ve of t**6/80 + t**5/8 + t**4/8 - 2*t**3 + 21*t**2 - 2. Let g(s) be the second derivative of r(s). What is o in g(o) = 0?
-4, -2, 1
Let s be ((-242)/40 - -6)*(-5)/3. Let f(p) be the second derivative of -4*p - s*p**4 + 0*p**2 + 0*p**3 + 0. Solve f(u) = 0.
0
Suppose 117 + 159 = -6*l. Let y = 140/3 + l. Determine k so that 1/3*k**3 + 0*k - 2/3*k**4 + 0 + y*k**2 - 1/3*k**5 = 0.
-2, -1, 0, 1
Find l, given that -115*l + 19/2*l**2 + 12 = 0.
2/19, 12
Let m be ((-20)/6 + 3)/((-24)/216). Let h(f) be the third derivative of 0 + 0*f**4 + 9*f**2 - 1/12*f**m + 0*f + 1/120*f**5. Suppose h(b) = 0. What is b?
-1, 1
Let u(n) be the second derivative of 0 + 10*n + 0*n**2 + 1/30*n**6 + 1/3*n**3 - 1/12*n**4 - 1/10*n**5. What is j in u(j) = 0?
-1, 0, 1, 2
Let u = 883/2 - 437. Let s(a) be the first derivative of u*a**2 + 5*a**3 + 3/4*a**4 - 27*a + 4. Factor s(w).
3*(w - 1)*(w + 3)**2
Factor 2/5 + 8/5*j**2 + 2/5*j**3 + 7/5*j - 1/5*j**5 - 2/5*j**4.
-(j - 2)*(j + 1)**4/5
Let t(x) be the second derivative of -x**6/1620 + x**4/27 - 13*x**3/6 + 16*x. Let s(f) be the second derivative of t(f). Determine n, given that s(n) = 0.
-2, 2
Suppose -18 = -5*s - 3*d, 3*s - d - d = 7. Factor -9*z**2 + z**2 + 2*z**2 + z - s*z - 4*z**3.
-2*z*(z + 1)*(2*z + 1)
Let v = 53 - 29. Suppose -5*o = -c - v, 3*o + 4*c - 5 = -9. Factor -2/3*m**o - 4/3*m**3 + 2/3 + 0*m**2 + 4/3*m.
-2*(m - 1)*(m + 1)**3/3
Let m(h) = h**3 - 10*h**2 + 8*h - 2. Let f be m(9). Let g = -6 - f. Factor 3*y**2 + 10*y - 3*y**3 + 3*y**g - 10*y - 3*y**4.
3*y**2*(y - 1)**2*(y + 1)
Let b(o) be the third derivative of o**6/80 - 13*o**5/80 - 43*o**4/32 - 9*o**3/4 - 2*o**2 + 89. Factor b(k).
3*(k - 9)*(k + 2)*(2*k + 1)/4
Let v(r) be the second derivative of -17*r + 1/2*r**3 + 0*r**4 - 3/20*r**5 + 0 + 0*r**2. Determine u so that v(u) = 0.
-1, 0, 1
Let x(f) be the second derivative of f**5/180 - f**4/24 + f**3/9 + 7*f**2/2 + 13*f. Let h(d) be the first derivative of x(d). Factor h(u).
(u - 2)*(u - 1)/3
Let c(m) be the second derivative of 1/2*m**5 + 5/42*m**7 - 5/2*m**3 + 0*m**2 - 5/3*m**4 + 2/3*m**6 + 0 + 25*m. Suppose c(f) = 0. What is f?
-3, -1, 0, 1
Let p be 1/(-6 - -5 - ((-135)/(-18))/(-5)). Let -2/3 - j - 1/3*j**p = 0. What is j?
-2, -1
Let z = -266621/7 + 38153. Let 180/7*t - z*t**2 + 375/7*t**3 - 24/7 = 0. What is t?
2/5
Factor -91/12*l + 0 + 5/3*l**2 - 1/12*l**3.
-l*(l - 13)*(l - 7)/12
Let n be (1 + (-185)/(-15))/((-1)/5). Let s = n - -67. Determine t so that -s*t**2 + 2*t - 3 = 0.
3
Let x be (-20006)/126 - 4/18. Let g = x - -161. Suppose 4/5 + 14/5*s + g*s**2 = 0. What is s?
-1, -2/5
Let -136*x**3 + 39*x**3 + 96*x**3 - 8*x - x**4 + 10*x**2 = 0. Calculate x.
-4, 0, 1, 2
Let a(n) = -n**3 - 11*n**2 + 25*n + 8. Let q(h) = 6*h**2 - 12*h - 3. Let v(t) = -3*a(t) - 7*q(t). Determine z so that v(z) = 0.
1
Let m(n) be the third derivative of -n**7/105 - n**6/20 + n**5/10 + 7*n**4/12 - 2*n**3 + n**2 + 5*n. Suppose m(x) = 0. Calculate x.
-3, -2, 1
Let a = -33 - -38. Determine k so that -52*k**4 + 68*k**3 + 25*k**3 + 9*k**a - 8 + 4*k**4 - 94*k**2 + 4*k**3 + 44*k = 0.
2/3, 1, 2
Let g(u) be the third derivative of -u**5/90 + u**4/18 + 5*u**3/3 - 185*u**2. Factor g(l).
-2*(l - 5)*(l + 3)/3
Let l(i) = 5*i**3 + 3*i**2 - 4*i - 7. Let f(p) = p. Let n(a) = -3*f(a) + 3*l(a). Let v(q) = -q**3 + q + 1. Let w(m) = -n(m) - 12*v(m). What is g in w(g) = 0?
-3, -1, 1
Let r(l) be the third derivative of 5/336*l**8 + 11*l**2 + 5/6*l**3 + 0*l - 1/6*l**5 + 1/42*l**7 + 0 - 1/12*l**6 + 5/24*l**4. Suppose r(f) = 0. Calculate f.
-1, 1
Factor 2/7*r**2 - 16/7 - 4/7*r.
2*(r - 4)*(r + 2)/7
Let y = -1813/17 - -107. Suppose y*g**3 + 10/17*g**2 + 0 - 2/17*g**4 + 4/17*g - 2/17*g**5 = 0. What is g?
-1, 0, 2
Let i(n) be the second derivative of -n**5/10 - n**4/2 + 5*n + 2. What is o in i(o) = 0?
-3, 0
Factor -3/2*b**2 - 117/2*b - 57.
-3*(b + 1)*(b + 38)/2
Let z(v) = 59 - 121 + 61. Let j(q) = -4*q**3 + 48*q**2 - 192*q + 250. Let l(m) = -j(m) + 6*z(m). Factor l(a).
4*(a - 4)**3
Let o(c) be the first derivative of -c**7/112 + 3*c**5/80 - c**3/16 + 10*c + 8. Let i(u) be the first derivative of o(u). Factor i(r).
-3*r*(r - 1)**2*(r + 1)**2/8
Let l be 44/198 + 4/(216/69). Find w, given that 0 + 1/2*w**3 + w + l*w**2 = 0.
-2, -1, 0
Suppose -3*x = -3*p - 2*p + 13, 4*p = 5*x + 13. Let k(v) = v - 6. Let t be k(8). Factor -2*a**2 - 3*a - a**2 + t*a**2 - p.
-(a + 1)*(a + 2)
Suppose -16/9*j + 32/9 + 2/9*j**2 = 0. What is j?
4
Suppose -m = -3*d + 9, -7 = -5*m + 99*d - 97*d. Let v(p) be the first derivative of -3/4*p**4 + 3/5*p**5 - m*p**3 + 6*p + 2 + 3/2*p**2. Factor v(s).
3*(s - 2)*(s - 1)*(s + 1)**2
Let m(l) be the third derivative of l**7/10080 + l**6/960 + l**5/240 + 5*l**4/24 - 22*l**2. Let h(o) be the second derivative of m(o). Solve h(x) = 0.
-2, -1
Let s(q) be the second derivative of -1/16*q**4 + 3/40*q**5 - 1/4*q**3 - 19*q + 1/40*q**6 + 0*q**2 + 0. Determine u, given that s(u) = 0.
-2, -1, 0, 1
Let d be 132/(-286) + 408/39 + -8. Determine m so that 2/17*m**5 + 0*m - 4/17*m**3 + 0 - 2/17*m**4 + 0*m**d = 0.
-1, 0, 2
Let j = 274/15 + -2774/165. Suppose -24/11*q**2 - 2/11*q**5 + 0 + 6/11*q**4 + j*q + 4/11*q**3 = 0. What is q?
-2, 0, 1, 2
Suppose -d + 0*d = -1. Factor 0*c**2 + 2*c**2 + d + 5 - 8*c.
2*(c - 3)*(c - 1)
Let g(b) be the second derivative of -1/14*b**7 + 1/2*b**4 + 0 - 3/4*b**5 + 2/5*b**6 + 0*b**2 - b + 0*b**3. Factor g(n).
-3*n**2*(n - 2)*(n - 1)**2
Suppose 0 = -30*p + 24*p + 12. Let d(n) be the second derivative of 4*n + 1/90*n**6 - 1/30*n**5 + 1/36*n**4 + 0*n**3 + 0*n**p + 0. Factor d(c).
c**2*(c - 1)**2/3
Let x(c) be the first derivative of 5*c**6/6 + c**5 - 15*c**4/4 - 25*c**3/3 - 5*c**2 - 140. Factor x(v).
5*v*(v - 2)*(v + 1)**3
Solve 25*a**3 + 88*a**4 - 163*a**4 - 70*a**2 - 25*a + 10 + 53*a**4 + 82*a**4 = 0 for a.
-1, -2/3, 1/4, 1
Let y be ((-20)/(-30))/((-4)/6) + -2. Let i be 6/81*y - (-368)/207. Determine d, given that i*d + 10/9*d**4 - 2/3 - 4/3*d**3 - 4/9*d**2 - 2/9*d**5 = 0.
-1, 1, 3
Let j(q) be the first derivative of 1/2*q**4 - 16/3*q - 4*q**2 + 7 - 1/9*q**3 - 1/15*q**5. Suppose j(s) = 0. Calculate s.
-1, 4
Solve 92/13*c - 48/13 - 2/13*c**3 - 46/13*c**2 + 4/13*c**4 = 0 for c.
-4, 1, 3/2, 2
Let u(c) be the first derivative of -2*c**6/3 - 68*c**5/5 + 35. Let u(p) = 0. What is p?
-17, 0
Solve -117/2*a**3 + 80*a**2 - 18*a + 0 - 7/2*a**4 = 0.
-18, 0, 2/7, 1
Let b(k) be the first derivative of 2*k**5/35 + k**4/2 + 14. Solve b(m) = 0 for m.
-7, 0
Suppose 0 - 8 = -4*i. Let n = 4829/15 + -964/3. Factor -4/5*v + 1/5*v**i + n.
(v - 3)*(v - 1)/5
Let j be 31/(15345/(-360))*((-6)/(-8))/(-3). Determine y so that -2/11*y**2 - j*y**3 + 0*y + 0 = 0.
-1, 0
Suppose 33 + 93 = 42*n. Let l(f) be the first derivative of 1/5*f**2 + 2/15*f**n + 0*f - 1. Let l(v) = 0. What is v?
-1, 0
Let y(h) be the first derivative of -4*h**5/5 + 7*h**4/9 + 80*h**3/27 + 8*h**2/9 - 41. Let y(c) = 0. Calculate c.
-1, -2/9, 0, 2
Let l(a) = a**2 - 24*a + 33. Let t(o) = 8*o**2 - 168*o + 232. Let w = 12 - 15. Let d(k) = w*t(k) + 20*l(k). Factor d(c).
-4*(c - 3)**2
Let p be (2/(-3))/(16/(-18)). Let r be (-1 - (1 - -1)) + (-105)/(-28). Factor 1/4*k**4 + p*k**3 + r*k**2 + 1/4*k + 0.
k*(k + 1)**3/4
Find p, given that 2/5*p**4 - 2/15*p**5 - 2/5*p**2 + 2/3*p**3 - 8/15*p + 0 = 0.
-1, 0, 1, 4
Let k = -609 + 611. Let t(n) be the second derivative of 0*n**k + 1/12*n**4 + 0 + 1/6*n**3 + 3*n. Factor t(y).
y*(y + 1)
Let g(u) be the first derivative of 1/40*u**5 - 1/24*u**4 - 10 + 1/4*u**2 - u - 1/12*u**3. Let y(j) be the first derivative of g(j). Factor y(q).
(q - 1)**2*(q + 1)/2
Let c = 592 + -592. Let b(g) be the first derivative of c*g + 1/14*g**4 + 4/21*g**3 + 1/7*g**2 + 7. Factor b(a).
2*a*(a + 1)**2/7
Suppose 0 = v + x - 8, 2*v = 2*x - 0 - 4. Suppose 4*a + v*g - 2 = -9, 0 = -4*a - g + 3. Factor -2*t + 0 + t**a - 3 + 5 - 1.
(t - 1)**2
Let n(o) be the first derivative of 2*o**3 - 1/78*o**4 + 0*o**2 + 0*o - 1/780*o**5 - 1 + 1/2340*o**6. Let j(h) be the third derivative of n(h). Factor j(g).
2*(g - 2)*(g + 1)/13
Let u(o) be the second derivative of o**6/315 + o**5/105 - o**4/126 - 2*o**3/63 + 35*o. Suppose u(i) = 0. Calculate i.
-2, -1, 0, 1
Suppose 6*y - 164 = -14. Suppose c + 6 = 29. Let y*z**3 - c*z**3 + z**2 - 2*z - 3*z**2 + 2 = 0. What is z?
-1, 1
Let g(o) be the second derivative of o**9/32130 - o*