8*k**4 - y*k**3.
2*(k - 1)**2*(k + 2)*(4*k - 1)
Let c(i) = -121*i**3 - 239*i**2 + 260*i + 23. Let p(n) = 122*n**3 + 247*n**2 - 259*n - 22. Let t(m) = 8*c(m) + 7*p(m). Find f, given that t(f) = 0.
-5/2, -2/19, 1
Let q be (-609)/(-1102)*19 + -6. Factor -4*a + 0 - q*a**3 + 33/4*a**2 + 1/4*a**4.
a*(a - 16)*(a - 1)**2/4
Let l be 275267/355 - 6/(-10). Let u = l - 774. What is x in -u*x**2 + 10/3 + 28/3*x = 0?
-1/3, 5
Let x(i) be the second derivative of 0*i**2 - 1 + 36*i - 7/2*i**3 - 3/5*i**5 + 29/4*i**4. Factor x(w).
-3*w*(w - 7)*(4*w - 1)
Let b be (3 - -1 - -2) + -4 + 1. Factor 34 + 44 + b*l - 42 + 0*l - 3*l**2.
-3*(l - 4)*(l + 3)
Let l(a) be the first derivative of a**5 + 155*a**4/4 - 165*a**3 + 505*a**2/2 - 170*a + 4409. Factor l(i).
5*(i - 1)**3*(i + 34)
Suppose -2*f + 5*f - 6 = 0. Factor 3*x**f + 126*x - 43*x - 41*x - 51*x + 6.
3*(x - 2)*(x - 1)
Let f(i) be the second derivative of -1/30*i**6 + 0*i**3 + 0*i**2 - 59*i - 1/20*i**4 + 0 - 2/25*i**5. Factor f(z).
-z**2*(z + 1)*(5*z + 3)/5
Suppose -4*z + 44 = 479*s - 475*s, 0 = 2*z - 3*s + 23. Let b(w) be the second derivative of 30*w**3 + 0 - 23*w + 5*w**4 + 80*w**z + 1/4*w**5. Factor b(x).
5*(x + 2)**2*(x + 8)
Find g, given that -80*g**2 - 2560*g - 349*g**3 + 2320*g + 384*g**3 = 0.
-12/7, 0, 4
Suppose -7*b = -1714 + 1364. Let x be ((-440)/b)/(-2) - (-4)/(-10). Factor 1/2*p**x + 1/4*p + 3/2*p**2 - 1/2 - 7/4*p**3.
(p - 2)*(p - 1)**2*(2*p + 1)/4
Let i(h) be the third derivative of h**6/360 + h**5/60 - 109*h**3/3 - 117*h**2 + h. Let b(j) be the first derivative of i(j). Let b(m) = 0. What is m?
-2, 0
Let x(j) be the third derivative of -j**5/120 - 253*j**4/12 + 1013*j**3/12 + 3866*j**2. Factor x(m).
-(m - 1)*(m + 1013)/2
Let r(y) = -y**4 + 3*y**2 + 3*y + 3. Let h be ((-120)/75)/(1/5). Let c(m) = 6*m - 8 + 4*m**4 + 5*m - 8*m**2 - 19*m. Let g(a) = h*r(a) - 3*c(a). Factor g(s).
-4*s**4
Let l be 2857/322 + (-21)/(-7) + -8. Let x = l - -19/46. Factor -150/7*s - 2/7*s**3 - x*s**2 - 250/7.
-2*(s + 5)**3/7
Suppose 412 = 348*w + 137 - 360 - 61. Let 2/3*g**5 + 2*g**4 - 14/3*g**w - 2/3*g**3 + 8/3 + 0*g = 0. What is g?
-2, -1, 1
Let 0 + 46*j**2 + 2/5*j**4 - 118/5*j**3 - 114/5*j = 0. Calculate j.
0, 1, 57
Let k(q) = -q**3 + 31*q**2 + 81*q - 493. Let w be k(33). Let v = 15/34 - -201/238. Factor 3/7*y**w + 12/7*y + v.
3*(y + 1)*(y + 3)/7
Let l(s) be the first derivative of s**4/4 - 4*s**3 + 21*s**2/2 - 7*s - 37. Let r(a) be the first derivative of l(a). Suppose r(k) = 0. Calculate k.
1, 7
Determine m so that -28*m**2 + 28*m**2 + 34*m**2 - 30*m**2 - 2514 - 1670*m = 0.
-3/2, 419
Let t(l) be the second derivative of 0*l**2 - 2*l - 1/9*l**5 + 2/135*l**6 + 0*l**3 - 60 + 2/9*l**4. Factor t(z).
4*z**2*(z - 3)*(z - 2)/9
Let p = 247 + -242. Factor -z**p - 7*z**4 + 7*z**4 - 5*z**4 + 0*z**3 - 4*z**3.
-z**3*(z + 1)*(z + 4)
Let b(k) be the third derivative of 2*k**7/105 - k**6/15 - k**5/15 + k**4/3 + 4712*k**2. Suppose b(c) = 0. Calculate c.
-1, 0, 1, 2
Let i(o) be the third derivative of -1/100*o**6 + 1/350*o**7 + 0 + 1/5*o**4 - 1/25*o**5 + 52*o**2 + 0*o + 0*o**3. Factor i(d).
3*d*(d - 2)**2*(d + 2)/5
Factor 0*h + 12*h**3 - 3*h**4 - 5065*h**2 + 5011*h**2 + 21*h**3 + 0*h.
-3*h**2*(h - 9)*(h - 2)
Suppose -v = 4*g - 45, -g - 5 = -5*v + 10. Factor -4*t**2 - 3*t**3 - 29*t - g*t + 4*t**3 + 43*t.
t*(t - 2)**2
Let k(c) be the second derivative of c**6/15 - 46*c**5/5 + 408*c**4 - 5040*c**3 + 21168*c**2 - 38*c - 70. Determine z so that k(z) = 0.
2, 6, 42
Suppose 2037*x - 364284 = -2259*x + 923*x. Suppose 30*d + 32/3*d**2 + 2/3*d**3 - x = 0. Calculate d.
-9, 2
Let s(k) be the first derivative of -8*k - 51 - 18*k**2 - 28/3*k**3. Determine b, given that s(b) = 0.
-1, -2/7
Factor -35*u**2 + 14883/7*u + 15129/7 + 1/7*u**3.
(u - 123)**2*(u + 1)/7
Let d(a) be the third derivative of -1/15*a**6 + 0 - 27/7*a**4 - 90/7*a**3 + 18*a**2 - 24/35*a**5 + 0*a - 2/735*a**7. Factor d(s).
-4*(s + 3)**3*(s + 5)/7
Let f(k) be the second derivative of k**7/840 - k**6/24 + 2*k**5/5 - 20*k**4/3 - 61*k - 1. Let a(d) be the third derivative of f(d). Factor a(r).
3*(r - 8)*(r - 2)
Let 0 - 735*x - 5/2*x**4 + 20*x**3 + 1435/2*x**2 = 0. What is x?
-14, 0, 1, 21
Let r be (11613/(-3024) - -4) + (-3)/(-48). Factor r*m**4 + 4/9*m + 0 - 2/3*m**2 + 0*m**3.
2*m*(m - 1)**2*(m + 2)/9
Let k = 2742 + -2737. Let a(i) be the first derivative of 0*i - 1/12*i**3 + 1/16*i**4 + 1/20*i**k + 17 - 1/8*i**2. Suppose a(d) = 0. Calculate d.
-1, 0, 1
Suppose -77 - 23 = -10*c. Factor 2 + 9*m - c*m - 7*m**2 - 2.
-m*(7*m + 1)
Let r be ((-16)/(-8))/((-2)/(-3)). Suppose 1 - 9 - r*i - 9*i**3 + 27*i + 3*i**3 + 2*i**2 = 0. Calculate i.
-2, 1/3, 2
Let c(p) be the second derivative of -1/10*p**4 + 2*p - 4/15*p**3 + 12/5*p**2 + 1/50*p**5 - 95. Factor c(a).
2*(a - 3)*(a - 2)*(a + 2)/5
Solve -1791*a**2 - 6988*a**3 - 90*a**2 + 6985*a**3 - 2649*a**2 - 816*a**2 + 5346 + 3*a = 0 for a.
-1782, -1, 1
Let d(k) be the second derivative of -7/18*k**5 + 0 + 22/3*k**4 + 1/135*k**6 - 34*k - 192*k**2 - 48*k**3. Suppose d(u) = 0. Calculate u.
-1, 12
Suppose -35 = -4*b + b + z, z = -5. What is p in 14*p**3 + 8 + b*p**4 - 1820*p - 18*p**2 - 6*p**5 + 0 + 1812*p = 0?
-1, 2/3, 1, 2
Suppose 0 = -5*n + 2*x + 36, 3*n + 3*x = -182 + 149. Factor -3/2*j**n - 15 - 21/2*j.
-3*(j + 2)*(j + 5)/2
Let m(o) be the first derivative of 11 + 1153/15*o**3 + 63*o**2 - 14*o**4 + 16/25*o**5 + 81/5*o. Solve m(h) = 0 for h.
-1/4, 9
Suppose -2*g - 22 = -26. Suppose -16*i**3 + 130*i**5 - 118*i**5 + 2*i + 8*i**g - 8*i**4 + 2*i = 0. Calculate i.
-1, -1/3, 0, 1
Let v(g) = -g**2 - 1698*g + 3404. Let c be v(2). Factor -2*j**3 - 54/7*j**2 + 2/7*j**c - 20/7 - 58/7*j.
2*(j - 10)*(j + 1)**3/7
Suppose 5*a = 4*a - 5*y - 5, -5*y = 5. Suppose z + 3*j = 23, 28*z - 27*z - 37 = -5*j. Factor -2/9*k + 10/9*k**z + a.
2*k*(5*k - 1)/9
Let g(r) be the second derivative of 1/24*r**4 - 1/6*r**3 + 0*r**2 + 1/40*r**5 - 38 - 2*r. Factor g(l).
l*(l - 1)*(l + 2)/2
Let k be (-7)/15 + 292/365. Let x be (-44)/(-60) - 2/5. Factor 1/6*j**4 - 1/6 + 0*j**2 - x*j + k*j**3.
(j - 1)*(j + 1)**3/6
Let m be (2600/2145)/((-25)/(-180)) + -6. Factor -2/11*y**2 + m + 4/11*y.
-2*(y - 5)*(y + 3)/11
Let w(i) be the second derivative of -i**6/6 - 89*i**5/2 + 1795*i**4/12 - 150*i**3 + 8460*i. Factor w(n).
-5*n*(n - 1)**2*(n + 180)
Let f be ((-130)/52)/(10/(-12)). Solve 2372*c**2 - c + f - 2369*c**2 - 5*c = 0 for c.
1
Suppose 3*l = 11 - 2. Suppose -5*c = l*c - 24. Suppose -10*o**2 - 3*o**c + 2*o - 3*o**5 + 11*o**2 - o**4 + 4*o**5 = 0. Calculate o.
-1, 0, 1, 2
Let z(f) be the first derivative of -f**4/12 - 7*f**3/9 + 5*f**2/6 + 25*f - 743. Let z(l) = 0. What is l?
-5, 3
Let q = -2703/2 - -9462/7. Let o(i) be the first derivative of q*i**2 + 0*i + 11 - 1/7*i**3. Factor o(h).
-3*h*(h - 1)/7
Let d(g) be the second derivative of g**4/78 - 938*g**3/39 + 219961*g**2/13 + 7042*g. Find s such that d(s) = 0.
469
Let p(z) be the third derivative of z**7/1365 + 4*z**6/65 + 35*z**5/26 - 625*z**4/78 + 2509*z**2. Suppose p(d) = 0. What is d?
-25, 0, 2
Suppose -8 = 2*q + 2*x, 134 = -3*q - 5*x + 110. Let p(r) be the first derivative of -1/3*r**3 - 3/8*r**q + 0*r - 4 - 1/16*r**4. Factor p(f).
-f*(f + 1)*(f + 3)/4
Factor -969*v**2 - 1400 + 14903*v + 284*v**2 - 5*v**3 - 12813*v.
-5*(v - 2)*(v - 1)*(v + 140)
Let c(t) be the first derivative of 0*t**2 - 11*t**5 - 25/4*t**4 - 10/3*t**6 + 203 + 0*t + 10/3*t**3. Solve c(p) = 0.
-2, -1, 0, 1/4
Let o be (-31 + 33)*-4 + 362/16 + -2. Suppose 43/4*u**2 + 11/4 - 7/8*u**3 - o*u = 0. Calculate u.
2/7, 1, 11
Find q, given that 32*q - 4*q**5 + 84478*q**2 - 84430*q**2 + 17*q**3 - 12*q**4 - 9*q**3 = 0.
-2, -1, 0, 2
Let h(p) = -p**5 + 11*p**4 + 5*p**3 + 3*p**2. Let q(l) = -2*l**4. Let j be (-4)/5 + 0 - (-36)/20. Let a(u) = j*h(u) + 5*q(u). Let a(i) = 0. Calculate i.
-1, 0, 3
Let l(r) be the third derivative of -r**7/105 - 7*r**6/40 + 43*r**5/12 - 17*r**4/4 + 462*r**2. Factor l(t).
-t*(t - 6)*(t + 17)*(2*t - 1)
Find s such that 48*s**5 + 915*s**3 + 201*s - 84*s + 284*s**2 + 1896*s**4 - 165*s**2 - 935*s**2 = 0.
-39, -1, 0, 1/4
Let c(x) be the third derivative of 0*x + 82 - x**5 - x**2 - 3/2*x**4 + 0*x**3 - 1/21*x**7 - 1/336*x**8 - 37/120*x**6. Factor c(d).
-d*(d + 2)**2*(d + 3)**2
Let l be (-18)/(-39)*(1 - 748/(-136)). What is i in 4/9*i + 0 - 13/9*i**l + 8/3*i**2 = 0?
-2/13, 0, 2
