 1/7*p**4 - 40/7*p**2. Factor d(y).
4*y*(y - 1)*(y + 20)/7
Suppose 127*v - 112 = 71*v. Let h(a) be the second derivative of -19*a + 0 - 1/10*a**5 + 0*a**v + 0*a**3 - 1/2*a**4. Determine q so that h(q) = 0.
-3, 0
Suppose 4*f - 20 = -4*u, -15 - 5 = 3*u - 4*f. Factor 64*a + 4*a**2 + u*a**2 + 80 - 3460*a**3 + 3456*a**3.
-4*(a - 5)*(a + 2)**2
Let t(y) be the third derivative of -y**5/60 + 523*y**4/24 - 87*y**3 + 20*y**2 + 25*y + 2. Factor t(c).
-(c - 522)*(c - 1)
Let t(a) be the third derivative of -a**6/160 + 243*a**5/80 - 945*a**4/2 + 5400*a**3 - 5291*a**2. Solve t(l) = 0 for l.
3, 120
Let s(z) be the first derivative of 2/3*z**6 + 0*z**3 + 16 + 5*z**4 + 24/5*z**5 + 0*z**2 + 0*z. Factor s(f).
4*f**3*(f + 1)*(f + 5)
Let c = -13536 + 13541. Let v(t) be the first derivative of -7/5*t**5 + 1/6*t**6 - 2/3*t**3 - 15/2*t**2 + 7/2*t**4 - c + 9*t. Factor v(y).
(y - 3)**2*(y - 1)**2*(y + 1)
Let s(h) be the second derivative of -h**6/60 + 3*h**5/10 - 2*h**4 + 16*h**3/3 + 191*h**2/2 + 14*h + 5. Let l(b) be the first derivative of s(b). Factor l(q).
-2*(q - 4)**2*(q - 1)
Let w(v) be the second derivative of -4 + 32/19*v**2 + 1/190*v**5 - 5/114*v**4 - 28/57*v**3 + 4*v. Factor w(m).
2*(m - 8)*(m - 1)*(m + 4)/19
Factor 135 + 3/2*h**3 - 153/2*h + 6*h**2.
3*(h - 3)**2*(h + 10)/2
Let o(z) = -5*z**5 + 5*z**4 - 34*z**3 - 8*z**2 - 6. Let p(h) = 24*h**5 - 23*h**4 + 171*h**3 + 46*h**2 + 29. Let b(y) = -29*o(y) - 6*p(y). Solve b(l) = 0.
-2, 0, 11
Let l(a) be the third derivative of -a**5/100 - 281*a**4/40 - 417*a**3/5 - a**2 - 231*a + 1. Suppose l(j) = 0. Calculate j.
-278, -3
Determine w so that -5272*w**2 - 5129*w**2 - 3*w**4 + 10554*w**2 + 150*w**3 = 0.
-1, 0, 51
Let d(a) = -5*a**2 - a - 6. Let l(j) = -54*j**2 - 2450*j - 4924. Let r(y) = 10*d(y) - l(y). Factor r(b).
4*(b + 2)*(b + 608)
Let m be (0/(7 - 11))/3. Let l(v) be the second derivative of -4/7*v**3 + 4*v - 1/28*v**4 - 24/7*v**2 + m. Factor l(f).
-3*(f + 4)**2/7
Let p(k) = 2*k**2 + 19*k + 48. Let m be p(-4). Suppose -m*t - 5*c - 33 = -8*t, c + 5 = 0. Factor -2/3*g**3 - 4/3*g + t*g**2 + 0.
-2*g*(g - 2)*(g - 1)/3
Let d(a) = a**3 + 15*a**2 + 34*a + 113. Let q be d(-13). Let t(b) be the first derivative of -3/20*b**4 - 2/15*b**3 + q + 7/10*b**2 - 2/5*b. Factor t(r).
-(r - 1)*(r + 2)*(3*r - 1)/5
Let l(w) be the third derivative of -w**6/30 - 97*w**5/15 - 1480*w**4/3 - 54400*w**3/3 + 7*w**2 + 69. Factor l(c).
-4*(c + 17)*(c + 40)**2
Find h, given that 20*h**2 - 4/5*h**3 + 0*h + 0 = 0.
0, 25
Let f(y) be the second derivative of 0*y**2 + 12*y + 5/6*y**3 + 2/3*y**4 + 0. Let s(x) = 39*x**2 + 24*x. Let c(z) = 24*f(z) - 5*s(z). Solve c(i) = 0 for i.
0
Let d(c) be the first derivative of -2*c**6/3 + 94*c**5/5 - 201*c**4 + 3056*c**3/3 - 2560*c**2 + 3072*c - 8105. Suppose d(s) = 0. Calculate s.
3/2, 2, 4, 8
Suppose 8 = -4*c + j + 12, c = -3*j + 14. Factor -190*w + 21*w**2 + 16*w**2 - 49*w**c + 9*w**2 + 67*w.
-3*w*(w + 41)
Suppose 7*a + 40 = 9*a. Factor 4 - m**2 + a*m**2 - 23*m**2.
-4*(m - 1)*(m + 1)
Let g(y) be the third derivative of -y**5/30 - 184*y**4 - 406272*y**3 + 1377*y**2. Let g(z) = 0. Calculate z.
-1104
Let l = 1006 - 1000. Let s(h) = -h**3 + 4*h**2 - 4*h + 2. Let n be s(2). Suppose 2*w**4 + 2 - 9 - 4*w**3 - 1 - l*w**n + 16*w = 0. What is w?
-2, 1, 2
Let c(q) be the second derivative of 0*q**4 + 0*q**3 - 7/60*q**6 - 1/84*q**7 + 0 - 3/20*q**5 + 186*q + 0*q**2. Factor c(l).
-l**3*(l + 1)*(l + 6)/2
Let g(c) be the first derivative of 112*c + 28/3*c**3 - 200*c**2 + 55. Find t such that g(t) = 0.
2/7, 14
Let f(d) be the first derivative of -d**7/840 + d**6/96 - d**5/60 - d**2 + 15*d - 81. Let z(k) be the second derivative of f(k). Factor z(j).
-j**2*(j - 4)*(j - 1)/4
Let k(m) = 2*m**2 + 2. Let p be 2 + 5 - (0 - -4). Let l be k(p). Solve l*c - 12*c**2 + 5 + 7*c**2 - 20 = 0.
1, 3
Let h(j) = 33*j - 118. Let o be h(21). Let y be 1*o/210 - (-2)/(-12). Solve 0 + 93/7*n**2 + y*n + 111/7*n**3 + 15/7*n**4 - 3*n**5 = 0 for n.
-1, -2/7, 0, 3
Let a be 39492/61432*-21*2/(-9). Solve 5/4*x**4 + 1/4*x**5 - 21/4*x**a + 23/4*x**2 - 2*x + 0 = 0.
-8, 0, 1
Let s be ((-1397)/9779)/((-3)/36). Solve -2/7*w**4 + s*w**3 - 8/7*w**2 + 10/7 - 12/7*w = 0 for w.
-1, 1, 5
Let s be 42/12*(-139280)/(-56). Find q, given that 8705 - 305*q**3 + 60*q**2 + 25*q**4 - s = 0.
0, 1/5, 12
Let j be (2/16)/(3924/6976). Factor 1/3*d - 2/9*d**2 + j - 1/3*d**3.
-(d - 1)*(d + 1)*(3*d + 2)/9
Let l = -73/2856 + 8/119. Let m(u) be the third derivative of 0 + 0*u**3 + 18*u**2 - l*u**4 + 1/60*u**5 + 0*u. Factor m(j).
j*(j - 1)
Let q(w) be the second derivative of -13*w**6/180 - 23*w**5/30 + 97*w**4/72 + 2*w**3/9 - 1348*w. Let q(i) = 0. What is i?
-8, -1/13, 0, 1
Suppose g + 10 = -2*m, 3*g + 797*m - 793*m + 18 = 0. Factor -8/3 + 0*c + 2/3*c**g.
2*(c - 2)*(c + 2)/3
Suppose 798*t - 796*t - 8 = 0. Determine r so that 20/7*r**4 + 4/7*r**5 + 8/7*r**2 - 8*r**3 + 52/7*r - t = 0.
-7, -1, 1
Let l = -9934/40047 - -375749504/3056921. Let b = -2/687 + l. What is o in 96*o - 64/3 + 6*o**5 + b*o**3 - 44*o**4 - 160*o**2 = 0?
2/3, 2
Let z(s) be the first derivative of 38*s**6/3 + 72*s**5/5 - 20*s**4 - 24*s**3 + 2*s**2 + 9211. Solve z(i) = 0.
-1, 0, 1/19, 1
Let q = 3933 - 3933. Let k(j) be the third derivative of 22*j**2 + q*j + 5/4*j**4 + 0 + 15/2*j**3 + 1/12*j**5. Let k(w) = 0. What is w?
-3
Let m(p) be the first derivative of -2*p**5/65 - p**4/26 + 20*p**3/13 + 3669. Determine f, given that m(f) = 0.
-6, 0, 5
Let k = -17070 - -17072. Suppose 8/3 - 14/3*m + 4/3*m**k + 2/3*m**3 = 0. What is m?
-4, 1
Let k(n) be the second derivative of -8 - 3*n - 1/10*n**5 + 52/3*n**3 - 5/3*n**4 - 56*n**2. Find b, given that k(b) = 0.
-14, 2
Suppose -2*q = -3*a + 2*a - 17, -101 = 3*a + 4*q. Let y = a + 45. Let k(r) = -r - 1. Let h(w) = 3*w**2 - 6*w - 18. Let f(j) = y*k(j) - h(j). Solve f(v) = 0.
-4, 0
Let i(s) be the second derivative of 0 + 7/12*s**7 - 371/24*s**4 + 687/40*s**5 - 94*s - 329/60*s**6 - 3*s**2 - 38/3*s**3. Solve i(y) = 0 for y.
-1/7, 2, 3
Let x(q) be the first derivative of -53*q**5/20 + 107*q**4/16 - 55*q**3/12 + q**2/8 + 2650. Factor x(j).
-j*(j - 1)**2*(53*j - 1)/4
Factor -8460*a**3 + 59*a**2 + 8613*a**3 + 63 - 3201*a - 674*a**2.
3*(a - 7)*(a + 3)*(51*a - 1)
Let p(y) be the second derivative of -y**5/20 - 3*y**4/4 + 11*y**3/6 + 6*y**2 - 4*y. Let l be p(-10). Find m such that 9 + l*m**3 - m**3 - 9 = 0.
0
Suppose 0 = d + 19 - 21. Let a be ((-6)/(-171))/(18/81) - -1. Let -4/19 - 20/19*w**5 - 34/19*w**2 + d*w**4 + a*w - 2/19*w**3 = 0. Calculate w.
-1, 2/5, 1/2, 1
Let n be 15003/(-13336)*6/(-27). Determine f, given that 15/4*f - 3/2*f**3 - n*f**5 - 3/2*f**4 - 9/2 + 4*f**2 = 0.
-3, -2, 1
Suppose -19*c = -20*c + 37. Suppose -c*t + 80 - 35*t**2 + 228*t**3 - 223*t**3 - 13*t = 0. What is t?
-2, 1, 8
Determine k, given that -635/4*k - 5/4*k**2 + 160 = 0.
-128, 1
Let x(t) be the third derivative of 847*t**5/6 + 421*t**4/3 - 4*t**3/3 - 1155*t**2. Find m, given that x(m) = 0.
-2/5, 2/847
Let o(s) be the second derivative of 1/10*s**5 + 56*s**2 + 76/3*s**3 - 12*s + 0 + 5*s**4 - 1/15*s**6. Factor o(q).
-2*(q - 7)*(q + 2)**3
Let v(m) = 3*m**3 - 143*m**2 + 649*m + 360. Let b(o) = -3*o**3 + 72*o**2 - 324*o - 180. Let w(x) = -5*b(x) - 3*v(x). Factor w(k).
3*(k - 4)*(k + 15)*(2*k + 1)
Suppose -5*w + 2009 = 4*q + 2046, -4*w = 5*q + 26. Factor 2/3*v**q + 2/3 + 4/3*v.
2*(v + 1)**2/3
Let u(v) be the second derivative of 0*v**3 + 0 - 1/3*v**4 + 37*v - 1/30*v**6 - 1/5*v**5 - 11*v**2. Let d(k) be the first derivative of u(k). Factor d(q).
-4*q*(q + 1)*(q + 2)
Let t be (-2 - -12) + (-94 + 97)/(9/2). Let t - 2*j**2 + 44/3*j = 0. What is j?
-2/3, 8
Let g(w) be the third derivative of -w**8/4032 + w**7/504 - w**6/144 - w**5/10 + w**3/6 + 118*w**2. Let h(v) be the third derivative of g(v). Factor h(d).
-5*(d - 1)**2
Let i be (16/(-7))/((-29)/203). What is y in 2*y**4 - 18*y**2 - 24 + 40*y + 20*y**2 - 4*y**3 - i*y**2 = 0?
-3, 1, 2
Let c(u) be the second derivative of -u**4/21 + 114*u**3/7 - 18*u - 14. What is a in c(a) = 0?
0, 171
Find f such that -9316125/2 - 6825*f - 5/2*f**2 = 0.
-1365
Suppose -67*y - 48*y + 394 = 82*y. Let c(f) be the first derivative of 0*f + 2/5*f**5 - 1/2*f**4 - 8 - 10/3*f**3 - 3*f**y. Solve c(b) = 0 for b.
-1, 0, 3
Let j(z) be the first derivative of -z**4/2 - 504*z**3 - 190512*z**2 - 32006016*