first derivative of -25*i**4 + 1340*i**3 + 1632*i**2 + 656*i + 519. Factor f(a).
-4*(a - 41)*(5*a + 2)**2
Let y = -128/211 - -1311/422. What is u in y*u**2 + 0 - 1/2*u**3 - 2*u = 0?
0, 1, 4
Let d(w) be the third derivative of w**8/5040 + w**7/420 - w**6/18 - w**5/12 + w**4/8 + 5*w**2 + 5*w. Let r(k) be the third derivative of d(k). Factor r(m).
4*(m - 2)*(m + 5)
Let g = -491163/60844 + 331/41. Let d = 3709/1484 + g. Determine r, given that d*r + 1/4*r**2 + 25/4 = 0.
-5
Let w = 449 + -447. Suppose w*m + 4 = -2*l, l - 3*m - 12 = 6. Let -t**2 - 1/3*t**4 + 4/3 - 4/3*t + 4/3*t**l = 0. What is t?
-1, 1, 2
Determine h so that 0 - 2/9*h**3 + 140/9*h - 22/3*h**2 = 0.
-35, 0, 2
Let r = 569 - 565. Factor -r*q**5 - 10*q - 25*q**2 + 0*q**5 + 2*q**5 + 5*q**4 - 15*q**3 + 7*q**5.
5*q*(q - 2)*(q + 1)**3
Let z(d) be the third derivative of 2/3*d**3 + 1/6*d**5 + 0 + 0*d - 7/12*d**4 + 89*d**2. Factor z(m).
2*(m - 1)*(5*m - 2)
Suppose -4*o - 9*p - 220 = -7*p + 4*p - 90, 46 = -2*p. Suppose 0 = w + w. Factor 5/4*r**5 + 25/4*r**3 + w*r + 5/2*r**o + 5*r**4 + 0.
5*r**2*(r + 1)**2*(r + 2)/4
Suppose 8007*b = 8028*b. Determine k, given that -6/11*k**2 - 54/11*k + b = 0.
-9, 0
Let z(w) be the second derivative of -w**6/120 - 3*w**5/80 + 13*w**4/48 + 5*w**3/8 - 167*w. Factor z(q).
-q*(q - 3)*(q + 1)*(q + 5)/4
Let w(l) be the first derivative of 1/4*l**2 - 188 + 1/18*l**3 + 1/3*l. Factor w(h).
(h + 1)*(h + 2)/6
Let v = -1351614/5 - -270330. Find g such that 39/5*g**2 - v*g + 0*g**3 - 3/5*g**4 + 0 = 0.
-4, 0, 1, 3
Let t(u) = -u**3 - 35*u**2 - 124*u - 1. Let y be t(-31). Let k be 0/(y/(7/(-42))). Let -2/5*r**3 + 0 - 1/10*r**5 + 0*r + 2/5*r**4 + k*r**2 = 0. What is r?
0, 2
Let w(r) = 14*r**4 - 31*r**3 + 83*r**2 - 128. Let c(k) = 2*k**4 + k**3 - k**2. Let z = -250 + 249. Let n(s) = z*w(s) + 5*c(s). Factor n(x).
-4*(x - 4)**2*(x - 2)*(x + 1)
Let n(z) be the first derivative of z**5/10 + 4*z**4 + 89*z**3/6 + 29*z**2/2 - 1813. Factor n(l).
l*(l + 1)*(l + 2)*(l + 29)/2
Suppose -4*y = 4*l - 4, -y = 3 - 0. What is n in 8*n - 20*n**4 - 3*n**4 + 21*n**l - 6*n**3 = 0?
-2, 0, 1
Let o(d) = -d**2 + 16*d - 36. Let i be o(11). Determine g, given that 58*g - i + 6*g - 69 - 168 - 4*g**2 = 0.
8
Let l(y) = -2*y**3 + 1666*y**2 + 8*y - 16. Let f(o) = 8*o**3 - 6662*o**2 - 36*o + 72. Let c(v) = -2*f(v) - 9*l(v). Suppose c(g) = 0. Calculate g.
0, 835
Factor -25*q**3 - 1/3*q**5 + 0 - 375*q**2 + 0*q + 25/3*q**4.
-q**2*(q - 15)**2*(q + 5)/3
Let d(h) = 12*h**3 - 1138*h**2 - 186*h + 172. Let b(i) = -9*i**3 + 1137*i**2 + 186*i - 174. Let a(v) = -8*b(v) - 7*d(v). Let a(m) = 0. What is m?
-94, -1/2, 1/3
Factor -10*o**2 + 252*o**3 + 161*o**2 - 22*o**2 + 135*o**4 - 6*o**2 + 6*o**5.
3*o**2*(o + 1)**2*(2*o + 41)
Let f(v) be the third derivative of v**8/672 + 29*v**7/210 + 7*v**6/15 - 397*v**2. Solve f(k) = 0.
-56, -2, 0
Let w(z) be the first derivative of -5*z**4/2 + 37*z**3/3 + 8*z**2 - 16*z - 2965. Find j such that w(j) = 0.
-4/5, 1/2, 4
Let c(o) = o**2 + 14*o + 8. Let p be c(-14). Suppose 12 = l + p. Factor 5*f**2 - f**3 + 3*f**l - 2*f**2 - 5*f**3 + 0*f**3.
3*f**2*(f - 1)**2
Let f be (40/48*(-6)/15)/((-3)/27). Let d(l) be the second derivative of 0 + 6*l**2 + 1/45*l**6 + 10*l - 7/18*l**4 - 1/10*l**5 + 5/3*l**f. Factor d(r).
2*(r - 3)**2*(r + 1)*(r + 2)/3
Let a(c) be the third derivative of 0 + c + 7/12*c**4 - 2/15*c**6 + 0*c**7 + 1/168*c**8 + 2*c**3 - 9*c**2 - 1/5*c**5. Solve a(i) = 0.
-2, -1, 1, 3
Suppose 5*q = -4*t + 106, 22 = 3*q - 2*t - 24. Let g(z) = -z**3 + 17*z**2 + 22*z - 44. Let c be g(q). Factor -b - 14*b**2 + c*b**2 - 2 - 12*b**2 + b**3.
(b - 1)*(b + 1)*(b + 2)
Let p be (-22)/33 - ((-8)/(-2))/((-6)/7). Let c(d) be the first derivative of 4*d**2 + 4/5*d**5 + 0*d + 4*d**p + 20/3*d**3 - 46. Suppose c(s) = 0. What is s?
-2, -1, 0
Suppose -4928 + 1185 - 7967 = -5744*g - 222. Factor 445/3*h**g - 10120/3*h - 5/3*h**3 + 9680/3.
-5*(h - 44)**2*(h - 1)/3
Let l(v) = 3*v**2 - 9*v + 41 - 9*v - 35 - 2*v**2 - 59. Let n be l(21). Factor -n*k**2 - 2/7 + 50/7*k**3 + 22/7*k.
2*(k - 1)*(5*k - 1)**2/7
Let 5*i + 4286*i**3 + 19*i - 378*i**2 - 4193*i**3 = 0. Calculate i.
0, 2/31, 4
Let s(i) be the second derivative of -1/3*i**3 + 0*i**2 + 7/24*i**4 - 2*i - 11. Determine q so that s(q) = 0.
0, 4/7
Let o(i) = -62 + 38*i - 144*i - 46 + 6*i**2 - 10*i**2. Let x(m) = -m**2. Let b(v) = o(v) - 6*x(v). Determine g so that b(g) = 0.
-1, 54
Find f such that -1/2*f**2 - 546 - 163/2*f = 0.
-156, -7
Let u(s) be the second derivative of -s**7/42 - 191*s**6/15 + 769*s**5/20 + 191*s**4/6 - 128*s**3 - 2*s - 598. Find c such that u(c) = 0.
-384, -1, 0, 1, 2
Let r(p) be the second derivative of -p**5/60 + 5*p**4/108 + 2*p**3/27 - 2*p**2/9 - 236*p. Factor r(x).
-(x - 2)*(x + 1)*(3*x - 2)/9
Suppose -g = 3*g - 336. Let y = -80 + g. Factor -16*q**3 + 17*q**3 + 45 - 25*q**2 + 15*q + y*q**3.
5*(q - 3)**2*(q + 1)
Let o(w) be the second derivative of 5*w**7/42 + 3*w**6/2 + 23*w**5/4 + 55*w**4/12 - 20*w**3 - 50*w**2 + 21*w - 2. Determine v so that o(v) = 0.
-5, -2, -1, 1
Let y(c) = -136*c**5 + 16*c**4 + 142*c**3 + 2*c**2 + 6*c + 6. Let h(f) = -3*f**4 - f**3 - f - 1. Let r(i) = -6*h(i) - y(i). Solve r(w) = 0 for w.
-1, -1/68, 0, 1
Factor -23101/3*j**2 - 23716/3 + 15708*j - 102*j**3 - 1/3*j**4.
-(j - 1)**2*(j + 154)**2/3
What is x in -110946459*x + 45549356*x - 65938112*x + 42430267049 - 5*x**3 + 44385*x**2 + 87110033346 = 0?
2959
Let j = 9396 + -9396. Let t(h) be the first derivative of 1/5*h**3 - 30 + j*h - 9/5*h**2. Factor t(n).
3*n*(n - 6)/5
Let w(j) be the third derivative of 60*j**2 + 1/84*j**7 + 11/48*j**6 + 0*j**5 + 0*j**3 + 0*j + 0*j**4 + 0. Factor w(p).
5*p**3*(p + 11)/2
Let m(v) be the third derivative of v**8/4032 - v**7/1260 - v**6/160 + 7*v**5/360 + 5*v**4/72 - v**3/3 - 1864*v**2. Find l, given that m(l) = 0.
-2, 1, 2, 3
Let a(s) be the second derivative of 2/63*s**7 + 12 + 3*s + 0*s**3 - 4/9*s**4 - 4/45*s**6 - 7/15*s**5 + 0*s**2. Factor a(p).
4*p**2*(p - 4)*(p + 1)**2/3
Let g be (-1925)/231 - ((-20)/4 - 8). Let -6*a - 4/3 - g*a**2 = 0. What is a?
-1, -2/7
Solve 58/11*u**2 + 2 + 86/11*u - 6/11*u**3 = 0.
-1, -1/3, 11
Let p = 128526 - 128523. Factor -81/2 + 0*g**2 + 1/2*g**4 + 27*g - 3*g**p.
(g - 3)**3*(g + 3)/2
Let w(f) be the first derivative of -18*f - 1/20*f**5 + 21/2*f**2 - 112 - 9/16*f**4 - 1/6*f**3. Factor w(i).
-(i - 2)*(i - 1)*(i + 6)**2/4
Let l(z) be the third derivative of -z**8/100800 - z**7/4200 + z**6/225 - 13*z**5/10 - 2*z**2 - 142. Let d(k) be the third derivative of l(k). Factor d(x).
-(x - 2)*(x + 8)/5
Let r be (-4)/(-3) + (-2)/(-5)*793/366. Factor -1/5*h**3 + r*h**2 + 9 - 39/5*h.
-(h - 5)*(h - 3)**2/5
Let q(k) be the third derivative of -60/11*k**3 - 8/11*k**4 + 0*k - 1/660*k**6 + 0 + 82*k**2 - 17/330*k**5. Factor q(a).
-2*(a + 5)*(a + 6)**2/11
Let z(u) be the third derivative of 1/1470*u**7 - 1/140*u**5 + 21*u**2 - 2*u + 0*u**3 + 1/84*u**4 + 0*u**6 + 0. Suppose z(h) = 0. Calculate h.
-2, 0, 1
Let t(l) = -l**3 + 2*l**2 - l + 2. Let i(m) = -18*m**5 - 44*m**4 - 28*m**3 - 20*m**2 + 6*m - 12. Let n = -44 - -50. Let f(o) = n*t(o) + i(o). Factor f(b).
-2*b**2*(b + 1)**2*(9*b + 4)
Let g(x) be the second derivative of -x**4/9 + 1252*x**3/3 - 587814*x**2 + 271*x + 2. Factor g(s).
-4*(s - 939)**2/3
Let i = 31 + -15. Let -72 + 27*y**3 + i*y**2 + 12*y - 18*y**3 - 13*y**3 = 0. What is y?
-2, 3
Let k be 3*(-110)/275*5/(-21). Suppose 0*d - 2/7*d**2 + 0 + 2/7*d**5 - k*d**3 + 2/7*d**4 = 0. What is d?
-1, 0, 1
Suppose 29 = 3*f + 4*r + 9, -5*f = -r - 41. Let q be 70/15*12/f. Determine m, given that 5 + m + 0 + m**2 - q = 0.
-2, 1
Let y(a) be the second derivative of a**4/48 - 11*a**3/6 - 357*a**2/8 + 5469*a. Determine x, given that y(x) = 0.
-7, 51
Suppose s = 6*s - 20. Let z be 4/78*(-3133)/(-723). Factor -1/9*v**s - 1/9*v + z*v**3 - 1/9 - 1/9*v**5 + 2/9*v**2.
-(v - 1)**2*(v + 1)**3/9
Let u(v) be the second derivative of 69 + 1/120*v**6 + 3*v + 1/6*v**3 - 1/80*v**5 - 1/12*v**4 + 0*v**2. Factor u(l).
l*(l - 2)*(l - 1)*(l + 2)/4
Let w = -214 + 216. Determine k so that 31*k - 5*k**4 + 6*k**3 + 27*k**3 + 4*k**4 - 43*k**2 - 30*k**w + 10*k**2 = 0.
0, 1, 31
Let w = 586/511 + -148/511. What is t in 3/7 - w*t**3 - 9/7*t**2 + 0*t = 0?
-1, 1/2
Let f(a) be the third derivative of -2*a**7/105 + 59*a**6/30 - 794*a**5/15 + 1712*a**4/3 - 1792*a**3 + 1