-5). Let y be (g/(-15)*-1)/((-2)/(-10)). Factor 2/3*v**4 - 4/3 + y*v**3 - 2*v**2 - 10/3*v.
2*(v - 2)*(v + 1)**3/3
Let f(z) be the second derivative of 2*z**7/21 + 2*z**6/15 - 3*z**5/5 - z**4/3 + 4*z**3/3 + 375*z. Find k, given that f(k) = 0.
-2, -1, 0, 1
Suppose i + 3 = 0, 13 = 5*x - 41*i + 40*i. Factor 5 - 125/6*g - 15/2*g**x.
-5*(g + 3)*(9*g - 2)/6
Let m(w) = -99*w + 202. Let o be m(2). Let c(x) be the first derivative of -48/7*x - 11 - 3/28*x**o + x**3 - 12/7*x**2. Factor c(p).
-3*(p - 4)**2*(p + 1)/7
Factor -36*b**3 - 20 - 4*b - 43*b**3 + 20*b**2 - 38*b**3 + 121*b**3.
4*(b - 1)*(b + 1)*(b + 5)
Let o = 26404/15 + -1760. Let d = -140 - -702/5. Factor -2/15 - o*c**2 + d*c.
-2*(c - 1)*(2*c - 1)/15
Let g(x) be the third derivative of 0*x + 14*x**2 - 1/105*x**7 + 0 + 1/30*x**5 + 0*x**3 + 0*x**6 + 0*x**4. Suppose g(r) = 0. What is r?
-1, 0, 1
Suppose 46 - 1 = 3*z. What is j in z + 52*j - 24*j**2 + 2*j**3 - 5*j**3 - 63 - 112*j = 0?
-4, -2
Let n(v) be the third derivative of -v**8/448 + v**7/70 + 3*v**6/20 - v**5/8 - 71*v**4/32 - 21*v**3/4 + 2*v**2 + 207. Determine l, given that n(l) = 0.
-3, -1, 2, 7
Let w(a) = a**4 + 2. Let g(x) = 5*x**4 - 4*x**3 + 26*x**2 + 16*x + 14. Let m(d) = 2*g(d) - 22*w(d). Suppose m(c) = 0. Calculate c.
-2, -1, 1/3, 2
Let q(y) be the second derivative of y**5 - 605*y**4/12 + 775*y**3 - 1125*y**2/2 - 770*y. Let q(n) = 0. Calculate n.
1/4, 15
Let a(i) = -4*i**4 + 70*i**2 + 36*i + 12. Let v(s) = 9*s**4 - s**3 - 139*s**2 - 70*s - 22. Let f(l) = 11*a(l) + 6*v(l). Determine t, given that f(t) = 0.
-2, -2/5, 0, 3
Let k be 42/12*(-12)/(-14) + 79. Factor -82*l**2 + k*l**2 + 4*l**3.
4*l**3
Let b(h) be the first derivative of 4*h**5/5 - 61*h**4 + 236*h**3/3 + 122*h**2 - 240*h + 365. Suppose b(g) = 0. Calculate g.
-1, 1, 60
Let t(m) be the second derivative of 5/2*m**2 + 0 + 10/9*m**3 + 5/36*m**4 + 6*m. What is k in t(k) = 0?
-3, -1
Let c(u) be the third derivative of 1/8*u**4 + 0*u + 1/10*u**5 + 0 + 21*u**2 - 1/40*u**6 - u**3. Factor c(l).
-3*(l - 2)*(l - 1)*(l + 1)
Let x(n) be the second derivative of n**6/30 - n**4/12 + n + 4. Let x(m) = 0. What is m?
-1, 0, 1
Let q(g) = -2*g**3 - 10*g**2 + 4*g + 52. Let t be q(-3). Suppose 0 + 8/7*b**3 + 0*b + 1/7*b**2 + 16/7*b**t = 0. What is b?
-1/4, 0
Let p(c) = -2*c**2 + 131*c + 1017. Let b be p(-7). Factor 0*i - 2/11*i**3 - 4/11*i**b + 0.
-2*i**2*(i + 2)/11
Let k(i) = 9755*i**3 + 4825*i**2 + 810*i + 80. Let j = 15 + -19. Let r(s) = 1084*s**3 + 536*s**2 + 90*s + 9. Let h(x) = j*k(x) + 35*r(x). Solve h(t) = 0 for t.
-1/6
Let v(p) = p**3 - 5*p**2 - 4*p**2 + 3*p**2. Let u(o) = -11*o**2 - 6*o**2 + 16*o**2. Let t(m) = 6*u(m) - v(m). Solve t(c) = 0 for c.
0
Find m, given that -12*m**3 + 88/5*m**2 + 18/5*m**4 - 2/5*m**5 + 0 - 48/5*m = 0.
0, 2, 3
Let c be ((-8)/(-16))/(((-2)/(-36))/1). Let i = 9 - c. Find n, given that i*n**4 + 2/9*n + 2/9*n**5 + 0 - 4/9*n**3 + 0*n**2 = 0.
-1, 0, 1
Let o(i) be the first derivative of 4*i**3/3 + 18*i**2 + 32*i + 45. Determine r, given that o(r) = 0.
-8, -1
Let u(x) be the second derivative of x**8/1344 - x**6/144 + 7*x**4/12 + 2*x. Let q(o) be the third derivative of u(o). What is b in q(b) = 0?
-1, 0, 1
Let x(a) = 16*a**2 - 53*a + 14. Let u(w) = -14*w**2 + 54*w - 12. Let l(g) = -7*u(g) - 6*x(g). Factor l(f).
2*f*(f - 30)
Let m(i) be the first derivative of -2*i**7/21 + i**6/15 + 5*i**2/2 - 2. Let t(s) be the second derivative of m(s). Suppose t(j) = 0. Calculate j.
0, 2/5
Let d = 1174/5 - 3711/20. Let v = 50 - d. Factor 9/4*f**2 - 15/4*f**3 + 27/4*f + v*f**4 + 0.
3*f*(f - 3)**2*(f + 1)/4
Let a(v) = 9*v**2 - 27*v + 18. Let z(j) = 2*j**2 - 2*j. Let c(w) = -a(w) + 3*z(w). Solve c(d) = 0.
1, 6
Let t(z) be the third derivative of 7*z**6/40 + 5*z**5/4 + 3*z**4/2 - 14*z**2 + 4*z. Factor t(p).
3*p*(p + 3)*(7*p + 4)
Let x be (-5100)/(-4816) + 6/(-8). Let r = -1/43 + x. Factor 1/7*m**2 + r*m + 0.
m*(m + 2)/7
Suppose -3*j + 0 = -9. Factor 63*m**4 + 65*m**2 + 45*m + 123*m**j + 46*m**2 + 4 + 12*m**5 - 2 + 4.
3*(m + 1)**3*(m + 2)*(4*m + 1)
Let y(f) be the first derivative of 0*f + 15/4*f**4 + 3*f**2 + 7 - 7/2*f**6 + 27/5*f**5 - 9*f**3. Determine m so that y(m) = 0.
-1, 0, 2/7, 1
Let n(a) be the third derivative of -a**8/161280 - a**7/20160 - 23*a**5/60 + 3*a**2. Let h(r) be the third derivative of n(r). Factor h(g).
-g*(g + 2)/8
Let s be 196/36 + -2 - (1 - -1). Let b(n) be the first derivative of -s*n**2 + 5 - 2*n**3 - 4/9*n - 23/18*n**4 - 14/45*n**5. Determine x, given that b(x) = 0.
-1, -2/7
Determine x, given that 7/2*x**5 + 20 - 101/2*x**3 - x**2 + 8*x**4 + 74*x = 0.
-5, -1, -2/7, 2
Let o(t) be the first derivative of -t**6/480 - t**5/16 - 9*t**4/32 + 47*t**3/3 + 36. Let q(j) be the third derivative of o(j). Factor q(n).
-3*(n + 1)*(n + 9)/4
Let y(d) be the first derivative of -d**4 + 132*d**3 - 6534*d**2 + 143748*d + 174. Factor y(w).
-4*(w - 33)**3
Suppose 0 = -4*t - 3 + 23. Suppose 5*o + 2*m - 14 = 11, 2*m - 10 = 0. Let -18*n**4 + o*n**t + 39*n**3 + 94*n**2 - 130*n**2 + 4*n + 8*n = 0. What is n?
0, 1, 2
Suppose -13*w + 1 + 38 = 0. Let j = 361/470 + 3/94. Determine s, given that j*s**4 + 0*s**w + 2/5*s**5 - 2/5*s + 0 - 4/5*s**2 = 0.
-1, 0, 1
Let i(o) be the first derivative of -2*o**6/15 + o**4/3 - 11*o + 8. Let d(p) be the first derivative of i(p). Let d(k) = 0. Calculate k.
-1, 0, 1
Solve 3*p**2 + 243 + 102*p + 163*p + 0*p**2 - 211*p = 0 for p.
-9
Solve -3/4*h**5 + 9/4*h**4 - 63/4*h + 9/2*h**3 - 27/4 - 15/2*h**2 = 0 for h.
-1, 3
Factor 33/7*t - 3/7*t**2 - 30/7.
-3*(t - 10)*(t - 1)/7
Factor -164/5*h + 0 + 2/5*h**2.
2*h*(h - 82)/5
Let m(v) be the first derivative of -9/28*v**4 + 0*v - 1/7*v**5 - 1/3*v**3 - 1/7*v**2 - 1/42*v**6 - 16. Suppose m(w) = 0. What is w?
-2, -1, 0
Let v(o) be the third derivative of -o**5/160 - 23*o**4/32 - 529*o**3/16 + 68*o**2. Factor v(z).
-3*(z + 23)**2/8
Let p(c) be the second derivative of -4/9*c**3 + 4*c - 5/72*c**4 + 7/120*c**5 + 0 - 1/3*c**2. Factor p(h).
(h - 2)*(h + 1)*(7*h + 2)/6
Let j(u) = -5*u**2 - 70*u - 15. Let l(w) = -w**2 - 18*w - 4. Let r(x) = 4*j(x) - 15*l(x). Factor r(y).
-5*y*(y + 2)
Let p(b) = b**2 - 1. Let h(w) = -w**2 + w - 2. Let k(v) = -2*v**2 + 2*v - 5. Let y(c) = -5*h(c) + 2*k(c). Let d(m) = 6*p(m) - 3*y(m). Solve d(g) = 0 for g.
-2, 1
Factor 27*h**2 - 8*h + 18*h**3 - 36 + 28*h + 3*h**4 - 13*h - 19*h.
3*(h - 1)*(h + 2)**2*(h + 3)
Solve -40 - 3*c**3 + 40 + 36*c + 0*c**4 - 3*c**4 + 24*c**2 = 0 for c.
-2, 0, 3
Let h = -13 + 15. Factor 60*m - 5*m**2 - 25*m + 0*m**h.
-5*m*(m - 7)
Let n(l) = -5*l**3 - 20*l**2 - 30*l - 10. Let b(o) = 5*o**3 + 21*o**2 + 31*o + 11. Let u(g) = 5*b(g) + 4*n(g). Find i, given that u(i) = 0.
-3, -1
Let m = 28806/19 - 1516. Let 2/19*k**2 + m*k - 4/19 = 0. What is k?
-2, 1
Let k = -938 + 938. Let b(o) be the second derivative of 0*o**2 + k*o**3 - 1/72*o**4 - 5*o + 0. Suppose b(p) = 0. What is p?
0
Let c = 121 - 38. Let z = -83 + c. Factor 0*o - 6/11*o**3 + 0*o**4 - 4/11*o**2 + z + 2/11*o**5.
2*o**2*(o - 2)*(o + 1)**2/11
Factor -3*d**4 - 4 + 12*d**3 + 6*d + 12*d**4 - 7*d**4 - 18*d**3 + 2*d**2.
2*(d - 2)*(d - 1)**2*(d + 1)
Suppose -45 = -2*u - 4*f + 19, -2*u - 2*f = -68. Factor -3*h**5 + h**5 - 35*h + 19*h - 40*h**2 - u*h**3 - 14*h**4.
-2*h*(h + 1)*(h + 2)**3
Let k = -676 + 678. Let h(x) be the second derivative of -1/2*x**k + 9*x + 0 + 1/12*x**4 + 0*x**3. Factor h(d).
(d - 1)*(d + 1)
Let g(m) = -m**2 + 1. Let n = -15 + 13. Suppose 0 + 4 = 2*p. Let r(w) = -2*w**2 - w + 1. Let b(j) = n*g(j) + p*r(j). Suppose b(v) = 0. Calculate v.
-1, 0
Let o be 3234/189 + -17 - (-52)/18. Suppose -4/7*l**2 + 0 + 2/7*l**o - 6/7*l = 0. What is l?
-1, 0, 3
Let b(g) be the first derivative of g**3/9 - 31*g**2/6 + 10*g + 113. Let b(h) = 0. What is h?
1, 30
What is u in 5/3 - 2*u + 1/3*u**2 = 0?
1, 5
Let v(c) be the second derivative of 1/20*c**5 - 1/24*c**4 + 0*c**2 - 1/6*c**3 + 0 - 19*c + 1/60*c**6. Find d, given that v(d) = 0.
-2, -1, 0, 1
Suppose -7/2*g**2 + 4*g**3 + 0 + 5/2*g**4 - 3*g = 0. Calculate g.
-2, -3/5, 0, 1
Suppose 2*w + 12 = 16. Let g(d) be the third derivative of -d**w + 0*d + 2/3*d**3 - 1/3*d**4 - 1/12*d**5 + 0. Factor g(c).
-(c + 2)*(5*c - 2)
Solve 14792/11 + 2/11*f**2 + 344/11*f = 0.
-86
What is y in 2/15*y**3 + 4/5*y**2 + 0*y + 0 = 0?
-6, 0
Let g(l) = -l**2 - l - 1. Let d(v) = -v**2. Let n(t) = -t**2 + 5