v(t) be the third derivative of t**8/10080 - t**6/360 + t**5/90 - 7*t**4/12 + 9*t**2. Let s(q) be the second derivative of v(q). Factor s(f).
2*(f - 1)**2*(f + 2)/3
Let y(b) = 5*b**3 - 744*b**2 + 60518*b - 1654104. Let l(v) = v**3 - 3*v**2 + v. Let t(m) = -2*l(m) + y(m). Suppose t(c) = 0. Calculate c.
82
Let c(o) be the third derivative of o**5/40 - 3*o**4/16 + o**3/2 + 61*o**2. Find y, given that c(y) = 0.
1, 2
Suppose -2*l - 4 = -4*v + 10, -4*l = -4*v + 8. Let a be l - (-3 + 1) - 2. Suppose 6*j**2 + 2 + 0 - a*j**3 + 6*j + 5*j**3 + 0*j**3 = 0. Calculate j.
-1
Suppose 0 = 5*p + 3 + 17, 2*p = 5*w - 83. Factor -16*r**2 - 3*r**4 + 34*r**2 - w*r**2.
-3*r**2*(r - 1)*(r + 1)
Let d = 50 + -27. Let g = d + -22. Factor -g - 30*h - 150*h**2 - 4 - 327*h**3 + 77*h**3 + 3.
-2*(5*h + 1)**3
Suppose 6 = -3*d - 3*m, -3*d - 14 = -0*m + m. Let h(w) = 26*w + 156. Let s be h(d). What is q in 0*q - 3/7*q**4 + s + 3/7*q**2 + 3/7*q**3 - 3/7*q**5 = 0?
-1, 0, 1
Let q(s) = s**2 + 9*s - 20. Let p be q(2). Determine y so that -1/3*y**p + 2/3*y - 1/3*y**3 + 0 = 0.
-2, 0, 1
Suppose 3*y + 5*l - 32 = 0, 4*y - 32 = -5*l + l. Let s be 1/(1/10)*1/y. Let -s*c**4 + 0 - c**3 + c + 5/2*c**2 = 0. What is c?
-1, -2/5, 0, 1
Let w(y) be the third derivative of 0*y - 5/2*y**3 + 8*y**2 + 0 - 5/12*y**4 - 1/42*y**7 + 1/3*y**5 + 1/12*y**6. Factor w(t).
-5*(t - 3)*(t - 1)*(t + 1)**2
Let b(r) be the second derivative of r**7/504 - r**6/9 + 8*r**5/3 - r**4/6 + 30*r. Let m(x) be the third derivative of b(x). Factor m(d).
5*(d - 8)**2
Let l(i) be the third derivative of -i**7/630 - 37*i**6/60 - 1369*i**5/15 - 50653*i**4/9 + 123*i**2 + 3. Factor l(g).
-g*(g + 74)**3/3
Let n(z) be the third derivative of -z**8/168 - 2*z**7/105 + z**6/30 + 2*z**5/15 - z**4/12 - 2*z**3/3 - 34*z**2. Find h, given that n(h) = 0.
-2, -1, 1
Let f be 2/(((-8)/(-60) + 0)*3). Solve 129*u**4 - 216*u**3 - 227*u**2 + 435*u**2 - 16*u**f - 29*u**4 - 88*u + 12 = 0.
1/4, 1, 3
Suppose 0 = 11*g - 5 + 5. Let u(j) be the third derivative of 0*j**3 + 0*j**5 - 1/210*j**7 + 0*j**4 + 1/360*j**6 - 1/252*j**8 + g*j + 4*j**2 + 0. Factor u(y).
-y**3*(y + 1)*(4*y - 1)/3
Let d(b) = -b**3 - 23*b**2 + 4. Let z be d(-23). Factor 4*i**2 + 2*i**5 + 4*i**3 + 2 - i**4 - 5*i**z + i - 7*i + 0*i.
2*(i - 1)**4*(i + 1)
Factor -52/5*l + 18/5 + 48/5*l**2 - 2/5*l**4 - 12/5*l**3.
-2*(l - 1)**3*(l + 9)/5
Let x(l) be the first derivative of 1/9*l**3 + 3*l - 18 + l**2. Factor x(g).
(g + 3)**2/3
Let n = -416/3 - -140. Suppose 95*q - 12 = 91*q - 2*f, -2*q - 4 = -4*f. What is u in 4/3*u + 8/3 - n*u**q = 0?
-1, 2
Let a(t) be the third derivative of -t**5/150 + t**4/30 - t**3/15 - 54*t**2 + 1. Find s such that a(s) = 0.
1
Let h(i) be the third derivative of -i**6/30 + 8*i**5/15 - 17*i**4/6 + 20*i**3/3 + 23*i**2. Solve h(x) = 0 for x.
1, 2, 5
Let t(d) be the second derivative of 0 + 16/11*d**2 - 9*d + 1/66*d**4 + 8/33*d**3. Factor t(v).
2*(v + 4)**2/11
Let a = 3356/2805 - -2/561. Let t(s) be the first derivative of 2/15*s**3 - a*s**2 + 18/5*s - 2. Factor t(d).
2*(d - 3)**2/5
Let y(c) be the first derivative of -c**4/12 - 19*c**3/9 + 41*c**2/6 - 7*c + 161. Factor y(m).
-(m - 1)**2*(m + 21)/3
Let b(p) be the first derivative of p**6/30 - p**5/10 + p**4/12 + 8*p + 4. Let z(k) be the first derivative of b(k). Let z(f) = 0. Calculate f.
0, 1
Let b(s) be the second derivative of s**4/16 - 25*s**3/8 + 69*s**2/4 + 7*s - 26. Determine j, given that b(j) = 0.
2, 23
Let q(z) = 2 - 83*z**3 + 78*z**2 - 7*z + 8*z + 18*z**4 - 18*z. Let d(l) = -53*l**4 + 248*l**3 - 233*l**2 + 52*l - 7. Let i(p) = 2*d(p) + 7*q(p). Factor i(a).
5*a*(a - 3)*(a - 1)*(4*a - 1)
Solve 50/9*v - 70/9*v**2 + 0 - 2/9*v**4 + 22/9*v**3 = 0 for v.
0, 1, 5
Let m(i) be the second derivative of -i**7/2520 + i**5/120 - 3*i**4/4 + 6*i. Let x(w) be the third derivative of m(w). Factor x(s).
-(s - 1)*(s + 1)
Let h(o) be the first derivative of o**4/20 + o**3/15 - o**2/10 - o/5 + 84. Factor h(j).
(j - 1)*(j + 1)**2/5
Let p(r) = 15*r**4 + 30*r**3 + 20*r**2 - 20*r. Let b(a) be the third derivative of a**7/210 - a**6/120 - 25*a**2. Let z(k) = -5*b(k) + p(k). Factor z(n).
5*n*(n + 2)**2*(2*n - 1)
Factor 10 + 3*c**2 - 21*c + 49 - 5 - 14 - 10.
3*(c - 5)*(c - 2)
Let v be (-7*2/(-7))/((-2)/12). Let p(o) = -o**3 - 10*o**2 + 24*o + 2. Let j be p(v). Factor 8/3*r**j + 4/9 + 22/9*r.
2*(3*r + 2)*(4*r + 1)/9
Let 3*p**5 + 36*p**2 + 0*p**2 - 2*p**4 - 16*p**4 + 23*p - 6*p**3 - 20*p - 18 = 0. What is p?
-1, 1, 6
Let n(f) be the third derivative of -f**7/120 + 47*f**6/480 + 7*f**5/80 - 47*f**4/96 - 7*f**3/12 - 863*f**2. Solve n(j) = 0 for j.
-1, -2/7, 1, 7
Let k(a) = a**3 - 7*a**2 - 9*a + 16. Let g be k(8). Factor -h**2 - 3*h**2 - g*h + 0*h + 12 + 0*h**2.
-4*(h - 1)*(h + 3)
Let b(f) be the second derivative of f**7/84 + 7*f**6/30 + 49*f**5/40 + f + 2. Solve b(j) = 0.
-7, 0
Let k(c) be the third derivative of -c**5/120 - c**4/24 + 2*c**3/3 + 53*c**2. Determine m, given that k(m) = 0.
-4, 2
Let z(r) = -55*r**3 + 190*r**2 - 240*r + 80. Let w(i) = 8*i**3 - 27*i**2 + 34*i - 12. Let g(c) = 20*w(c) + 3*z(c). Factor g(a).
-5*a*(a - 4)*(a - 2)
Suppose -6 = -5*b + 62*n - 65*n, 8 = -5*b + 4*n. Factor -1/4*y**3 + 1/2*y**2 + b - 1/4*y.
-y*(y - 1)**2/4
Let c be (-2)/(-3) - -1 - (-21)/63. Let -5*v**2 - v**2 + 4*v**c - v**2 - 9*v - 6 = 0. Calculate v.
-2, -1
Let l(p) be the third derivative of p**7/1155 + p**6/165 + p**5/110 - p**4/33 - 4*p**3/33 - 230*p**2. Suppose l(g) = 0. Calculate g.
-2, -1, 1
Factor -22/7*l**3 + 1/7*l**5 - 3/7*l**4 - 38/7*l**2 - 27/7*l - 1.
(l - 7)*(l + 1)**4/7
Let p be ((-7)/(-21))/((-2)/(-60)). Factor -20*q + p*q**2 - 99 + 37 + 22 + 5*q**3.
5*(q - 2)*(q + 2)**2
Let a = -9839 - -9842. Factor -3/2*z + 3/4*z**2 + 0 + 3/4*z**a.
3*z*(z - 1)*(z + 2)/4
Factor 4*h**4 - 8 + 20*h - 3075*h**5 + 6139*h**5 - 3065*h**5 - 14*h**2 - h**3.
-(h - 2)**2*(h - 1)**2*(h + 2)
Let y(c) be the first derivative of -c**6/180 + c**4/12 + 32*c**3/3 - 1. Let z(v) be the third derivative of y(v). Factor z(g).
-2*(g - 1)*(g + 1)
Let k be 4/((-58)/10 + 6). Let g be k/(-15)*(-3)/30. Factor g*z**3 - 2/15*z + 2/15 - 2/15*z**2.
2*(z - 1)**2*(z + 1)/15
Suppose -50 = -11*k - 6. Factor 2*s**k + 9*s**3 + 30*s**2 - 24*s**2 + s**4.
3*s**2*(s + 1)*(s + 2)
Let r(m) be the second derivative of 0*m**3 + 1/75*m**6 + 0*m**4 + 0 + 0*m**2 + 1/100*m**5 - 2*m + 1/210*m**7. Factor r(y).
y**3*(y + 1)**2/5
Let v(q) = q + 13. Let g be v(-11). Suppose 0 = -4*i - g*i + 12. Factor -3*m**5 - 5*m**2 - 3*m - 1 - 3*m**4 + 11*m**i + 6*m**3 - 2.
-3*(m - 1)**2*(m + 1)**3
Let l(g) be the first derivative of -3*g**5/5 + 9*g**3 - 6*g**2 - 36*g + 437. Factor l(t).
-3*(t - 2)**2*(t + 1)*(t + 3)
Let a(h) be the first derivative of 3*h**4/8 - 4*h**3 + 39*h**2/4 - 9*h + 157. Find r such that a(r) = 0.
1, 6
Let q(n) = -14*n - 46. Let j be q(-11). Let t = j - 103. Find p such that 5/3*p**t + 0 - 2/3*p**4 + 2/3*p**2 - 5/3*p**3 + 0*p = 0.
-1, 0, 2/5, 1
Let y(g) = -7*g - 257. Let a be y(-37). Factor -2/7*f**a - 2/7*f + 0.
-2*f*(f + 1)/7
Let f(r) be the second derivative of -3*r**6/40 + 17*r**5/20 - 21*r**4/8 - 9*r**3/2 + 7*r**2/2 - 8*r. Let g(s) be the first derivative of f(s). Factor g(z).
-3*(z - 3)**2*(3*z + 1)
Suppose 0 = 5006*v - 4980*v - 1404. Factor 324 + 1/4*w**4 + v*w**2 - 6*w**3 - 216*w.
(w - 6)**4/4
Let r(i) be the first derivative of 1/2*i**4 + 2/5*i**5 - i**2 + 0*i - 11 - 2/3*i**3. Find a such that r(a) = 0.
-1, 0, 1
Let z(h) be the second derivative of h**4/36 - 4*h**3/9 + 8*h**2/3 - 50*h. Let z(l) = 0. Calculate l.
4
Let c = -10 - -2. Let g be (-108)/c*2/3. Find b, given that 2*b - 7*b**2 - 12*b**3 + 2*b**5 - 8*b - g*b**2 = 0.
-1, 0, 3
Suppose 1/4*l**3 - 5/2*l**2 + 1/4*l**5 + 2 - l + l**4 = 0. What is l?
-2, 1
Let l(o) be the first derivative of -2/7*o - 2/21*o**3 + 2/7*o**2 - 11. Determine m so that l(m) = 0.
1
Suppose -2 - 14 = 4*g. Let x be 5/7 - g/14. Suppose -12*p**3 - 2 - 6 + 8*p**2 + 12*p - x + 1 = 0. Calculate p.
-1, 2/3, 1
Let t(u) = -24*u**3 - 24*u**2 + 17*u - 4. Let s(k) = -8*k**3 - 7*k**2 + 6*k - 1. Let h(b) = 14*s(b) - 4*t(b). Factor h(n).
-2*(n - 1)*(n + 1)*(8*n + 1)
Factor -2*w + 2/9*w**3 + 8/9*w**2 - 8.
2*(w - 3)*(w + 3)*(w + 4)/9
Let d(b) be the second derivative of -b**5/8 - 335*b**4/24 - 424*b. Factor d(j).
-5*j**2*(j + 67)/2
Let z be ((-4)/(-3))/((-2)/(-6)). Factor -c**3 