 t(p) = p**4 + 3*p**2 - 2. Let f(a) = -44*t(a) - 2*v(a). Factor f(y).
-4*y*(y + 1)*(y + 3)*(y + 12)
Let s(v) be the third derivative of -v**6/30 + 19*v**5/15 - 3*v**4 + 2*v**2 + 271*v + 12. Factor s(z).
-4*z*(z - 18)*(z - 1)
Suppose -1 = f - g, 0 = -5*f - 2*g - 3*g + 25. Suppose -f*l = -v - 1 - 37, 0 = 2*v. Solve l*b + 1 - 4*b + 3*b**2 - 1 = 0.
-5, 0
Factor 0 + 14*y - 23/2*y**2 + 1/4*y**4 - 11/4*y**3.
y*(y - 14)*(y - 1)*(y + 4)/4
Let c(j) be the first derivative of 21/2*j**2 - 6*j - 191 + 4*j**3. Suppose c(n) = 0. Calculate n.
-2, 1/4
Let b = -499049/4 - -124763. Find a, given that -1/4*a**3 + 9/4 - 5/4*a**2 - b*a = 0.
-3, 1
Let a(z) be the third derivative of z**7/840 - 61*z**6/480 - 21*z**5/40 - 2*z**2 - 2612. Factor a(b).
b**2*(b - 63)*(b + 2)/4
Let v(s) be the first derivative of -21 + 7/6*s**6 + 32*s**2 - 16*s - 16/3*s**3 + s**5 - 11*s**4. Find a, given that v(a) = 0.
-2, 2/7, 1, 2
Factor 117 - 43 - 125*c**2 + 15*c + 238 + 122*c**2.
-3*(c - 13)*(c + 8)
Suppose -8*a + 3*a - 50 = -3*i, i + 3*a + 2 = 0. Suppose 2*p = -i, 9*x - p - 13 = 7*x. Factor -4*t**2 + x*t**2 - 8 - t**2 + 6*t.
-(t - 4)*(t - 2)
Suppose 3 = 5*x - 17. Suppose -5*k + 0*m + 13 = 3*m, 2*m - 10 = -x*k. Factor -6*z - 9*z**2 - 4*z + 7*z**k - 3*z**2.
-5*z*(z + 2)
Let h(c) be the third derivative of -c**6/280 + 3*c**5/140 + 3*c**4/28 - 4*c**3/7 + 1324*c**2. Determine g so that h(g) = 0.
-2, 1, 4
Let m = 60 + -55. Suppose s + m*s = 24. Suppose -3 + 3 - s*t - 4*t**2 + 0 = 0. What is t?
-1, 0
Find f, given that 227/11*f**2 - 82/11*f**3 - 78/11*f + 0 + 5/11*f**4 = 0.
0, 2/5, 3, 13
Let s(c) = c**3 + 66*c**2 + 31*c + 142. Let t be s(-66). Let j = 24754/13 + t. Factor -j*v**2 - 162/13 + 36/13*v.
-2*(v - 9)**2/13
Let i(a) be the first derivative of 0*a + 9/2*a**4 + 14/3*a**3 + 2*a**2 + 191 + 1/3*a**6 + 2*a**5. Factor i(l).
2*l*(l + 1)**3*(l + 2)
Suppose 28 = u + 26. Factor 3*q**2 + 4*q + 6*q**u - 12*q**2 + 23*q.
-3*q*(q - 9)
Let d(p) be the first derivative of 3*p**5/20 - 3*p**4/4 - 5*p**3/4 + 27*p**2/2 - 27*p + 1341. Determine b, given that d(b) = 0.
-3, 2, 3
Let l(v) be the second derivative of -v**7/21 + v**6 + 33*v**5/10 + 17*v**4/6 + 24*v + 8. Determine d so that l(d) = 0.
-1, 0, 17
What is n in 36*n**4 + 48 - 69*n - 44*n**3 + 188*n**2 + 174*n - 92*n**4 + 119*n = 0?
-3/2, -1, -2/7, 2
Let u = -122 + 134. Factor 20*n**5 - 26*n**3 - 23*n**2 - 8*n - u*n**4 + n**2 - 22*n**5 - 2*n**2.
-2*n*(n + 1)**2*(n + 2)**2
Let y(p) be the second derivative of p**6/90 + p**5/8 - p**4/6 - 53*p**3/6 - 8*p. Let a(i) be the second derivative of y(i). Determine q so that a(q) = 0.
-4, 1/4
Let z be -589*(-71)/2201 + -16. Let j be 5/6 + 2/4. Determine f so that -j*f**2 - 8/9 + 2/9*f**z + 2*f = 0.
1, 4
Let o(a) be the third derivative of 5/4*a**4 + 0 + 0*a - 1/12*a**5 + 97*a**2 + 35/6*a**3. Factor o(q).
-5*(q - 7)*(q + 1)
Let a(r) = 62*r - 431. Let c be a(7). Let j(w) be the second derivative of -18*w + 0 - 1/6*w**4 - 2*w**2 + w**c. Find q, given that j(q) = 0.
1, 2
Let g(i) be the third derivative of -13/1050*i**7 - 17/24*i**4 - 53/150*i**5 + 0 - 29/300*i**6 - 5/6*i**3 - 1/1680*i**8 + 183*i**2 + 0*i. Factor g(r).
-(r + 1)**3*(r + 5)**2/5
Let s = -9422 - -9425. Let t(g) be the third derivative of -16*g**2 + 1/36*g**4 - 1/540*g**5 - 4/27*g**s + 0*g + 0. Factor t(l).
-(l - 4)*(l - 2)/9
Find k, given that 0 - 11/8*k**3 + 0*k - 53/8*k**2 = 0.
-53/11, 0
Let x(w) = -7*w**3 - 77*w**2 + 227*w - 245. Let h(g) = 3*g**3 + 36*g**2 - 114*g + 122. Let r(u) = 15*h(u) + 6*x(u). Factor r(q).
3*(q - 2)**2*(q + 30)
Let p(d) = -3*d**2 - 4*d - 1. Let x(s) = 4*s**2 - 17*s + 81. Let l(k) = -p(k) - x(k). Factor l(a).
-(a - 16)*(a - 5)
Suppose -18 = 3*d + 2*u, 16*d - 5*u + 156 = 248. Let 5/2*q**d + 10240 - 320*q = 0. What is q?
64
Suppose -1710 = -8*k + 514. Let g = 1947/7 - k. Factor 0 - g*y**5 + 0*y + 3/7*y**2 + 5/7*y**3 + 1/7*y**4.
-y**2*(y - 3)*(y + 1)**2/7
Let w be (-6)/21 - ((-243)/70)/9. Let t(g) be the second derivative of 4*g**2 + 0 + 1/3*g**4 - 7/3*g**3 + 21*g + w*g**5. Find n, given that t(n) = 0.
-4, 1
Let n(b) be the third derivative of b**8/896 - 19*b**7/560 + b**6/160 + 401*b**5/80 + 2301*b**4/64 + 1521*b**3/16 - 1596*b**2. Suppose n(i) = 0. Calculate i.
-3, -1, 13
Let q = 418 + -414. Suppose 4 + 5 = -3*o - 3*j, q*j + 28 = 4*o. Factor -1/2*p - 2*p**o - 5/2*p**3 + 0 - p**4.
-p*(p + 1)**2*(2*p + 1)/2
Let 126025 + 1/2*p**3 + 356*p**2 + 127445/2*p = 0. Calculate p.
-355, -2
Let u be 612/(-170)*150/(-810). What is r in 0 + 32/3*r**2 - u*r**3 - 128/3*r = 0?
0, 8
Let o = -695 + 698. Suppose -o*f + 28*f + 11*f = 0. Determine p so that -2/7*p**2 + f - 6/7*p = 0.
-3, 0
Let w be 260/210 + (-12)/21. Let c(a) be the third derivative of -1/4*a**4 + 1/60*a**6 + 0*a + w*a**3 + 0 - 12*a**2 + 0*a**5. What is g in c(g) = 0?
-2, 1
Let h be (-108)/(-18)*(1 + 0). Let f be (40/h)/(5*(-2)/(-15)). Let d(p) = -p - 1. Let b(t) = 2*t**2 - 12*t - 10. Let l(j) = f*d(j) - b(j). Factor l(i).
-2*i*(i - 1)
Let b = 5337 - 5335. Let w(h) be the first derivative of -12 - 4/9*h**3 + 0*h + 1/6*h**4 + 1/3*h**b. Factor w(g).
2*g*(g - 1)**2/3
Let y = -19 + 15. Let a be (y/5)/((-20)/100). Factor 0*o**2 - 4*o**4 - 3 - 2*o**4 + 3*o**a + 6*o**2.
-3*(o - 1)**2*(o + 1)**2
Let w be (35/(-50))/(-7) - (-98)/20. Suppose -20*l**3 + 65321*l**w - 5*l**4 + 5*l**2 + 15*l**2 - 65316*l**5 = 0. What is l?
-2, 0, 1, 2
Let l(i) be the second derivative of -40*i - 1/30*i**6 + 0 + 1/12*i**4 - 9/20*i**5 + 3/2*i**3 + 0*i**2. What is m in l(m) = 0?
-9, -1, 0, 1
Suppose 0 = -5*b + h - 6, 4*b + 23 = 4*h - 1. Suppose -1/5*v**4 + 0*v - 3/5*v**2 + b - 4/5*v**3 = 0. What is v?
-3, -1, 0
Let t(c) = 9*c**2 + 634*c + 2642. Let a be t(-66). Suppose 6272 + 672*s + 2/7*s**3 + 24*s**a = 0. What is s?
-28
Let p be (5 + -7)/(3/(-10)) - (13 + -7). Let t(g) be the first derivative of -2/27*g**3 - p*g - 6 + 4/9*g**2. Factor t(q).
-2*(q - 3)*(q - 1)/9
Suppose -11*k - 11*k = -2*k - 60. Let v(y) be the third derivative of -13*y**2 + 0*y**k + 1/30*y**6 + 0 - 1/5*y**5 + 1/3*y**4 + 0*y. Factor v(w).
4*w*(w - 2)*(w - 1)
Suppose -9*o**2 + 332*o - 3*o**2 - 11*o**2 + 23*o**2 - 1296 - 2*o**2 = 0. What is o?
4, 162
Suppose -59*v - 53394 = -53394. Solve v + 15/4*u**3 + 7/2*u**2 + 1/4*u**4 + 0*u = 0.
-14, -1, 0
Let p(f) = -4*f**2 + 4*f - 10. Let x be p(3). Let j = x + 40. Factor j*o**2 + 6*o**2 + 0*o**2 - 3*o**2 - 12*o + 3*o**3.
3*o*(o - 1)*(o + 4)
Let i(n) be the first derivative of -10 - 15/8*n**4 - 65/12*n**3 - 5*n - 15/2*n**2 - 1/4*n**5. Factor i(t).
-5*(t + 1)**2*(t + 2)**2/4
Factor -1438/5*a**2 + 2882/5*a - 1442/5 - 2/5*a**3.
-2*(a - 1)**2*(a + 721)/5
Let i(k) = 86*k + 107*k**2 - 230*k**2 - 42 + 42*k**3 - 9*k + 37*k. Let h(y) = -y**4 + 2*y**3 - y**2 + 2*y + 1. Let n(w) = 3*h(w) + i(w). Factor n(z).
-3*(z - 13)*(z - 1)**3
Let a(n) be the second derivative of 2*n**6/15 - 17*n**5/5 - 37*n**4/3 - 38*n**3/3 + n + 2295. Suppose a(f) = 0. Calculate f.
-1, 0, 19
Let w(f) be the third derivative of -f**6/120 + 23*f**5/45 - 55*f**4/72 - 25*f**3/3 + f**2 + 139*f. Factor w(i).
-(i - 30)*(i + 1)*(3*i - 5)/3
Let b(h) be the second derivative of h**6/15 - 11*h**5/2 - 19*h**4/2 + 55*h**3/3 + 56*h**2 - 47*h + 1. Factor b(o).
2*(o - 56)*(o - 1)*(o + 1)**2
Suppose 1338/7*p**2 + 6/7*p**5 + 774/7*p**3 + 1020/7*p + 174/7*p**4 + 288/7 = 0. Calculate p.
-24, -2, -1
Factor 6998718 - 39027369 - 31510*k - 17615354 - 5*k**2.
-5*(k + 3151)**2
Let v(c) be the second derivative of -8*c**7/189 - 28*c**6/135 - c**5/15 + 23*c**4/54 + 16*c**3/27 + c**2/3 - 5*c - 62. Solve v(d) = 0.
-3, -1/2, 1
Solve 40/3*r**2 + 8/3*r**3 + 0*r + 0 - 10/3*r**4 - 2/3*r**5 = 0 for r.
-5, -2, 0, 2
Find s such that 0 + 2/7*s**4 - 16/7*s**3 + 256/7*s - 32/7*s**2 = 0.
-4, 0, 4, 8
Suppose -3*f - 3*w - 33 = 0, -5*f + 3*w + 11 - 50 = 0. Let u = f + 14. Factor -10*s**3 + s**2 + 25*s**3 - 4*s**4 - 6*s**2 - 11*s**4 + 5*s**u.
5*s**2*(s - 1)**3
Let j(v) = -12*v**5 - 783*v**4 - 2427*v**3 - 2793*v**2. Let c(r) = 3*r**5 + 200*r**4 + 607*r**3 + 698*r**2. Let o(x) = -15*c(x) - 4*j(x). Solve o(b) = 0 for b.
-39, -3, -2, 0
Let b(f) = 5*f**3 + 5*f**2. Let v(s) be the second derivative of -1/12*s**4 + 0*s**2 - 12*s + 0*s**3 - 1/20*s**5 + 0. Let q(h) = -b(h) - 3*v(h). Factor q(i).
-2*i**2*(i + 1)
Let y be ((-100)/45)/((-25)/60) + -2. Let u(n) be the second derivative of 25/12*n**4 +