. Let c(b) be the third derivative of 0*b + 1/24*b**r + 0 - 1/15*b**5 - 3*b**2 + 0*b**3. Solve c(h) = 0.
0, 1/4
Let d(m) = 34*m**2 - 126*m + 3980. Let x(f) = -3*f**2 - 1. Let t(l) = 4*d(l) + 44*x(l). Find i, given that t(i) = 0.
63
Determine p, given that 14/3 - 2/9*p**2 + 40/9*p = 0.
-1, 21
Let s be (-16)/(-28) + 820/(-70) + 12. Find y such that -3/7*y**2 + 3/7*y**5 - 9/7*y**3 + 0 + 3/7*y**4 + s*y = 0.
-2, -1, 0, 1
Let s = -1021 - -1023. Let t = 15/38 - -2/19. Find z, given that 1/2*z**3 - 1/4 - 3/4*z + 3/4*z**4 - t*z**s + 1/4*z**5 = 0.
-1, 1
Let s(p) = -6*p - 89. Let x be s(-17). Suppose -x*g = 5*g - 36. Find r such that 1/5*r - 1/5 + r**g + 3/5*r**3 = 0.
-1, 1/3
Let c be -2*(-2)/(-8)*36/17. Let o = -21/68 - c. Factor 7/4*n + 1/2*n**2 + o.
(n + 3)*(2*n + 1)/4
Let d be (-5)/(-10)*(113 - 32). Suppose -q + 8 = -2*i, 3*q - 14 - 1 = 3*i. Factor 81/2*z**5 - 12*z + 0 - 42*z**q - 27*z**3 + d*z**4.
3*z*(z - 1)*(3*z + 2)**3/2
Factor -1/3*m**2 - 20/3*m - 17.
-(m + 3)*(m + 17)/3
Let q(i) = i + 9. Let u be q(-5). Suppose 5*w**3 + 0*w**5 + 8*w**4 + 5*w**4 - 3*w**u + 5*w**5 = 0. What is w?
-1, 0
Let p(l) = -10*l**2 + 38*l + 8. Let z be p(4). Let s(v) be the third derivative of v**2 + 0 - 1/100*v**5 - 3/10*v**3 + z*v + 1/10*v**4. Factor s(m).
-3*(m - 3)*(m - 1)/5
Let o(p) = -5*p**3 - 65*p**2 - 95*p - 45. Let k(v) = 3*v**3 + 33*v**2 + 49*v + 23. Let u(l) = -5*k(l) - 2*o(l). Let u(f) = 0. What is f?
-5, -1
Solve -558 - 50*r + 2*r**2 - 79*r + 45*r + 251 + 221 = 0.
-1, 43
Let d(m) be the second derivative of 2*m**7/21 - 7*m**6/6 + 87*m**5/20 - 10*m**4/3 - 8*m**3/3 + 81*m. Determine i, given that d(i) = 0.
-1/4, 0, 1, 4
Suppose -9*l + 11*l - 240 = 0. Let b = -356/3 + l. Factor -16/3*y - 4*y**2 - b.
-4*(y + 1)*(3*y + 1)/3
Suppose -3*f - 4*h + 9*h + 11 = 0, 4*f - 13 = 5*h. Let -2*k**2 + 8*k**f - k**3 + 457*k + 6 - 468*k = 0. What is k?
1, 2, 3
Let r(c) be the first derivative of 1/120*c**5 - 1/12*c**4 + c + 1/3*c**3 - 2/3*c**2 + 3. Let s(p) be the first derivative of r(p). Factor s(v).
(v - 2)**3/6
Find f, given that -4*f**3 + 8*f + 1/2*f**4 - 4*f**2 + 1/2*f**5 + 8 = 0.
-2, -1, 2
Let b(m) be the third derivative of -m**5/80 + 11*m**4/96 - m**3/4 - 227*m**2. Factor b(i).
-(i - 3)*(3*i - 2)/4
Suppose -7*g + 4*g = -9. Let n be g + (1 - -1 - 2). Factor -2*i - 3*i**5 - 6*i**3 - 3 - n*i**4 - i + 6*i**2 + 12*i**3.
-3*(i - 1)**2*(i + 1)**3
What is l in 20*l + 106*l**2 + 105*l**2 + 20 - 206*l**2 = 0?
-2
Let h(n) be the third derivative of n**7/1260 - n**6/120 + n**5/90 + n**4/24 - 5*n**3/36 + n**2 + 94. Factor h(l).
(l - 5)*(l - 1)**2*(l + 1)/6
Factor 27/2 + 83/4*o + 1/4*o**3 + 15/2*o**2.
(o + 1)*(o + 2)*(o + 27)/4
Let h be -3 - 21/(-6) - (10 + -10). Suppose -2*d = -4*v + 3*d + 17, -4*d = 4. Find p, given that p**2 + 0 - 1/2*p - h*p**v = 0.
0, 1
Let h = 31883/72 + -3982/9. Let a = -25/4 + 53/8. Solve 0 - 3/8*q**5 - h*q**4 + a*q**2 + 3/8*q**3 + 0*q = 0 for q.
-1, 0, 1
Let v(w) be the first derivative of -w**5/21 + w**4/21 - 27*w**2/2 + 12. Let j(t) be the second derivative of v(t). Suppose j(l) = 0. What is l?
0, 2/5
Let b(u) be the third derivative of -5*u**8/48 + 5*u**7/21 + u**6/24 - u**5/3 + 271*u**2. Factor b(t).
-5*t**2*(t - 1)**2*(7*t + 4)
Let z(r) be the third derivative of 39*r**2 + 0 - 1/15*r**5 - 5/6*r**4 + 0*r - 8/3*r**3. Factor z(v).
-4*(v + 1)*(v + 4)
Let o be 8/10 - (-36)/30. Let w be o*-1 + (-54)/(-21). Let -2/7*b**2 + w + 2/7*b = 0. Calculate b.
-1, 2
Let f(c) be the second derivative of c**7/1470 - 2*c**3/3 - 10*c. Let q(r) be the second derivative of f(r). Factor q(p).
4*p**3/7
Let p be (37 - 16/4) + -3. Find x such that 7*x**3 - 3*x**3 - 58*x**2 + p*x**2 + 60*x - 36 = 0.
1, 3
Suppose -2*i + 24 + 16 = 0. Suppose -15*h = -i*h + 25. Suppose 0*p**2 + 4/7*p**h + 8/7*p**4 + 4/7*p**3 + 0*p + 0 = 0. What is p?
-1, 0
Suppose 6872*k - 6877*k = -20. Solve -2/5*p**2 + 4/15 + 2/15*p**k + 2/15*p**3 - 2/15*p = 0.
-2, -1, 1
Let x(a) be the first derivative of -17 - 2*a**2 + 0*a - 4/3*a**3. Factor x(v).
-4*v*(v + 1)
Let n(i) = 2*i**2 - 4*i - 10. Let x be n(-2). Factor x*a**2 + 12/7 + 54/7*a.
6*(a + 1)*(7*a + 2)/7
Factor -2/11*b**3 + 56/11 + 2*b**2 - 64/11*b.
-2*(b - 7)*(b - 2)**2/11
Let v(j) be the first derivative of 1/21*j**3 + 0*j**2 - 9/7*j - 45. Determine w, given that v(w) = 0.
-3, 3
Let n(w) = -2*w**3 + w**2 - w - 2. Let m(g) = -9*g**3 + 5*g**2 - 8*g - 12. Let k(h) = m(h) - 5*n(h). Factor k(s).
(s - 2)*(s + 1)**2
Let a(l) = 50*l - 4098. Let g be a(82). Find k such that -32/7 - 68*k**3 - 484/7*k**g - 4*k**5 - 216/7*k - 204/7*k**4 = 0.
-4, -1, -2/7
Let x be (1 + 309/21 - 12) + (-12)/14. Find q, given that 4/7*q**2 + x*q + 24/7 = 0.
-3, -2
Let i(s) = 2*s + 58. Let y be i(-28). Let h(c) be the second derivative of -1/78*c**4 + 1/13*c**3 + 0 - 2/13*c**y + 2*c. Factor h(a).
-2*(a - 2)*(a - 1)/13
Suppose 1296 = 2*f + 10*f. Let l(y) be the first derivative of 2/5*y**5 + 36*y**3 - 8 + 162*y - f*y**2 - 6*y**4. Factor l(x).
2*(x - 3)**4
Suppose -188 = -3*d - 0*m - 2*m, m = -4*d + 249. Suppose p + d - 65 = 0. Factor -1/3*t**p - 1/3*t**2 + 0 + 2/3*t.
-t*(t - 1)*(t + 2)/3
Let f(a) be the second derivative of -3/14*a**3 + 9/140*a**5 + 3/14*a**2 + 0 - 1/28*a**4 + 2*a. Factor f(w).
3*(w - 1)*(w + 1)*(3*w - 1)/7
Let u be (9 - 6) + -2 + 1. Suppose -2*d + 4*f - 3 + 7 = 0, 0 = -u*f. What is p in 0 - 4/7*p - 4/7*p**d = 0?
-1, 0
Let q(s) = -5*s**2 - 10*s. Let b(o) = 14*o**2 + 29*o. Let a = 112 - 101. Let n(u) = a*q(u) + 4*b(u). Factor n(h).
h*(h + 6)
Let t(j) be the third derivative of -4*j**7/945 + 2*j**6/9 + 251*j**5/270 + 53*j**4/36 + 32*j**3/27 - j**2 + 591. What is w in t(w) = 0?
-1, -1/2, 32
Let k(d) be the first derivative of 8/15*d**6 + 0*d**2 - 5*d**4 - 8/5*d**3 - 12/25*d**5 + 0*d + 21. Suppose k(p) = 0. What is p?
-2, -1/4, 0, 3
Find k such that -48 - 4/3*k**2 - 16*k = 0.
-6
Let x(c) be the first derivative of c**5/90 + 39*c**2/2 + 6. Let f(o) be the second derivative of x(o). Factor f(t).
2*t**2/3
Let q(t) be the second derivative of -7*t**4/48 - 125*t**3/12 + 9*t**2 - 148*t. Determine y so that q(y) = 0.
-36, 2/7
Let x(h) be the third derivative of 0*h**3 + 0 + 0*h + 1/24*h**4 + 1/48*h**5 + 6*h**2. Suppose x(l) = 0. Calculate l.
-4/5, 0
Let r be (1 - (-1)/2)/((-5)/(-10)). Factor 9/5*p**2 + 12/5 + 36/5*p - 3*p**r.
-3*(p - 2)*(p + 1)*(5*p + 2)/5
Suppose -657*l - l**3 - 5*l**3 + 24*l**2 + 649*l - 10*l**4 = 0. Calculate l.
-2, 0, 2/5, 1
Let x(l) = 8*l**2 - 320*l + 5120. Let y(v) = 9*v**2 - 320*v + 5120. Let o(h) = 4*x(h) - 3*y(h). Suppose o(r) = 0. Calculate r.
32
Factor 1/8*z**2 + 9/2 - 3/2*z.
(z - 6)**2/8
Let j be (1 - 17)*(8 + -10). Factor -1985*b**3 + 1981*b**3 + 24*b**2 - 15*b - 33*b + j.
-4*(b - 2)**3
Let m = -48935 - -48937. Determine r, given that 4/3*r**4 + 0*r - 2/3*r**5 + 0 + 0*r**m - 2/3*r**3 = 0.
0, 1
Suppose -7*v = -v - 12. Factor 6*i + 0*i**v + 7*i**2 - 3*i - 4*i**2.
3*i*(i + 1)
Let r be (-22)/44 - (-2)/(8/22). Let m = r - 2. Factor 2/11*f**m + 0 + 0*f**2 - 8/11*f.
2*f*(f - 2)*(f + 2)/11
Suppose -g - 15 = -8. Let q(r) = 2*r**3 + 15*r**2 + 3*r. Let t(a) = -3*a**3 - 30*a**2 - 7*a. Let v(b) = g*q(b) - 3*t(b). What is m in v(m) = 0?
-3, 0
Factor -33*j - 59*j - 2*j**2 + 80 + 116 + 52 - 338.
-2*(j + 1)*(j + 45)
Let f(v) be the third derivative of -v**5/12 - 45*v**4/8 - v**2 - 209. Find k, given that f(k) = 0.
-27, 0
Let v(y) be the first derivative of -y**4/12 + y**3/3 + y**2 - 8*y/3 + 150. Factor v(r).
-(r - 4)*(r - 1)*(r + 2)/3
Suppose 17/5*i + 42/5 + 1/5*i**2 = 0. What is i?
-14, -3
Let x = -32 - -47. Factor -5*a**5 + 50*a**2 - 25*a**2 + x*a**4 - 19*a**2 - 26*a**2.
-5*a**2*(a - 2)**2*(a + 1)
Let p(a) be the second derivative of -24*a + 1/16*a**4 + 1/8*a**3 - 9/4*a**2 + 0. What is h in p(h) = 0?
-3, 2
Let g be (-16)/(-96) + -2 + 182/60. Let y be (-21)/(-20)*(-40)/(-15). Suppose -g*u**2 + y*u - 4/5 = 0. What is u?
1/3, 2
Let o be (306/(-12))/17*2/(-810). Let t(p) be the second derivative of 1/108*p**4 + 0*p**2 + o*p**6 + p + 0 + 1/90*p**5 + 0*p**3. Find n such that t(n) = 0.
-1, 0
Factor 204*q**2 - 7*q + 48*q**2 + 4*q**3 - 204 + 7*q - 48*q**2 - 4*q.
4*(q - 1)*(q + 1)*(q + 51)
Let h(m) be the second derivative of 6*m + 0 + 2/5*m**3 + 1/15*m**4 + 4/5*m**2. Factor h(q).
4*(q + 1)*(q + 2)/5
Factor 5*w**3 - 11049 - 125*w + 11049.
5*w*(w - 5)*(w + 5)
Solve -379*j**2 + 8