(g). Let w(v) be the first derivative of c(v). Factor w(p).
-3*(p - 5)**2
Let u(l) be the first derivative of -l**3/3 + l**2/2 + 12. Let q(k) = -7*k**2 - 8*k - 49. Let y(f) = -q(f) + 6*u(f). Solve y(v) = 0 for v.
-7
Suppose -7*x + 266 = 231. Let h(y) be the first derivative of 6/35*y**x + 2/21*y**3 + 1/21*y**6 + 0*y**2 + 3/14*y**4 - 1 + 0*y. Find c such that h(c) = 0.
-1, 0
Let r(m) be the first derivative of -m**6/3 + 6*m**5/5 + 7*m**4/2 - 22*m**3/3 - 6*m**2 + 16*m - 39. Suppose r(c) = 0. What is c?
-2, -1, 1, 4
Let c(u) be the second derivative of 1/80*u**5 + 0*u**2 - 17*u - 1/48*u**4 + 0*u**3 + 0. Determine s so that c(s) = 0.
0, 1
Suppose 2*n = 3*n - 3. Factor 5 - 5*s**5 + 5*s**4 - 5*s**n - 5*s + 7*s**3 - 36*s**2 + 8*s**3 + 26*s**2.
-5*(s - 1)**3*(s + 1)**2
Let d(p) = -9*p**3 - 217*p**2 - 70*p - 8. Let b(w) = -36*w**3 - 864*w**2 - 279*w - 30. Let g(v) = -4*b(v) + 15*d(v). Determine l so that g(l) = 0.
-22, -1/3, 0
Let k(l) = l**3 + l**2 - 133. Let r be k(0). Let g = r + 135. Solve -12*b**g - 3/5*b**5 - 21/5*b**4 - 24/5*b - 54/5*b**3 + 0 = 0 for b.
-2, -1, 0
Factor 334*j**2 - 332*j**2 - 2 + 2 + 8*j - 2*j.
2*j*(j + 3)
Let j(c) = -2*c + 1. Let o(a) = -7*a**3 - 2*a**2 + 11*a. Let i(x) = -6*j(x) - 3*o(x). Factor i(b).
3*(b - 1)*(b + 1)*(7*b + 2)
Let x(q) = -2*q**2 - 4*q + 7*q**2 + 3*q - 8 + 0*q. Let o(h) = h + 8 - 5*h**2 - 3 - 4*h**2 + 6*h**2. Let c(n) = -8*o(n) - 5*x(n). Factor c(k).
-k*(k + 3)
Let q(p) be the third derivative of -1/30*p**6 - 2/105*p**7 + 0*p - 19*p**2 + 0*p**3 + 0*p**4 + 1/84*p**8 + 1/15*p**5 + 0. What is h in q(h) = 0?
-1, 0, 1
Let i(s) be the second derivative of s**4/60 - 19*s**3/30 + 9*s**2/5 - 16*s. Suppose i(r) = 0. Calculate r.
1, 18
Let p = -13 + 52. Suppose 4*l - p = -15. What is u in 23*u - 2*u + 4*u**2 + 5*u**2 + l = 0?
-2, -1/3
Let k(r) be the third derivative of 3/80*r**5 + 0*r**3 + 14*r**2 + 0*r**6 + 0*r - 1/280*r**7 + 0 + 1/16*r**4. Factor k(i).
-3*i*(i - 2)*(i + 1)**2/4
Let u(b) be the third derivative of 3*b**8/560 + 2*b**7/25 - 59*b**6/600 + b**5/30 - 22*b**2. Find v, given that u(v) = 0.
-10, 0, 1/3
Let h be (-1)/(-4) - (-1)/(-4). Suppose 3 = 2*d - 5, 2*u - 3*d + 8 = h. Factor -3 + 3 + 1 + 2*y + y**u.
(y + 1)**2
Suppose -g = -3*g - 42. Let w = g - -25. Factor -5/2*u**3 - 1/2*u + w*u**2 - 1.
-(u - 1)**2*(5*u + 2)/2
Suppose 76*q**2 + 3*q - 27 + 10 - 4*q**3 - 59 + q = 0. Calculate q.
-1, 1, 19
Let g(c) = -c + 11. Let q be g(6). Suppose -5 - q = -5*u. Determine r so that -45*r**2 - 15*r**3 + r + 47*r**u - 12*r**4 - 20*r**4 + 5*r**5 - 21*r**5 = 0.
-1, -1/4, 0, 1/4
Find r such that 7/2*r**2 - 5*r - 1/2*r**4 + 2*r**3 + 0 = 0.
-2, 0, 1, 5
Let p = -14 + -30. Let y = p + 44. Suppose -2/5*v**4 - 2/5*v**5 + 2/5*v**3 + 0 + y*v + 2/5*v**2 = 0. Calculate v.
-1, 0, 1
Let a(t) be the first derivative of 16*t**5/15 - t**4 - 20*t**3/9 + 2*t**2 + 4*t/3 + 26. Find g such that a(g) = 0.
-1, -1/4, 1
Let l be (-62)/(-155)*(-1)/(-4). Let b(j) be the second derivative of 4/9*j**4 + 0 - 2/3*j**2 + l*j**5 + 1/3*j**3 - 10*j. Factor b(q).
2*(q + 1)*(q + 2)*(3*q - 1)/3
Let b = 179523/31 - 28953/5. Let k = -2/31 + b. Factor 0 + 0*g - 2/5*g**3 - k*g**2.
-2*g**2*(g + 1)/5
Let 3*j**4 - 220*j**2 - 216*j**2 - 18*j**3 + 415*j**2 = 0. What is j?
-1, 0, 7
Suppose -3/5*d**3 - 69312/5*d + 0 - 912/5*d**2 = 0. Calculate d.
-152, 0
Let n(b) be the first derivative of -2*b**5/5 + 4*b**4 + 38*b**3/3 + 10*b**2 - 464. Determine o, given that n(o) = 0.
-1, 0, 10
Let p(x) be the first derivative of x**5 + 25*x**4/2 - 20*x**3 - 25*x**2 + 55*x - 450. Find u such that p(u) = 0.
-11, -1, 1
Let f(u) be the first derivative of -u**6/90 + 4*u**5/45 + 3*u**2/2 - 23. Let g(n) be the second derivative of f(n). Factor g(q).
-4*q**2*(q - 4)/3
Let s = -17687/11 - -1608. Let o(n) be the second derivative of 11*n + 5/66*n**4 - s*n**3 - 2/11*n**2 + 0. Find l such that o(l) = 0.
-2/5, 1
Let s(n) be the second derivative of 0 + 5/12*n**4 - 33*n + 245/2*n**2 + 35/3*n**3. Suppose s(u) = 0. Calculate u.
-7
Suppose -4*t - 4*k + 168 = 0, t - 4*k - 108 = -t. Suppose 4*c - t = -46. What is s in c*s + 1/7*s**2 + 0 = 0?
0
Let o(l) be the second derivative of l**5/10 - 2*l**4 - 43*l**3/3 - 30*l**2 - 185*l. Find b, given that o(b) = 0.
-2, -1, 15
Let w be (-1909)/(-138) + 2/12. Let g(p) = 5*p**3 - 7*p**2 + 13*p - 4. Let y(h) = -h**3 + h**2 - h. Let d(q) = w*y(q) + 2*g(q). Let d(x) = 0. What is x?
-2, 1
Let k(y) be the first derivative of 0*y + 0*y**2 - 15/4*y**4 + y**5 - 3 + 10/3*y**3. Find j, given that k(j) = 0.
0, 1, 2
Suppose -3*k + 11 = 2. Let v be (-3)/((-9)/12) + -17 + 15. Factor 1 - 2 + 2*o**4 + v*o**2 - k*o**4.
-(o - 1)**2*(o + 1)**2
Suppose 4*f - 27 = -3*p, -4*f = -0*p - 4*p - 48. Suppose 2*g = -3*k + 1 - f, -2*k - 3*g - 12 = 0. Find z such that 4/11*z + 18/11*z**3 + k + 2*z**2 = 0.
-1, -2/9, 0
Let t(d) be the third derivative of -d**5/30 - 13*d**4/24 - 5*d**3/2 + 180*d**2 + d. Factor t(g).
-(g + 5)*(2*g + 3)
Suppose 6/19*s + 8/19 + 2/19*s**4 - 6/19*s**3 - 10/19*s**2 = 0. Calculate s.
-1, 1, 4
Let w = -187 + 216. Suppose 14*t = w*t - 30. Factor 2/5*x**4 + 1/5*x**3 + 0*x + 0*x**t + 1/5*x**5 + 0.
x**3*(x + 1)**2/5
Let i(l) be the first derivative of l**4 - 8*l**2 + 51 + l**4 + 4*l**5 + l**4 + l**4 - 8*l**3 + 4*l. Suppose i(v) = 0. What is v?
-1, 1/5, 1
Solve 21*b + 0 + 69/2*b**2 + 3/2*b**4 + 15*b**3 = 0 for b.
-7, -2, -1, 0
Let b(r) be the second derivative of 0 - 1/75*r**6 - 7/5*r**4 + 11/50*r**5 - 32/5*r**2 + 64/15*r**3 - 40*r. Let b(u) = 0. Calculate u.
1, 2, 4
Factor -18*o**2 + 8*o**3 - 5*o**4 + 58*o**3 - 32*o**2 - 31*o**3.
-5*o**2*(o - 5)*(o - 2)
Let a = 49751/31633 - 6/4519. Factor -a*l - 4/7 + 3/7*l**2.
(l - 4)*(3*l + 1)/7
Let c(x) be the first derivative of x**3/18 + x**2/3 + 2*x/3 + 94. Solve c(d) = 0.
-2
Let u(f) = -6*f + 12. Let x be u(2). Factor -4*b**3 + b**5 + 3*b**4 + 3*b**3 - 2*b - 3*b**2 + 2*b**3 + x*b**4.
b*(b - 1)*(b + 1)**2*(b + 2)
Factor -25*i + 60 + 5/2*i**2.
5*(i - 6)*(i - 4)/2
Let l = -6 + 1. Let z be (36/15)/((-2)/l). Factor 2*d - 14*d**3 - 6*d**4 + 12*d**4 + z*d.
2*d*(d - 2)*(d - 1)*(3*d + 2)
Let r(u) be the second derivative of 24*u + 0*u**2 + 1/130*u**5 - 1/26*u**4 + 0 + 0*u**3. Let r(x) = 0. Calculate x.
0, 3
Solve 46/5*g**2 + 0 - 44/5*g - 2/5*g**3 = 0 for g.
0, 1, 22
Let x(b) = -28*b**2 - 15*b - 5. Let c(v) = 3*v**2 + v. Let n(i) = -18*c(i) - 2*x(i). Let n(a) = 0. What is a?
-5, -1
Factor -2/3*o**4 + 28/15*o**3 - 8/5*o**2 + 2/15 + 4/15*o.
-2*(o - 1)**3*(5*o + 1)/15
Let i(d) be the third derivative of 1/20*d**5 + 0 - 19*d**2 + 3/4*d**4 + 0*d + 5/2*d**3. Factor i(b).
3*(b + 1)*(b + 5)
Let j = 118771/7 + -16967. Determine o, given that 4/7 - j*o**2 + 2/7*o = 0.
-1, 2
Let r(s) be the second derivative of -s**5/20 - 7*s**4/8 - 5*s**3 - 3*s**2/2 + 28*s. Let p(y) be the first derivative of r(y). Factor p(d).
-3*(d + 2)*(d + 5)
Factor 16/11*o - 8/11 + 2/11*o**3 - 10/11*o**2.
2*(o - 2)**2*(o - 1)/11
Let g(v) = -7*v**2 - v**3 - 10 + 11*v**2 + 0*v**2 + 9*v**2 - 11*v. Let p be g(12). Determine t so that -3*t**2 + 66 - 10*t - 71 - 2*t**p = 0.
-1
Let y be 124/930 + 2/10. Let h(t) be the first derivative of y*t**3 + 1/2*t**2 - 3/16*t**4 + 5 + 0*t. Factor h(f).
-f*(f - 2)*(3*f + 2)/4
Let c(y) = 5*y**2 - 96*y + 91. Let s(d) = -6*d**2 + 98*d - 92. Let v(h) = -4*c(h) - 3*s(h). Suppose v(m) = 0. What is m?
1, 44
Let n = 7 - 5. Let t be ((-4)/(-5))/((-2)/(-10)). Factor k**4 - 10*k**n + 4*k**2 + 9*k**3 - t*k**4.
-3*k**2*(k - 2)*(k - 1)
Let o(c) be the second derivative of c**5/25 + 4*c**4/15 - 59*c. Solve o(d) = 0 for d.
-4, 0
Let r(z) be the first derivative of -15*z + 5/8*z**4 - 35/4*z**2 + 31 + 0*z**3. Determine q, given that r(q) = 0.
-2, -1, 3
Suppose -4*y - 12 = -5*y. Suppose -p + 2*k + 0*k + y = 0, k - 3 = -4*p. Find z such that 0*z + 9/4*z**p - 3 - 3/4*z**3 = 0.
-1, 2
Let f(w) be the first derivative of w**4/48 + w**3/6 + w**2/2 - 6*w + 1. Let l(h) be the first derivative of f(h). Find c such that l(c) = 0.
-2
Let b(k) be the second derivative of k**5/60 + 11*k**4/36 + 5*k**3/9 - 13*k + 10. Factor b(v).
v*(v + 1)*(v + 10)/3
Let p(a) = 3*a**2 - 1. Let w be 2/((-12)/(-4) - 1). Let x be p(w). Factor -3*t**5 - 11*t**3 - 4*t**3 + 9*t**x + 0*t**5 + 11*t**4 - 2*t.
-t*(t - 1)**3*(3*t - 2)
Let g(s) be the third derivative of -s**5/510 + s**4/102 + 5*s**3/17 - 87*s**