*2 - 10814*h. Suppose q(l) = 0. Calculate l.
-6, -3, 4
Let a(z) be the first derivative of -z**6/40 + 2*z**5/5 - 2*z**4 - 16*z**2 + 19. Let n(b) be the second derivative of a(b). Factor n(h).
-3*h*(h - 4)**2
Let d = 8 - -202. Let t = d + -210. Suppose -5/6*m**5 + t*m**4 + 5/2*m**3 + 0*m - 5/3*m**2 + 0 = 0. What is m?
-2, 0, 1
Let i(j) be the first derivative of 2*j**6 - 459*j**5 + 108861*j**4/4 + 27840*j**3 - 13824*j**2 + 2771. Determine q, given that i(q) = 0.
-1, 0, 1/4, 96
Let b = 101900/1881 - 222/209. Let x = -475/9 + b. Let 4/3*i**3 + 0 + x*i + 4/3*i**2 = 0. What is i?
-1/2, 0
Let o(q) = -q**2 - 5*q - 2. Let z be o(-4). Suppose x - 5*k = -35, -6*k - 28 = x - 10*k. Suppose -7/6*y**4 - 2/3*y - 23/6*y**3 - 10/3*y**z + x = 0. What is y?
-2, -1, -2/7, 0
Let y = 253718/3 + -84572. Factor 4*f**2 + 0 + y*f**3 - 14/3*f.
2*f*(f - 1)*(f + 7)/3
Let v(p) = 16*p - 1018. Let q be v(67). Let r be (-32)/72 + 132/q. Factor -3/5*a**r + 0*a + 3/5.
-3*(a - 1)*(a + 1)/5
Let w be -293 + 1 - (-11 - -10)*3. Let s = 1453/5 + w. Find n, given that 56/5*n**4 - 8/5*n**2 + s*n - 54/5*n**3 + 8*n**5 + 0 = 0.
-2, -2/5, 0, 1/2
Let w be (-1)/(-1*4/60). Suppose -4*y + w = 7. What is m in 20*m**4 - 3*m - 16 - 11*m**3 + 4*m**5 + y*m**2 - 29*m - 6*m**2 + 39*m**3 = 0?
-2, -1, 1
Let s(i) be the second derivative of -i**6/180 - 3*i**5/20 + 11*i**4/6 - 11*i**3/2 + 29*i. Let m(v) be the second derivative of s(v). Factor m(y).
-2*(y - 2)*(y + 11)
Factor 13*f**2 + 79*f**3 - 81*f**3 - 680 + 170*f + 498 + f**2.
-2*(f - 13)*(f - 1)*(f + 7)
Let q = 3481/11914 + -11/1702. Factor 2/21*z**2 + 0 + q*z.
2*z*(z + 3)/21
Factor -4115400 + 3/5*k**3 - 342*k**2 + 64980*k.
3*(k - 190)**3/5
Let o(t) be the second derivative of t**5/5 + 21*t**4 + 720*t**3 + 5400*t**2 + 45*t - 6. Factor o(c).
4*(c + 3)*(c + 30)**2
Let a = 65956 - 65954. Factor -a*u**2 + 0 + 6*u - 1/2*u**3.
-u*(u - 2)*(u + 6)/2
Let w(f) be the second derivative of -f**7/168 + 11*f**6/72 - 5*f**5/12 + 8*f**3/3 - 77*f. Let p(x) be the second derivative of w(x). Factor p(i).
-5*i*(i - 10)*(i - 1)
Determine t so that -28/3*t**4 + 29/3*t**3 - 4/3 - 4/3*t + 19*t**2 = 0.
-1, -1/4, 2/7, 2
Let p(i) = 66*i**3 + 554*i**3 - 2523 - 2995*i**2 - 32 + 4790*i. Let s(u) = -619*u**3 + 2994*u**2 - 4788*u + 2554. Let k(h) = -6*p(h) - 5*s(h). Factor k(m).
-5*(5*m - 8)**3
Let o = -4487 - -4489. Let m(u) be the third derivative of u**o + 2/75*u**5 + 1/15*u**3 - 1/12*u**4 + 0*u + 0. Let m(b) = 0. Calculate b.
1/4, 1
Let k(o) be the second derivative of 0 + 5*o**2 + 1/3*o**3 + 1/360*o**6 - 38*o + 11/72*o**4 + 1/30*o**5. Let i(w) be the first derivative of k(w). Factor i(j).
(j + 1)*(j + 2)*(j + 3)/3
Determine l so that -102/11*l + 8 + 2/11*l**3 + 12/11*l**2 = 0.
-11, 1, 4
Suppose -531 + 608 = -2*d - 7*p, 0 = -d - 2*p - 22. Factor d + 1/6*n**4 + 1/2*n**2 - 2/3*n**3 + 0*n.
n**2*(n - 3)*(n - 1)/6
Suppose -78*m + 49*m + 42*m - 39 = 0. Let n(r) be the second derivative of 0 + 0*r**m - 15*r - 1/10*r**5 + 0*r**4 + 0*r**2. Determine u so that n(u) = 0.
0
Factor 0 + 4/7*f**3 + 328/7*f**2 - 332/7*f.
4*f*(f - 1)*(f + 83)/7
Let g(l) = 7*l + 91. Let i be g(-12). Let m be (-20)/(-72) + (i/(-9) - -1). Let 2*d - m*d**2 - 3/2 = 0. Calculate d.
1, 3
Let s(k) = -3*k**3 - 32*k**2 - 217*k - 650. Let t(w) = -43*w**3 - 451*w**2 - 3034*w - 9101. Let f(v) = 87*s(v) - 6*t(v). Let f(c) = 0. What is c?
-9, -8
Let r(m) be the first derivative of -m**5 + 10*m**4 + 215*m**3/3 + 145*m**2 + 120*m + 1631. Let r(p) = 0. What is p?
-2, -1, 12
Let h(b) be the second derivative of -b**7/1785 + b**6/255 - 2*b**5/255 + 71*b**2/2 + 3*b + 8. Let w(r) be the first derivative of h(r). Factor w(n).
-2*n**2*(n - 2)**2/17
Let x(w) be the first derivative of -w**4/10 - 13154*w**3/15 - 10810943*w**2/5 + 21635042*w/5 + 3847. Factor x(r).
-2*(r - 1)*(r + 3289)**2/5
Let d be ((-22)/385*14)/((-33)/55). Suppose d + 7/3*y**2 - 16/3*y = 0. What is y?
2/7, 2
Let k(z) be the second derivative of 71*z**7/231 - 61*z**6/165 - z**5/11 - 3*z + 319. Factor k(c).
2*c**3*(c - 1)*(71*c + 10)/11
Let m be (-2)/(-5) - (702/(-45) - -1). Let t be 1/(3/m) + 7/(-2). Suppose -t*x + 3/2*x**2 + 0 = 0. What is x?
0, 1
Let d = 6 + 6. Suppose -4*c = 2*c - d. Factor 72*u - 4*u**c - 152 - 183 + 51 - 40.
-4*(u - 9)**2
Let q(h) = 2*h**2 - 2*h + 1. Let r(z) be the third derivative of -17*z**4/24 + 3*z**3/2 + 265*z**2. Let l(w) = 5*q(w) - 5*r(w). Factor l(t).
5*(t + 8)*(2*t - 1)
Let c(h) be the second derivative of 19/9*h**4 + 1/30*h**5 + 0*h**2 - 3*h + 361/9*h**3 + 0. Solve c(f) = 0.
-19, 0
Let g(s) be the first derivative of s**4/2 + 15*s**3/2 - 12*s**2 + 68*s + 55. Let u(c) be the first derivative of g(c). Suppose u(m) = 0. What is m?
-8, 1/2
Let h be 13/(26/20) + -7. Let x(j) be the first derivative of -4 - h*j + 7/2*j**2 - 4/3*j**3. Let x(l) = 0. What is l?
3/4, 1
Suppose -1082/3*h**2 + 5/3*h**3 + 19584*h - 7776 = 0. What is h?
2/5, 108
Let d(w) = -46*w + 573. Let v be d(12). Suppose -v*z = 2*z - 46. Let 0 + 10/3*o**z - 4*o + 2/3*o**3 = 0. What is o?
-6, 0, 1
Let z(t) = 129*t**2 + 12114*t + 5934. Let h(j) = 8*j**2 + 757*j + 371. Let s(q) = -33*h(q) + 2*z(q). Find p such that s(p) = 0.
-125, -1/2
Suppose -16*g + 190 = -290. Let t be ((-16)/10)/(((-279)/g)/31). Factor -6 - 4*f**3 + t*f**2 + 4*f + 2/3*f**4.
2*(f - 3)**2*(f - 1)*(f + 1)/3
Let s be (3 - (29/5 - 2))*-10. Factor s + 22 - 369*a + 394*a + 5*a**2.
5*(a + 2)*(a + 3)
Let y(g) be the second derivative of -19/36*g**4 + 2/45*g**6 + 65*g + 7/18*g**3 + 1/2*g**2 + 1/12*g**5 + 0. Factor y(s).
(s - 1)**2*(s + 3)*(4*s + 1)/3
Let i(b) be the first derivative of -24/7*b + 68 - 16/7*b**2 - 2/3*b**3 - 1/14*b**4. Factor i(x).
-2*(x + 2)**2*(x + 3)/7
Factor 1/8*v**2 + 329/4*v + 108241/8.
(v + 329)**2/8
Suppose 0 = -v + 4*u + 18, u + 4 + 0 = 0. Determine g, given that 20*g**2 - 9*g**2 + v*g**3 - 4*g**3 - 7*g**2 - 2*g = 0.
0, 1
Determine r so that 243*r + 195*r - 145 + 4*r**2 - 78 + 3 = 0.
-110, 1/2
Let d = 358/189 + -28/27. Let x(q) be the second derivative of 8/3*q**6 - 4*q**2 - 6*q**4 + 4/5*q**5 + 2*q + d*q**7 - 26/3*q**3 + 0. What is b in x(b) = 0?
-1, -2/9, 1
Let w(v) = v**4 - 10*v**3 + 20*v + 32. Let j(m) = m**4 - 2*m**3 + 2*m**2 - 2*m. Let y(d) = 4*j(d) - 2*w(d). Factor y(k).
2*(k - 2)*(k + 2)**2*(k + 4)
Factor -1/2*f**2 + 38 + 15/2*f.
-(f - 19)*(f + 4)/2
Let t = 4854 + -33878/7. Let f(d) be the first derivative of 18 - 4*d**2 + t*d**5 - 4/7*d - 80/7*d**3 - 50/7*d**4. Factor f(x).
4*(x - 1)*(5*x + 1)**3/7
Factor 51/4*v + 27/4*v**2 + 1/4*v**3 + 25/4.
(v + 1)**2*(v + 25)/4
Suppose -24949*x + 24950*x = 5*w - 36, -5*x + w = -36. Solve -3/2*o**3 + 3/2*o**2 + 0 + x*o = 0.
-2, 0, 3
Let z = -33 + 57. Factor 3*j**2 + 26*j + 2*j**2 - 10 - 45 + z*j.
5*(j - 1)*(j + 11)
Let v(s) be the first derivative of -s**7/420 + s**6/60 - 7*s**3 + s - 90. Let j(w) be the third derivative of v(w). Factor j(i).
-2*i**2*(i - 3)
Let u be (4/(8/9))/((-101)/(6060/(-90))). Solve 1/5*y**u - 5*y - 28/5 + 4/5*y**2 = 0.
-7, -1, 4
Let n = -963658 + 963661. Factor 5408/5*s - 208/5*s**2 + 2/5*s**n + 0.
2*s*(s - 52)**2/5
Factor -170/3*v - 1/6*v**2 + 575/2.
-(v - 5)*(v + 345)/6
Let o(b) be the first derivative of b**4/12 + 175*b**3/3 + 349*b**2/2 + 523*b/3 - 5750. Suppose o(s) = 0. What is s?
-523, -1
Factor 177*n**4 + 178*n**4 - 99*n - 141*n**2 + 155*n**4 - 45*n**3 - 513*n**4.
-3*n*(n + 1)*(n + 3)*(n + 11)
Let p be (-7 - ((-132)/77 + (-2 - 3)))*-1. Let u be (1 + -1)/(2 + 0). Factor -p*x**5 + 0*x**3 - 8/7*x**2 + 0*x + 6/7*x**4 + u.
-2*x**2*(x - 2)**2*(x + 1)/7
Suppose 836*g - 523 - 239 - 272 = 319*g. Factor 0 + 3*u**3 + 0*u - 15/8*u**g.
3*u**2*(8*u - 5)/8
Let r = 400 - 391. Let l = -17/3 + r. What is g in -4 + l*g + 2/3*g**2 = 0?
-6, 1
Let h = -79416 + 397088/5. Let -2/5*p**3 + h*p**2 + 22/5*p + 12/5 = 0. What is p?
-1, 6
What is p in 1/2*p**2 + 2024072 + 2012*p = 0?
-2012
Let n(r) be the third derivative of r**5/510 - 7*r**4/51 - 128*r**3/51 + 667*r**2. Solve n(z) = 0.
-4, 32
Suppose -3*p = -2*y + 19, -4*p - 30 = -31*y + 26*y. Find r, given that 125*r**4 - 1214*r**5 - 830*r**3 + 1209*r**5 + 500*r + 480*r**y + 940*r = 0.
-1, 0, 2, 12
Factor -9/2*b - 13/6 - 1/6*b**3 - 5/2*b**2.
-(b + 1)**2*(b + 13)/6
Let m(j) = 17*j**2 - 1992*j + 564. Let h(n) = 39*n**2 - 3985*n + 1126. Let d(o) = -4*h(o) + 10*m(o). Factor d(v).
2*(v - 284)*(7*v - 