*r**4 - 30*r**3 + 66*r**2 - 66*r + 16. Let k(q) = a*p(q) - 4*z(q). Factor k(l).
-2*(l - 10)*(l - 1)**3
Let l(m) be the first derivative of -4 + 0*m - 2/11*m**4 - 1/11*m**2 - 10/33*m**3. Suppose l(d) = 0. Calculate d.
-1, -1/4, 0
Let a(b) be the first derivative of b**5/20 + 11*b**4/16 + 3*b**3/2 - 400. Factor a(m).
m**2*(m + 2)*(m + 9)/4
Let a(c) be the second derivative of 3*c**5/20 + 5*c**4 + 50*c**3 - 142*c - 1. Suppose a(f) = 0. Calculate f.
-10, 0
Let j(w) = 16*w**3 + 104*w**2 - 11*w + 11. Let s(h) = -3*h**3 - 21*h**2 + 2*h - 2. Let b(p) = 2*j(p) + 11*s(p). Let b(m) = 0. Calculate m.
-23, 0
Factor -15*i - 1/4*i**2 + 61/4.
-(i - 1)*(i + 61)/4
Let g(x) be the second derivative of x**5/4 - 35*x**4/4 + 100*x**3 - 520*x**2 - 620*x - 2. Factor g(j).
5*(j - 13)*(j - 4)**2
Let z(t) = -10*t**3 - 840*t**2 + 1665*t - 830. Let i(l) = 13*l**3 + 839*l**2 - 1663*l + 829. Let y(r) = 5*i(r) + 6*z(r). Factor y(x).
5*(x - 167)*(x - 1)**2
Let l = 1861 - 1861. Let u(y) be the second derivative of 0*y**2 + l - 1/9*y**3 - 8*y - 1/54*y**4. Factor u(v).
-2*v*(v + 3)/9
Let y be 3*(-49)/84 - -2. Find p such that -1/4*p**2 + 0*p + y = 0.
-1, 1
Let g(y) be the third derivative of y**8/1680 - y**7/210 + y**6/72 - y**5/60 - 10*y**3/3 + 25*y**2. Let h(f) be the first derivative of g(f). Factor h(r).
r*(r - 2)*(r - 1)**2
Factor -457*c - 4*c**2 + 457*c + 9*c**2 - 20.
5*(c - 2)*(c + 2)
Let m(f) be the first derivative of f**4 - 220*f**3/3 + 606*f**2 - 1764*f + 565. Determine u, given that m(u) = 0.
3, 49
Let u be (99/(528/(-16)))/(3/(-5)). Let -o**3 + 1/2 - 1/3*o**2 + 1/6*o**u + 5/6*o - 1/6*o**4 = 0. Calculate o.
-1, 1, 3
Let c(i) be the first derivative of i**6/6 - 63*i**5 + 33075*i**4/4 - 385875*i**3 - 18. Let c(q) = 0. What is q?
0, 105
Suppose -2*f = -8*f - 6*f. Suppose 4*k = -8, 0 = -2*a - 5*k - f - 2. Find x such that 24/7*x + 96/7*x**a + 2/7 + 176/7*x**3 + 102/7*x**2 = 0.
-1, -1/3, -1/4
Let l(o) be the second derivative of 0 - 3/2*o**2 - 3/2*o**3 - 3/4*o**4 - 4*o - 3/20*o**5. Solve l(j) = 0 for j.
-1
Let p = -1691/7 + 242. Solve -6/7*r**2 + 0*r + p*r**3 + 0 = 0.
0, 2
Suppose 19*q - 10*q = 11*q. Let r = 8/165 - -2/15. Factor 4/11*u**3 + q*u + 6/11*u**2 - r.
2*(u + 1)**2*(2*u - 1)/11
Let v(o) be the third derivative of o**9/60480 - o**7/1680 - o**6/360 + 31*o**5/60 + 23*o**2. Let c(j) be the third derivative of v(j). Factor c(l).
(l - 2)*(l + 1)**2
Solve 0 + 0*s - 4/5*s**4 - 2*s**3 - 6/5*s**2 = 0.
-3/2, -1, 0
Let n be ((-6)/(-14) - 0) + 1760/385. Let f(q) be the first derivative of -1/20*q**4 + 0*q**3 + 6 + 0*q**2 - 1/25*q**n + 0*q. Factor f(m).
-m**3*(m + 1)/5
Let -2/9*m**2 + 26/9*m - 8 = 0. Calculate m.
4, 9
Let d(f) = f**3 - 11*f**2 - 13*f + 18. Let s be d(12). Suppose -3*r + z - 1 = -4, -2*z - s = 5*r. Solve -8/9*p**2 - 2/9*p**4 + r - 8/9*p**3 + 0*p = 0.
-2, 0
Let h(j) = 35*j**2 - 1. Suppose 3*b - 6 = -3*f, 0 = -2*f + 4*b - 2*b. Let d be h(f). Factor -d*c + 34*c + 2*c**2 - 2.
2*(c - 1)*(c + 1)
Let k(m) = -8*m**4 - 27*m**3 - 13*m**2 + 7*m + 5. Let p(b) = 135*b**4 + 460*b**3 + 220*b**2 - 120*b - 85. Let l(t) = -35*k(t) - 2*p(t). Factor l(h).
5*(h + 1)**3*(2*h - 1)
Factor -19/2*t**2 - 21/2*t - 1.
-(t + 1)*(19*t + 2)/2
Let s(p) = 17*p**3 - 310*p**2 - 653*p - 326. Let n(v) = 15*v**3 - 310*v**2 - 650*v - 325. Let t(i) = -6*n(i) + 5*s(i). Solve t(a) = 0 for a.
-1, 64
Factor 4*t**2 + 194*t**3 - 4*t**5 - 396*t**3 + 12*t**4 + 190*t**3.
-4*t**2*(t - 1)**3
Let j(q) = -23*q**2 - 42*q + 65. Let a(t) = -11 - 8 + 14*t + 0*t + 8*t**2 - 3. Let x(z) = 17*a(z) + 6*j(z). Suppose x(r) = 0. What is r?
-8, 1
Let h(v) be the first derivative of 98*v + 11 + 2/3*v**3 + 14*v**2. Factor h(m).
2*(m + 7)**2
Let i be (-145 + 150)*8/13. Determine r so that -48/13*r**4 + 2/13 + i*r**3 + 4/13*r**2 - 10/13*r = 0.
-1/2, 1/3, 1/2
Let g(h) be the third derivative of h**6/660 + h**5/330 - 2*h**3/3 + 10*h**2. Let u(p) be the first derivative of g(p). Factor u(f).
2*f*(3*f + 2)/11
Let j(b) be the third derivative of b**5/100 - 3*b**4 + 360*b**3 + 85*b**2. What is h in j(h) = 0?
60
Let b(m) = 739*m**2 + 108*m + 4. Let j(f) = -741*f**2 - 108*f - 4. Let z(q) = -6*b(q) - 5*j(q). Factor z(c).
-(27*c + 2)**2
Let d(m) be the second derivative of -m**7/14 - 3*m**6/10 - 9*m**5/20 - m**4/4 - 192*m + 1. Suppose d(i) = 0. Calculate i.
-1, 0
Let d be 8/5 - 4*(-10)/100. Let y(p) be the first derivative of -3/20*p**4 - 1/5*p**d + 9 + 0*p + 1/3*p**3. Let y(c) = 0. What is c?
0, 2/3, 1
Factor k + 5*k**3 - k**3 - 4*k**2 + 0*k**3 + 6 - 3*k**3.
(k - 3)*(k - 2)*(k + 1)
Let r = -1717 - -1717. Determine o, given that 0 + 0*o**2 + 11/6*o**4 - 4/3*o**5 - 1/2*o**3 + r*o = 0.
0, 3/8, 1
Let i(v) be the second derivative of 0 + 7/4*v**5 + 55/6*v**3 + 20/3*v**4 - 16*v + 5*v**2. Find q such that i(q) = 0.
-1, -2/7
Let x(y) be the third derivative of 0 - 1/20*y**5 + 1/70*y**7 + 0*y - 3/40*y**6 + 3/8*y**4 + 0*y**3 - 48*y**2. Suppose x(k) = 0. What is k?
-1, 0, 1, 3
Let v(r) be the first derivative of r**6/6 - 3*r**4/4 - 2*r**3/3 - 121. Solve v(b) = 0 for b.
-1, 0, 2
Let s = 21779/13 - 1675. Suppose -2/13*c + s - 2/13*c**2 = 0. What is c?
-2, 1
Let y = 155/203 + -18/29. Let f(h) be the second derivative of y*h**3 + 0*h**4 - 1/70*h**5 + 0 - 2/7*h**2 - 6*h. Suppose f(t) = 0. Calculate t.
-2, 1
Let u(d) be the third derivative of d**5/240 - 5*d**4/96 + d**3/4 - 142*d**2. Find r, given that u(r) = 0.
2, 3
Let z(v) be the second derivative of v**4/6 + 2*v**3/3 - 8*v**2 - 662*v. Solve z(d) = 0 for d.
-4, 2
Let y(p) be the first derivative of 2*p**5/55 + 5*p**4/22 + 14*p**3/33 + 3*p**2/11 - 114. Factor y(u).
2*u*(u + 1)**2*(u + 3)/11
Let s(k) be the third derivative of 3/112*k**8 + 0 + 0*k - 3*k**2 + 0*k**4 + 11/210*k**7 + 1/60*k**6 + 0*k**5 + 0*k**3. Determine m, given that s(m) = 0.
-1, -2/9, 0
Factor 25*v**4 - 40*v**3 + 8*v**2 - 75*v**3 - 25*v + 147*v**2 - 40*v**3.
5*v*(v - 5)*(v - 1)*(5*v - 1)
Suppose y + 20 = 2*d + 2*d, -5*d = -3*y - 25. Determine p, given that -2 - 7 - 45*p - 5*p**d - 80*p**2 + 2 - 3 - 70*p**3 - 30*p**4 = 0.
-2, -1
Let o(t) be the second derivative of 49*t**5/20 + 259*t**4/6 + 142*t**3/3 + 20*t**2 - 481*t. Find g such that o(g) = 0.
-10, -2/7
Let l(v) be the third derivative of -1/1470*v**7 + 0 + 0*v**4 + 0*v**6 + 0*v + 1/210*v**5 - 1/42*v**3 - 5*v**2. Factor l(k).
-(k - 1)**2*(k + 1)**2/7
Find t, given that 2/11*t**3 - 48/11*t + 0 - 46/11*t**2 = 0.
-1, 0, 24
Suppose 4*o - 9 = o. Find d, given that -6*d - 2*d**2 - 7*d**o - 4*d**2 + d**2 + 8*d = 0.
-1, 0, 2/7
Let b(x) be the third derivative of x**7/30 - 13*x**6/60 + 9*x**5/20 - x**4/6 - 2*x**3/3 + 8*x**2 - 1. Determine s, given that b(s) = 0.
-2/7, 1, 2
Let y(p) be the second derivative of -p**8/784 + p**7/490 + 13*p**2/2 - 17*p. Let v(j) be the first derivative of y(j). Suppose v(s) = 0. What is s?
0, 1
Factor -5/6*u**2 + 15/2 + 20/3*u.
-5*(u - 9)*(u + 1)/6
Let s be (121/(-240))/(-1) + 23/(-46). Let a(z) be the third derivative of 0*z - s*z**5 + 7*z**2 - 1/24*z**4 + 0*z**3 + 0. Let a(q) = 0. What is q?
-4, 0
Suppose 2*j + 2*m = 4 - 0, -5*j = -4*m - 10. Factor 0*g**2 + 2*g**j + 0*g**2 + 12*g + 12 + g**2.
3*(g + 2)**2
Let k be (26/364)/((-20)/(-7)). Let s = k + 197/120. Factor -3*t + 7/3*t**4 + 3*t**3 - s*t**2 - 2/3.
(t - 1)*(t + 1)**2*(7*t + 2)/3
Let o(w) be the second derivative of 7/4*w**4 - 1/40*w**5 + 686*w**2 - 21*w - 49*w**3 + 0. Find v such that o(v) = 0.
14
Let r = -52 - -57. Solve -w**r - 38*w**4 + 0*w**3 + 39*w**4 + w**3 - w**2 = 0.
-1, 0, 1
Let q(y) be the second derivative of y**5/90 + y**4/54 - y**3/3 - y**2 + 254*y. Find k, given that q(k) = 0.
-3, -1, 3
Let q(r) = r**2 - 7*r + 4. Suppose -2*k + 13 = 5. Let g(x) = x**2 - 8*x + 4. Let i(j) = k*q(j) - 3*g(j). Factor i(w).
(w - 2)**2
Let p be (-11 + 26)*20/378. Let r = p + -4/7. Solve 0 - 2/9*l**2 - r*l = 0 for l.
-1, 0
Let r(y) be the first derivative of 3*y**5/5 - 3*y**4/2 + y**3 - 16. Factor r(f).
3*f**2*(f - 1)**2
Suppose 0 = -4*m + 4*j + 4, 5*j - j = -4*m + 12. Suppose -1/3*b**m + 1/3 - 1/3*b**3 + 1/3*b = 0. What is b?
-1, 1
Find v, given that 0*v**5 - 8 + 14 + 215*v - 290*v**2 - 66 + 5*v**5 + 180*v**3 - 50*v**4 = 0.
1, 3, 4
Find b, given that -8/9 - 10/9*b**4 + 8/9*b + 4/9*b**3 + 10/3*b**2 = 0.
-1, 2/5, 2
Let u be -46 + (4 - 5 - -3). Let w = -44 - u. Factor 2/9*v**3 + w + 2/9*v**2 + 0*v.
2*v**2*(v + 1