s**2 - 5*s + 2. Let k be m(0). Find n such that 171*n**k - 20*n**3 - 38*n**2 - 64*n + 35*n**2 = 0.
0, 2/5, 8
Let q(k) = -56*k**2 + 59*k**2 - 36*k**3 - 9 + 16*k**3 + 14*k**3. Let v(f) = 24 - 2*f**2 - 6*f**2 + 10*f**3 + f**3 - 5. Let i(r) = 5*q(r) + 3*v(r). Factor i(z).
3*(z - 2)**2*(z + 1)
Let n(m) be the second derivative of m**6/60 + 2427*m**5/40 + 491265*m**4/8 + 1471369*m**3/12 + 9009*m. Factor n(k).
k*(k + 1)*(k + 1213)**2/2
Let a = 289486 + -289483. Find y, given that -2/3 - 5/6*y**a + 4/3*y + 1/6*y**4 - 1/6*y**2 + 1/6*y**5 = 0.
-2, 1
Let k(a) be the first derivative of 4*a**3/9 + 176*a**2/3 + 116*a + 289. Suppose k(i) = 0. Calculate i.
-87, -1
Let l(d) = d**3 + 12*d**2 - 33*d + 34. Let m be l(-12). Let j = 869/2 - m. Factor 0 + j*g**3 - 3*g**4 + 0*g + 3*g**2.
-3*g**2*(g - 2)*(2*g + 1)/2
Let v(k) = 195*k - 44 - 8*k**2 - 50 + 25. Let d be v(24). Let -4/3 + 2*n**4 + 26/9*n + 86/9*n**d + 106/9*n**2 = 0. What is n?
-3, -1, 2/9
Suppose 3*a = 7*a + 8, 4*u = -a + 1198. Let w = 303 - u. Suppose -32/13*n + 8/13 - 6*n**2 - 294/13*n**5 + 70/13*n**4 + 326/13*n**w = 0. Calculate n.
-1, -1/3, 2/7, 1
Factor -3*k**3 + 61*k**2 + 3134*k + 106*k**2 - 456 - 179*k + 106*k**2 + 8031.
-3*(k - 101)*(k + 5)**2
Solve 2/15*g**2 + 508/15 - 34*g = 0 for g.
1, 254
Let o(k) be the first derivative of k**4/14 - 1870*k**3/21 + 31289*k**2 - 436178*k/7 - 3145. Suppose o(q) = 0. What is q?
1, 467
Let o(r) be the first derivative of -2*r**3/3 - 8*r**2 + 66*r - 123. What is t in o(t) = 0?
-11, 3
Let x(m) be the third derivative of -m**7/70 + 11*m**6/20 - 21*m**5/4 + 603*m**2 + 5. Factor x(u).
-3*u**2*(u - 15)*(u - 7)
Let s be 2 + 4*(4 - 3). Let k = 12 - s. Let 10*p + 2 + k - 2*p - 3*p**2 + 5*p**2 = 0. What is p?
-2
Let k(j) be the second derivative of 0 + 25/18*j**4 + 1/12*j**5 + 40/9*j**3 + 0*j**2 - 97*j. Factor k(d).
5*d*(d + 2)*(d + 8)/3
Determine g so that -3200 - 4461*g**2 - 18*g - 142*g + 8923*g**2 - 4464*g**2 = 0.
-40
Let f = 222 - 220. Factor 0*n - 6*n - 4*n**2 - 8*n + f*n.
-4*n*(n + 3)
Let u be (-28)/((-280)/50) - 2. Let q(l) be the second derivative of 0 + 5/18*l**u + 16*l - 2/3*l**2 - 1/36*l**4. Solve q(o) = 0 for o.
1, 4
Let u(s) be the first derivative of s**6/12 + 7*s**5/10 - 5682. What is b in u(b) = 0?
-7, 0
Let f be ((-4)/3)/2*(-333)/(-11248). Let n = f - -1529/456. Factor 5/6*w**2 + n - 10/3*w.
5*(w - 2)**2/6
Let d(h) = 18*h**2 - 14*h - 317. Let x(a) = 16*a**2 - 12*a - 318. Let i(t) = -6*d(t) + 7*x(t). Find k, given that i(k) = 0.
-9, 9
Factor -1626*g**3 + 1539*g**3 + 24 + 4*g - 4*g**5 + g**5 + 27*g**4 + 129*g**2 + 0*g**5 - 94*g.
-3*(g - 4)*(g - 2)*(g - 1)**3
Let u(g) be the first derivative of -21/2*g**2 - 108/5*g**3 - 6/5*g + 75. Factor u(l).
-3*(4*l + 1)*(27*l + 2)/5
Let s(r) = r**3 - 330*r**2 - 1337*r - 2. Let g be s(-4). Suppose 32/3*k**g + 2/3*k**4 + 0*k + 16/3*k**3 + 0 = 0. What is k?
-4, 0
Let n(v) be the third derivative of -v**7/4620 - v**6/990 - v**3/2 + v**2 + 12. Let u(q) be the first derivative of n(q). Factor u(m).
-2*m**2*(m + 2)/11
Find u, given that 0 + 4284/5*u**2 + 52*u**4 + 4/5*u**5 - 1956/5*u**3 - 2592/5*u = 0.
-72, 0, 1, 3
Suppose 0*x - 25*x - 11 = -61. Let c(i) be the second derivative of -49/15*i**3 + 0 - 1/50*i**5 + 7/15*i**4 + 0*i**x + 17*i. Determine p, given that c(p) = 0.
0, 7
Factor -328/11*b - 2/11*b**2 - 326/11.
-2*(b + 1)*(b + 163)/11
Let r be (1 + 1)*-2*(-5 - -2). Suppose -r*h**4 - 130*h + 165*h**2 + 2*h**3 - 10*h**3 - 13*h**3 - 63*h**2 + 3*h**5 + 58*h = 0. What is h?
-3, 0, 1, 2, 4
Let r(x) = 20*x**2 + 121*x + 5. Let v be r(-6). Let c(i) = 3*i**2 + 24*i - 21. Let k(a) = a**2. Let l(u) = v*c(u) + 6*k(u). Factor l(n).
3*(n - 7)*(n - 1)
Let r(x) = 5*x**4 - 53*x**3 - 308*x**2 - 465*x - 215. Let s(c) = 2*c**4 - 26*c**3 - 153*c**2 - 232*c - 107. Let b(t) = -3*r(t) + 7*s(t). Factor b(j).
-(j + 1)**2*(j + 8)*(j + 13)
Suppose -4025 = 10*h - 15*h. Let d = h - 3215/4. Solve d*i**3 - i**4 + 1/4 - 5/4*i + 3/4*i**2 = 0.
-1, 1/4, 1
Let 3481/6*o**2 + 1121/2*o**3 + 0 - 39/2*o**4 + 1/6*o**5 + 0*o = 0. Calculate o.
-1, 0, 59
Let k = -129865 - -1688259/13. Factor -k + 12/13*d + 2/13*d**2.
2*(d - 1)*(d + 7)/13
Let i be -10*(22 + -21)/(20/(-8)). Let t(s) be the first derivative of 1/16*s**i + 0*s - 1/4*s**2 - 1/12*s**3 + 8. Factor t(n).
n*(n - 2)*(n + 1)/4
Let g(k) be the third derivative of 4/3*k**4 - 1/30*k**6 + 1/15*k**5 - 7 - 8*k**3 - 4*k**2 + 0*k. Factor g(l).
-4*(l - 2)**2*(l + 3)
Let b(h) be the second derivative of -h**7/441 + 4*h**6/105 - 37*h**5/210 - h**4/7 + 128*h**3/63 + 32*h**2/7 - 8547*h. Determine q, given that b(q) = 0.
-1, 4, 6
Let o(z) = -7*z**3 + 912*z**2 - 10*z + 5. Let s(b) = -4*b**3 + 456*b**2 - 6*b + 3. Let p(v) = -3*o(v) + 5*s(v). Factor p(k).
k**2*(k - 456)
Suppose -3*o = 705*o. Let -4/9*v**2 + o + 8/9*v = 0. What is v?
0, 2
Let p(a) be the first derivative of -25*a**6/54 + a**5/9 + 133*a**4/18 + 404*a**3/27 + 100*a**2/9 + 32*a/9 - 1893. Solve p(v) = 0 for v.
-2, -1, -2/5, 4
Let 20/7*v**4 - 128/7*v**2 + 24/7*v**3 - 4/7*v**5 + 0 - 128/7*v = 0. What is v?
-2, -1, 0, 4
Let i(b) be the second derivative of 4*b + 1/24*b**4 - 5/12*b**3 + 0*b**2 + 11. Suppose i(x) = 0. What is x?
0, 5
Let w(n) be the first derivative of 6*n - 1 + 8/3*n**3 + 1/3*n**4 + 8*n**2. Let t(c) be the first derivative of w(c). Find a such that t(a) = 0.
-2
Let v(y) be the second derivative of 0 - 19/30*y**5 + 20/9*y**4 + 2/45*y**6 + 0*y**2 + 25/9*y**3 - 76*y. Factor v(f).
2*f*(f - 5)**2*(2*f + 1)/3
Let r(f) = -7*f**3 - 14*f**2 + 2*f + 9. Suppose -135 = -85*s + 100*s. Let w(h) = 3*h**3 + 7*h**2 - 2*h - 4. Let p(u) = s*w(u) - 4*r(u). Let p(z) = 0. What is z?
0, 2, 5
Let n(k) be the third derivative of -k**5/630 - 187*k**4/252 - 62*k**3/21 + 2*k**2 + 77. Solve n(x) = 0.
-186, -1
Suppose 9*m = 12*m + 6, 5*w = 5*m - 1285. Let j = w + 259. Let 2/9*x**4 + 4/9*x**2 - 2/3*x**3 + j + 0*x = 0. Calculate x.
0, 1, 2
Let p(i) be the second derivative of i**6/216 + 2*i**5/9 + 35*i**4/18 + 19*i**3/3 - i**2 + 9*i - 4. Let c(o) be the second derivative of p(o). Solve c(v) = 0.
-14, -2
Let k = -381840 - -1527361/4. Factor 5/4*y**2 - 3/4*y - k*y**3 - 9/4.
-(y - 3)**2*(y + 1)/4
Solve 0 - 84/11*b - 2/11*b**2 = 0 for b.
-42, 0
Let n = -6808/7 + 20452/21. Factor 5/3*j - 1/3*j**2 - n.
-(j - 4)*(j - 1)/3
Let m(i) be the first derivative of i**4/12 - 2*i**2 - 67*i - 50. Let w(t) be the first derivative of m(t). Factor w(l).
(l - 2)*(l + 2)
Let a(c) be the third derivative of -c**5/80 - 99*c**4/32 - 161*c**3/2 + 959*c**2 - 2. Determine q so that a(q) = 0.
-92, -7
Let f be (300/(-45))/(8/(-6)). Let p be 1/5 + 9/5. What is z in 10*z**p - 5*z**4 - 102*z**3 + 102*z**3 - f = 0?
-1, 1
Let w(g) be the first derivative of 2*g**3/15 - 939*g**2/5 - 5230. Determine l, given that w(l) = 0.
0, 939
Let w(y) = 5*y**2 - 42*y + 147. Let u(v) = 124*v + 2352 - 583*v + 81*v**2 - 213*v. Suppose 5*n + 7 = -3. Let o(g) = n*u(g) + 33*w(g). Let o(p) = 0. Calculate p.
7
Determine c so that 5*c**2 - 530 + 145 + 31 - 270*c - 310*c - 231 = 0.
-1, 117
Let p(x) be the second derivative of -x**4/4 + 22*x**3 - 240*x**2 - 1010*x. Let p(g) = 0. What is g?
4, 40
Let j = -12599720/155249 - -1542/19. Let k = 621006/40855 + j. Find h, given that -16/5 + k*h**3 - 20*h**2 + 4/5*h**5 + 64/5*h - 28/5*h**4 = 0.
1, 2
Let k(q) be the third derivative of -q**6/120 - q**5/60 - q**3/6 - q**2 + 1. Let w(d) = -d**3 - 21*d**2 + 10*d + 124. Let s(u) = 4*k(u) + w(u). Factor s(o).
-5*(o - 2)*(o + 3)*(o + 4)
Suppose -2*t = -6 - 0. Factor -1333 - 43*d**2 + 483*d + 3*d**3 + 892 - 2*d**t.
(d - 21)**2*(d - 1)
Let r(y) = 3*y**4 - 596*y**3 + 89396*y**2 - 177034*y + 88209. Let q(v) = -v**4 + v**2 + 11*v. Let o(c) = -2*q(c) - r(c). Factor o(k).
-(k - 297)**2*(k - 1)**2
Let r(z) be the first derivative of 4*z**3/3 - 2188*z**2 + 1196836*z + 898. Factor r(s).
4*(s - 547)**2
Suppose 59*k - 66*k + 98 = 0. Let 2301*j**3 - j**4 - 4*j**2 - k*j + 0*j**4 - 2*j**5 - 2285*j**3 - 3*j**4 + 8 = 0. Calculate j.
-4, -1, 1
Suppose 4*d - 2 = -5*g, 5*g + 0 = -d + 8. Let b = 6 - 2. Determine x, given that -11*x**3 + 2*x + 2*x**5 - 10*x**2 - 4 + 18*x**g + 0 - b*x**4 + 7*x**3 = 0.
-1, 1, 2
What is t in -3*t**2 - 1/2*t**3 + 0 - 1/2*t**5 + 0*t + 2*t**4 = 0?
-1, 0, 2, 3
Let x = -804573/13 - -61891. Suppose 8/13 + 2/13*j**2 - x*j = 0. What is j?
1, 4
Let o(u) be t