
Let h(p) be the first derivative of -3/7*p**4 - p**2 - 1/35*p**5 + 75 + 1/21*p**6 + 22/21*p**3 + 3/7*p. Factor h(c).
(c - 1)**3*(c + 3)*(2*c - 1)/7
Let s(z) = -13*z**2 + 108*z - 1287. Let x(f) = 7*f**2 - 52*f + 643. Let w(r) = -5*s(r) - 9*x(r). Factor w(u).
2*(u - 18)**2
Let g(n) be the second derivative of 7*n**5 + 2/21*n**7 + 49/3*n**4 - 26/15*n**6 - 6*n + 0*n**2 + 1 + 0*n**3. Factor g(o).
4*o**2*(o - 7)**2*(o + 1)
Let x(y) be the first derivative of -7/12*y**3 - 3/8*y**2 + 19 + 0*y - 5/16*y**4 - 1/20*y**5. Factor x(g).
-g*(g + 1)**2*(g + 3)/4
Find h, given that 0*h**3 - 93/4*h**4 + 0*h**2 + 0 + 3/4*h**5 + 0*h = 0.
0, 31
Suppose -93*n - 119*n + 2*n**2 - 96 - 345 - 105 + 114 = 0. What is n?
-2, 108
Let i = 1104607/1472820 + 2/368205. Factor -i*n**3 + 0*n + 1/4*n**5 + 0*n**4 + 0 - 1/2*n**2.
n**2*(n - 2)*(n + 1)**2/4
Let n be (2/(-4))/(2 - 52/24). Suppose -4*r - r = -5*g - 85, -13 = -r + n*g. Determine c so that -r*c + 2*c**2 + 11*c + 12*c - 6*c**2 = 0.
0, 1
Determine h, given that 26/5*h**3 + 8/5 - 128/5*h**2 + 94/5*h = 0.
-1/13, 1, 4
Let s(c) be the second derivative of -c**4/21 - 1312*c**3/21 - 215168*c**2/7 + 1390*c. What is l in s(l) = 0?
-328
Let o be 17 - 56*24/(-96). Let t(p) be the third derivative of o*p**2 + 0*p + 0*p**3 + 1/2520*p**8 + 1/525*p**7 + 0 + 0*p**6 + 0*p**4 - 2/225*p**5. Factor t(c).
2*c**2*(c - 1)*(c + 2)**2/15
Let m = 55 + -47. Suppose 0 = -3*r - r + m. Factor 3*a**2 + 2*a**3 + 4 + 3*a**r - a**2 - 8*a - 3*a**3.
-(a - 2)**2*(a - 1)
Let -6352*m + 12*m**2 + 1367395 + 507215 + 647134 - 4*m**2 - 4*m**2 = 0. Calculate m.
794
Solve -273/4*k - 3/8*k**2 - 24843/8 = 0 for k.
-91
Solve 57209*l**3 + 166 - 57203*l**3 + 544*l + 118*l**2 + 146 = 0.
-13, -6, -2/3
Let r(g) be the second derivative of g**6/840 - g**5/420 + 89*g**2/2 + 14*g + 2. Let s(q) be the first derivative of r(q). Factor s(m).
m**2*(m - 1)/7
Let j(u) be the third derivative of -u**6/240 + 73*u**5/30 + 587*u**4/48 + 49*u**3/2 - 5835*u**2. Factor j(d).
-(d - 294)*(d + 1)**2/2
Let s = 864 - 727. Factor -96*z**2 - 30*z**3 + 27*z + 14*z - 3*z**4 - s*z.
-3*z*(z + 2)*(z + 4)**2
Let u = 70328/1905 + -4570/127. Suppose -8/15 + 0*g + 2/15*g**5 - 2/15*g**3 + u*g**2 - 2/5*g**4 = 0. What is g?
-1, 1, 2
Factor -70530*i**2 - 6*i**3 + 70582*i**2 - 8*i - 29*i + 5*i.
-2*i*(i - 8)*(3*i - 2)
Let g(c) be the first derivative of c**6/8 - 21*c**5/10 + 39*c**4/16 + 1226. What is y in g(y) = 0?
0, 1, 13
Let r(a) be the third derivative of a**6/60 - 509*a**5/10 + 259081*a**4/4 - 131872229*a**3/3 - 5630*a**2. Suppose r(y) = 0. What is y?
509
Let m = 2483006/9 - 275866. Factor 2/9*f**2 - m*f + 5618/9.
2*(f - 53)**2/9
Let s(b) be the third derivative of -b**6/300 + 31*b**5/50 + 39*b**4/4 + 297*b**3/5 + 113*b**2 - 1. Factor s(z).
-2*(z - 99)*(z + 3)**2/5
Let s be 8/2 - 9/(702/696). Let i = s - -346/65. What is v in 0 + 4/5*v**3 - 1/5*v**4 + i*v - v**2 = 0?
0, 1, 2
Let t(b) be the second derivative of -b**5/10 + 5*b**4/2 + b**3/3 - 15*b**2 + 2355*b. Factor t(o).
-2*(o - 15)*(o - 1)*(o + 1)
Suppose 4*l = 32 - 24. Factor 2*x + 12*x**l - 2*x - 170*x**5 + 8*x**3 - 10*x + 172*x**5 - 12*x**4.
2*x*(x - 5)*(x - 1)**2*(x + 1)
Let i(z) be the first derivative of -2*z**6/3 + 28*z**5/5 - 11*z**4 + 20*z**3/3 + 34. Suppose i(p) = 0. What is p?
0, 1, 5
Let m(i) be the first derivative of 2*i**3/39 + 4*i**2 + 200*i/13 + 13623. Factor m(a).
2*(a + 2)*(a + 50)/13
Let g be ((-4)/38)/(-1) + 216/114. Find y, given that y**g + 17*y - 18*y - 16*y = 0.
0, 17
Let m be 30 