 1)**2/2
Let o(h) be the second derivative of -3*h - 7/3*h**4 - 218/75*h**6 - 16/15*h**3 + 2/3*h**7 + 0 + 113/25*h**5 + 8/5*h**2. Determine r, given that o(r) = 0.
-2/7, 2/5, 1
Suppose -5*w = -6 - 4. Suppose 4*k - w*d = 24, 3*k - 1 = -5*d - 9. Factor -6*j - 2*j**2 - k*j**2 + 3*j**2 - 3.
-3*(j + 1)**2
Let h be (9 + -21)/(-4) + 16/(-6). Suppose 0 = 5*z - 13*z. Determine f, given that 0 + 2/3*f**2 + z*f + h*f**3 = 0.
-2, 0
Let g(t) be the third derivative of -5*t**8/336 + t**7/21 + t**6/12 - 2*t**5/3 + 35*t**4/24 - 5*t**3/3 - 19*t**2. Let g(m) = 0. Calculate m.
-2, 1
Let c(g) be the first derivative of -9/4*g**4 + 25 - 3/4*g**6 + 0*g + 3/4*g**2 + 12/5*g**5 + 0*g**3. Suppose c(l) = 0. Calculate l.
-1/3, 0, 1
Let v(p) = p**4 + 3*p**3 + 4*p**2 - 2. Let z(j) = -5*j**4 - 14*j**3 - 15*j**2 + 9. Let g(c) = 9*v(c) + 2*z(c). Suppose g(n) = 0. What is n?
-3, 0, 2
Suppose 2*o - t - 1 = 0, 4*t + 4 = -2*o - 0*o. Solve -4 + q**3 - 2*q**2 - 8*q + q + 0*q**2 + o*q**2 = 0 for q.
-1, 4
Suppose r = 5*j - 8, 0 = -30*j + 28*j + 2*r. Factor 1/4*h**j + 0 + 0*h - 3/4*h**4 + 1/2*h**3.
-h**2*(h - 1)*(3*h + 1)/4
Let b(h) be the second derivative of -13*h**6/6 - 3*h**5 + 5*h**4/12 - h - 13. Factor b(f).
-5*f**2*(f + 1)*(13*f - 1)
Let w(s) be the third derivative of 0*s**4 + 0*s**3 + 1/120*s**6 + 1/60*s**5 + 0 - 1/105*s**7 + 0*s - 10*s**2. Factor w(b).
-b**2*(b - 1)*(2*b + 1)
Let d(k) = -2*k**5 + 8*k**3 - 2*k**2 + 2. Let q(n) = 2*n**5 - 8*n**3 + 3*n**2 - 3. Let v(l) = 6*d(l) + 4*q(l). What is g in v(g) = 0?
-2, 0, 2
Let x(f) be the third derivative of -f**7/70 + f**6/20 + f**5/20 - f**4/4 - 56*f**2. Factor x(v).
-3*v*(v - 2)*(v - 1)*(v + 1)
Solve -1/5*g**4 - 10*g + 0 + 73/5*g**2 - 22/5*g**3 = 0 for g.
-25, 0, 1, 2
Let q(f) be the first derivative of -f**4/12 + 5*f**3/42 + f**2/7 + 3*f + 5. Let i(l) be the first derivative of q(l). Suppose i(y) = 0. Calculate y.
-2/7, 1
Let -1/10*b**4 + 249/5*b**2 - 50*b - 82/5*b**3 + 167/10 = 0. What is b?
-167, 1
Let v(z) be the second derivative of 5*z**3 - 1/4*z**4 + 0 - 75/2*z**2 + 5*z. What is p in v(p) = 0?
5
Let x(v) be the second derivative of -v**6/70 + 9*v**5/140 + v**4/7 - 167*v. Factor x(w).
-3*w**2*(w - 4)*(w + 1)/7
Let r = -168 + 168. Suppose -9*y - y - 10*y = r. Factor y*x**2 + 0 - 1/4*x**3 + 0*x**4 + 1/8*x + 1/8*x**5.
x*(x - 1)**2*(x + 1)**2/8
Let f(q) be the third derivative of q**8/840 + 3*q**7/175 + 2*q**6/75 + 21*q**2 + 1. Factor f(w).
2*w**3*(w + 1)*(w + 8)/5
Let o(u) be the first derivative of -5*u**3 - 5/2*u**2 + 15*u + 5/4*u**4 - 16. Factor o(p).
5*(p - 3)*(p - 1)*(p + 1)
Let f(t) = -t**4 - 4*t**3 + 48*t**2 + 315*t + 517. Let u(p) = p - 1. Let j(z) = f(z) + 5*u(z). Factor j(n).
-(n - 8)*(n + 4)**3
Let z(h) be the first derivative of -h**5/5 - 21*h**4 - 588*h**3 + 232. Factor z(k).
-k**2*(k + 42)**2
Let f = -11/75 + 97/150. Let i(p) be the second derivative of 1/4*p**4 + f*p**3 - 3/2*p**2 - 3/20*p**5 - 6*p + 0. Factor i(l).
-3*(l - 1)**2*(l + 1)
Let m(n) be the third derivative of n**6/40 - 2*n**5/5 + 3*n**4/2 - n**2 - n. Determine y so that m(y) = 0.
0, 2, 6
Suppose -16*o = 8*o - 120. Suppose -5*j + o = -10. Factor -8/5*w**j + 16/5 - 12/5*w**2 + 4/5*w**4 + 16/5*w.
4*(w - 2)**2*(w + 1)**2/5
Let u(q) be the second derivative of q**9/1512 + q**8/840 - q**7/210 + 4*q**3/3 - 25*q. Let l(s) be the second derivative of u(s). Factor l(x).
2*x**3*(x - 1)*(x + 2)
Let z be ((-3096)/16 - -6)/(1/((-40)/14)). Determine y, given that z + 900/7*y**2 + 6/7*y**4 + 3000/7*y + 120/7*y**3 = 0.
-5
Let r(s) be the first derivative of -s**3 + 3/2*s**2 + 6*s - 17. Factor r(h).
-3*(h - 2)*(h + 1)
Let m = -172 + 174. Let a(o) be the third derivative of 0 - 1/300*o**5 - 1/60*o**4 + 0*o + 1/30*o**3 + 1/300*o**6 - 5*o**m. Solve a(y) = 0 for y.
-1, 1/2, 1
Let k(h) be the first derivative of h**4/4 - 7*h**3/3 + 7*h**2 - 8*h - 89. Factor k(m).
(m - 4)*(m - 2)*(m - 1)
Find h such that 0 + 8/5*h**2 + 24/5*h**3 - 14/5*h**4 + 0*h = 0.
-2/7, 0, 2
Let s(h) be the third derivative of h**8/28 + h**7/21 - 13*h**6/60 + h**5/15 - 22*h**2. What is v in s(v) = 0?
-2, 0, 1/6, 1
Let o = -2207 + 2207. Factor o*h**3 + 3/8*h**4 + 3/8 + 0*h - 3/4*h**2.
3*(h - 1)**2*(h + 1)**2/8
Let l(a) = -2*a**2 + 38*a - 35. Let t be l(18). Let h(q) be the first derivative of 1/3*q**4 - 1/5*q**5 + 0*q - t - 1/3*q**2 + 1/9*q**3. Factor h(o).
-o*(o - 1)**2*(3*o + 2)/3
Let v(f) be the first derivative of f**6/450 - f**5/150 - 16*f**3/3 + 14. Let h(x) be the third derivative of v(x). Factor h(l).
4*l*(l - 1)/5
Let d = -81 - -84. Factor 75*z - 24*z**2 - 19*z**2 - 2*z**2 - 113*z**3 + 118*z**d + 125.
5*(z - 5)**2*(z + 1)
Let x be (-1248)/252 - (-4 + -1). Let n(f) be the first derivative of x*f**6 - 1/7*f**2 + 0*f - 4/35*f**5 + 0*f**4 - 6 + 4/21*f**3. Suppose n(l) = 0. What is l?
-1, 0, 1
Let o(f) = -2*f**2 + 30*f + 6. Let z(q) = -17*q**2 - 4 - q + 6 - 1 + 16*q**2. Let l(n) = -o(n) + 6*z(n). Let l(i) = 0. Calculate i.
-9, 0
Let l(f) be the second derivative of f**6/40 - 3*f**5/40 + f**4/16 - 8*f - 1. Factor l(p).
3*p**2*(p - 1)**2/4
Let y(m) be the first derivative of -2*m**5/35 + 25*m**4/14 - 374*m**3/21 + 363*m**2/7 + 67. Factor y(a).
-2*a*(a - 11)**2*(a - 3)/7
Let v(z) be the first derivative of -4*z**5/25 + 11*z**4/10 - 6*z**3/5 - 14*z**2/5 + 16*z/5 + 228. What is g in v(g) = 0?
-1, 1/2, 2, 4
Let p(m) be the first derivative of 5/4*m**4 + 10*m - 5/2*m**2 - 12 - 10/3*m**3. Determine i so that p(i) = 0.
-1, 1, 2
Factor 92/5*m**4 - 1/5*m**5 - 54*m**3 + 0 - 89/5*m + 268/5*m**2.
-m*(m - 89)*(m - 1)**3/5
Let t(c) be the third derivative of -c**5/270 - c**4/27 + 5*c**3/27 - 39*c**2. Suppose t(i) = 0. Calculate i.
-5, 1
Let l = -4 + 6. Suppose -10*q + 3*q - 55*q**2 - 17*q + 20 + 59*q**l = 0. Calculate q.
1, 5
Suppose -3*l - 1 = -7. Suppose 2*p - 27 = -l*c + 21, p - 5*c = 12. Let -4*k**3 - 12*k**2 + 3*k**5 + 4*k - k + p*k**3 - 12*k**4 = 0. What is k?
0, 1
Let q be 1718/(-1148) + (45/6 - 6). Let p = 2305/2583 - q. Factor -p*y**2 - 4/9 - 10/9*y - 2/9*y**3.
-2*(y + 1)**2*(y + 2)/9
Let p(s) = -s**2 + 4*s. Let c(z) = -47*z**2 + 13*z - 2. Let l(r) = 2*c(r) + 6*p(r). What is v in l(v) = 0?
1/10, 2/5
Let j(f) be the second derivative of 0*f**4 - 10*f - 1/60*f**5 + 0 + 1/18*f**3 + 0*f**2. Factor j(d).
-d*(d - 1)*(d + 1)/3
Let o(t) be the second derivative of t**6/90 + 2*t**5/45 - 16*t**2 - 22*t. Let v(i) be the first derivative of o(i). Suppose v(s) = 0. What is s?
-2, 0
Let 0 - 2/5*p**2 - 4/5*p = 0. Calculate p.
-2, 0
Let o(q) be the first derivative of -1/15*q**3 + 1/10*q**4 + 1/25*q**5 - 1/5*q**2 - 25 + 0*q. Factor o(h).
h*(h - 1)*(h + 1)*(h + 2)/5
Let q(d) = d**2 - 43*d + 123. Let o be q(40). Let 9/4 - 1/4*a**o + 7/4*a**2 - 15/4*a = 0. What is a?
1, 3
Let t(x) = 0*x + 58 + 3*x + 5*x + 0*x. Let z be t(-7). Find y such that -1/2 + 1/2*y**z + 0*y = 0.
-1, 1
Factor -2425*u**3 + u**2 - 3*u**2 + 2423*u**3.
-2*u**2*(u + 1)
Suppose 8 = y + y. Find j such that 1 - y - 3*j**2 + 6 = 0.
-1, 1
Suppose -2*o = 9*o - 55. Let c(j) be the third derivative of 0 - 1/60*j**6 + 0*j**3 + o*j**2 + 0*j - 1/150*j**5 - 1/175*j**7 + 1/60*j**4. Factor c(u).
-2*u*(u + 1)**2*(3*u - 1)/5
Suppose -4/3*y**2 + 184/3*y - 2116/3 = 0. Calculate y.
23
Let l(u) = -4 + 2 + 1. Let p be (-3)/(9*-1)*-3*1. Let r(b) = -b**2. Let a(j) = p*l(j) + r(j). Let a(g) = 0. What is g?
-1, 1
Let u = 35 - 32. Suppose 2*a**3 + 4*a**4 + 2*a**u - 1151 + 44*a + 1135 - 36*a**2 = 0. What is a?
-4, 1
Let w be 24/28*19 - (-4)/(-14). What is k in -32*k - 18*k + 4*k**2 + 30*k + w = 0?
1, 4
Let f(r) be the first derivative of r**4 + 0*r + 18 + 4/3*r**3 - 4/5*r**5 - 2*r**2. Determine u, given that f(u) = 0.
-1, 0, 1
Let i = -715 - -718. Let n(s) be the first derivative of -9*s + 3*s**2 + i - 1/3*s**3. Factor n(z).
-(z - 3)**2
Let r(w) be the third derivative of w**8/112 - w**7/14 + w**6/10 - 292*w**2. Factor r(t).
3*t**3*(t - 4)*(t - 1)
Suppose -31*o + 34*o - 6 = 0. Find s, given that -2 + 3*s**2 + 2*s**3 - 14 + o*s**2 - 8*s - s**2 = 0.
-2, 2
Determine v so that 0 - 22/7*v**3 + 6/7*v - 19/7*v**2 + v**4 + 4/7*v**5 = 0.
-3, -1, 0, 1/4, 2
Find u such that -226*u**2 + 82*u**2 - 72*u - 2*u**3 + 114*u**2 - u**3 = 0.
-6, -4, 0
Let p = 3 + 1. Let u(j) = 3*j**3 + j**2 + 7*j + 4. Let s(y) = 6 + 3*y + y**3 - 7 + 3 + 0. Let f(k) = p*u(k) - 10*s(k). Determine t so that f(t) = 0.