et d(p) = -k(p) - 2*u(p). Solve d(r) = 0.
-13, -1/4, 1
Let p = 159 - 793/5. Factor -2/15*k**3 + 2/15*k + 2/5 - p*k**2.
-2*(k - 1)*(k + 1)*(k + 3)/15
Let b(w) be the third derivative of -w**6/240 - 3*w**5/16 - 11*w**4/4 - 121*w**3/24 + 2*w**2 + 7*w. Factor b(x).
-(x + 11)**2*(2*x + 1)/4
Let b(f) be the first derivative of 121*f**4 - 1672*f**3 + 888*f**2 - 160*f + 75. Factor b(x).
4*(x - 10)*(11*x - 2)**2
Factor -52/5*m**3 + 2/5*m**4 + 288/5 + 386/5*m**2 - 624/5*m.
2*(m - 12)**2*(m - 1)**2/5
Suppose 0 = -4*j - 223 + 227. Let u be (-38)/(-152) - -1*j/28. Factor 0 + 0*i + 1/7*i**3 - u*i**2.
i**2*(i - 2)/7
Suppose 55*p - 57*p = -4. Suppose -10 = -4*w + b, -2*w + p*b + 6 = -w. Factor 1/4*n**w + 0 - 1/4*n**3 + 1/2*n.
-n*(n - 2)*(n + 1)/4
Suppose 1571*q - 1572*q = -2. Let p(y) be the second derivative of 0*y**q + 7/4*y**4 + 0 - 7*y - y**3. Factor p(n).
3*n*(7*n - 2)
Factor 5*p**3 + 11*p + 10*p**2 - 21*p - 5*p.
5*p*(p - 1)*(p + 3)
Let t(f) be the third derivative of -14*f**2 + 1/20*f**5 - 1/1050*f**7 + 0 - 2/3*f**3 - 1/30*f**4 + 0*f - 1/300*f**6. Factor t(p).
-(p - 2)**2*(p + 1)*(p + 5)/5
Let h(n) be the third derivative of -n**7/165 - 6*n**6/55 - 181*n**5/330 - 12*n**4/11 - 28*n**3/33 - 32*n**2 - 7. Find g such that h(g) = 0.
-7, -2, -1, -2/7
Let z(x) be the first derivative of 5*x**5/12 + 5*x**4/8 - 5*x**3/3 - 9*x**2/2 - 5. Let p(g) be the second derivative of z(g). Let p(v) = 0. Calculate v.
-1, 2/5
Suppose 43*d = 38*d + 4*m + 12, -m = 4*d + 3. Suppose -4/3*c**3 + 2/3*c**5 + d + 2/3*c + 0*c**2 + 0*c**4 = 0. What is c?
-1, 0, 1
Let a(i) be the second derivative of -2*i**6/15 - 17*i**5/5 + 6*i**4 - 38*i. Suppose a(z) = 0. What is z?
-18, 0, 1
Suppose 50*q = 46*q - 84. Let l = q - -21. Factor l - 4/5*r - 4/5*r**2 - 1/5*r**3.
-r*(r + 2)**2/5
Let v(w) be the second derivative of -w**6/3 - w**5/4 + 65*w**4/12 - 5*w**3 + 107*w. Factor v(f).
-5*f*(f - 2)*(f + 3)*(2*f - 1)
Suppose 0 = m - f - 17, 5*f = -m - 0*f - 1. Let k be m/(-28) + (-34)/(-52). Let 0*l + 0*l**3 - 4/13*l**2 + 2/13 + k*l**4 = 0. Calculate l.
-1, 1
Let c(y) = -895*y + 895. Let u be c(1). Solve 4/3*k**4 - 52/3*k**2 - 20/3*k**3 - 28/3*k + u = 0 for k.
-1, 0, 7
Let m be (-2 - (-80)/50)/((-16)/30). Suppose -9/4*a**4 + 3/2*a**2 + 3/2*a**3 + 3/4 + m*a**5 - 9/4*a = 0. Calculate a.
-1, 1
Solve 14/9*r + 4 - 2/9*r**2 = 0.
-2, 9
Find r, given that 0*r**2 - 5/11*r**3 + 5/11*r - 2/11*r**4 + 2/11 = 0.
-2, -1, -1/2, 1
Let r(q) be the first derivative of 0*q - 9 + 3/8*q**2 - 1/12*q**3. Factor r(m).
-m*(m - 3)/4
Let h(d) be the third derivative of 5*d**7/21 - 4*d**6/3 + 32*d**5/15 - 26*d**2 - 2*d. What is i in h(i) = 0?
0, 8/5
Factor -68*h**2 + 14*h**3 - 6*h**3 + 8*h**3 + 52*h - 16*h + 72.
4*(h - 3)*(h - 2)*(4*h + 3)
Let o(y) be the first derivative of 4*y**3/15 + 16*y**2/5 - 16*y + 30. Let o(s) = 0. Calculate s.
-10, 2
What is k in 0 + 2/15*k**5 + 0*k + 32/5*k**2 + 44/15*k**3 - 10/3*k**4 = 0?
-1, 0, 2, 24
Determine f, given that -296/3*f**2 + 204*f**3 - 168*f**4 + 18*f**5 - 16/9 + 194/9*f = 0.
1/3, 8
Let m(b) = -8*b + 354. Let n be m(44). Factor 1/6*i**n - 1/3*i + 0.
i*(i - 2)/6
Suppose 3*u = -b - b + 10, -5*u + 4*b = -46. Factor -u*c**4 - 2*c**2 + 16*c**3 - 6*c**3 - 3*c**2 + c**4.
-5*c**2*(c - 1)**2
Let y(q) = 5*q**2 + q. Let z(c) = -c**2 - 10334*c + 10334*c. Let m(g) = -g**3 - g**2 - g + 4. Let l be m(0). Let d(t) = l*z(t) + y(t). Factor d(w).
w*(w + 1)
Let h(z) be the second derivative of 0 - 8/15*z**6 + 27/10*z**5 + 32*z + 17/3*z**3 - 11/2*z**4 - 3*z**2. Factor h(o).
-2*(o - 1)**3*(8*o - 3)
Let t(r) = r**2 + 6. Let j(m) = m**2 - m - 1. Let l(i) = -6*j(i) + 3*t(i). Factor l(d).
-3*(d - 4)*(d + 2)
Let m(w) = 3*w**4 - 31*w**3 + 191*w**2 + 223*w. Let d(z) = -10*z**4 + 94*z**3 - 571*z**2 - 668*z. Let j(o) = -6*d(o) - 21*m(o). Determine t so that j(t) = 0.
-1, 0, 15
Let k(t) be the second derivative of 2*t**7/189 - 4*t**6/135 - t**5/5 + 2*t**4/27 + 16*t**3/27 - 686*t - 2. Suppose k(r) = 0. Calculate r.
-2, -1, 0, 1, 4
Let y(w) = 15*w**4 + 79*w**3 + 132*w**2 + 21*w - 61. Let f(s) = -30*s**4 - 159*s**3 - 264*s**2 - 43*s + 123. Let o(v) = 3*f(v) + 5*y(v). Factor o(i).
-(i + 2)**3*(15*i - 8)
Suppose -21*v + 22*v + 2 = 4*t, -2 = -2*v + 2*t. Let q(f) be the second derivative of 1/5*f**v - 1/30*f**4 - 2*f - 1/50*f**5 + 1/15*f**3 + 0. Factor q(y).
-2*(y - 1)*(y + 1)**2/5
Suppose -31*y**2 - 3 - 9*y + 3 + 9*y**3 - 3*y**4 + 20*y**2 + 14*y**2 = 0. What is y?
-1, 0, 1, 3
Let g(y) be the second derivative of 0 - 1/18*y**3 + 0*y**2 + 1/18*y**4 - 26*y. Suppose g(n) = 0. What is n?
0, 1/2
Let s(t) be the first derivative of -t**5/180 - t**4/48 + t**3/18 - 25*t**2/2 + 38. Let k(b) be the second derivative of s(b). Factor k(g).
-(g + 2)*(2*g - 1)/6
Let n(z) = 15*z**2 + 49*z - 130. Let x be n(-5). Let x + 1/4*b + 3/4*b**3 - 1/4*b**4 - 3/4*b**2 = 0. What is b?
0, 1
Let f(h) be the first derivative of h**7/3780 - h**5/540 + 16*h**3/3 + 24. Let q(a) be the third derivative of f(a). Find j such that q(j) = 0.
-1, 0, 1
Let k = -40 + 40. Suppose k = -w + 4*w + w. Factor -4/7*i - 6/7*i**2 + w - 2/7*i**3.
-2*i*(i + 1)*(i + 2)/7
Let c(m) be the third derivative of -12*m**2 + 1/35*m**7 + 1/30*m**5 + 2*m + 0*m**4 + 0*m**3 - 1/20*m**6 + 0 - 1/168*m**8. Factor c(d).
-2*d**2*(d - 1)**3
Let q(s) be the second derivative of 2*s**3 + 2*s + 13/6*s**4 - 4*s**2 + 4/15*s**5 + 0. Let m(a) be the first derivative of q(a). Factor m(n).
4*(n + 3)*(4*n + 1)
Let j be (-46)/(-2 - -4) + 2. Let l = -16 - j. Solve -2*g**2 - 2*g + l*g - g = 0 for g.
0, 1
Let g(j) be the first derivative of -6*j + 29 - 2*j**2 + 2/3*j**3. Factor g(f).
2*(f - 3)*(f + 1)
Let v(y) = y**2 - 9*y - 7. Let u be v(10). Let i + i**3 - u*i + i**3 = 0. What is i?
-1, 0, 1
Let l(h) be the third derivative of -h**6/30 + h**5/3 - 4*h**4/3 + 8*h**3/3 - 6*h**2 - 3*h. Determine i so that l(i) = 0.
1, 2
Let i(q) be the third derivative of -q**6/300 - 7*q**5/75 + q**4/60 + 14*q**3/15 + 4*q**2 + 15*q. Suppose i(n) = 0. What is n?
-14, -1, 1
Let b(s) = 7*s - 22. Let n be b(7). Factor -2*k**2 - n*k + 32*k**3 - 35*k**3 + 20*k**2.
-3*k*(k - 3)**2
Let p(r) = -6 + 14 - 4 - 5. Let z(i) = i**4 - 5*i**3 + 8*i**2 - 4*i + 2. Let n(u) = 6*p(u) + 3*z(u). Determine x so that n(x) = 0.
0, 1, 2
Factor 4486*b**2 + 1/4*b**4 + 68*b**3 + 19044 - 18768*b.
(b - 2)**2*(b + 138)**2/4
Let n(y) = y**3 + y**2 - y + 1. Let v(h) = -13*h**3 - 14*h**2 + 10*h - 11. Let s(c) = -22*n(c) - 2*v(c). Let s(i) = 0. Calculate i.
-1, -1/2, 0
Let o be 942/6280*8/5. Find u, given that -8/25 - 8/25*u + 2/5*u**2 + o*u**3 = 0.
-2, -2/3, 1
Let o(b) be the second derivative of b**6/270 + b**5/90 - b**4/3 - 19*b**3/6 + 7*b. Let l(p) be the second derivative of o(p). Factor l(u).
4*(u - 2)*(u + 3)/3
Let q(k) be the third derivative of k**8/3360 - k**7/672 + k**6/360 - k**5/480 - 7*k**3/3 - 14*k**2. Let f(i) be the first derivative of q(i). Factor f(s).
s*(s - 1)**2*(2*s - 1)/4
Let 496/3*h**2 + 32/3 - 272/3*h - 27*h**5 + 392/3*h**3 - 42*h**4 = 0. Calculate h.
-2, 2/9, 2
Let k be (5 + 0 - (-58)/(-12))/((-8)/(-630)). Determine d, given that -147/8*d + 39/8*d**3 + 0 - k*d**2 - 3/8*d**4 = 0.
-1, 0, 7
Let l(n) = -175 - 237 + 83*n + 3*n**2 - 8*n**2. Let a(h) = -5*h**2 + 84*h - 411. Let c(r) = -7*a(r) + 6*l(r). Let c(z) = 0. Calculate z.
9
Let d(o) = o**3 + 6*o**2 + 7*o + 12. Suppose 0*f + 6*f + 30 = 0. Let c be d(f). Factor 2/3*u**c + 0*u - 2/3*u**3 + 0.
-2*u**2*(u - 1)/3
Suppose -2*d = 7*d - 198. Factor -10 - 3*a - d*a - 11*a**2 + 26*a**2.
5*(a - 2)*(3*a + 1)
Let w be (-4)/(-7)*(420/45 + 0). Let m(h) be the second derivative of 0 - 10*h + 1/5*h**5 + 32*h**2 + w*h**3 - 7/3*h**4. Find l such that m(l) = 0.
-1, 4
Let 4/13*r**2 + 2/13*r**3 - 192/13 - 64/13*r = 0. What is r?
-4, 6
Let m(j) = 32*j - 6. Let b be m(-4). Let p = -936/7 - b. Find a such that -4/7*a**3 + 0*a**2 - p + 4/7*a + 2/7*a**4 = 0.
-1, 1
Suppose 74*n = -99*n - 103*n + 1104. Factor 3/4*c**2 - 1/4*c + 1/4*c**n + 0 - 3/4*c**3.
c*(c - 1)**3/4
Let w = -53 + 64. Determine k, given that 6*k**3 + 5*k**3 - w*k**3 + 5*k**3 = 0.
0
Let b(l) = 2*l**3 + 12 - 12 - l**3 + 1. Let x(m) = -6*m**3 - 3*m**2 - 3. Let h be (1 + 0)/((-2)/6). Let f(q) = h*b(q) - x(q). Factor f(y).
3*y**2*(y + 1)
Let b(z) be the third derivative of z**8/112 + 23*z**7/70 + 39*z**6/8 + 733*z**5/20 + 287*z**4/2 + 294*z**3 - 2*z**2