be the second derivative of -g**6/72 + 35*g**5/6 - 6125*g**4/6 - 11*g**3/2 - g**2 - 110*g. Let k(a) be the second derivative of v(a). Factor k(m).
-5*(m - 70)**2
Let l(m) be the third derivative of -m**8/84 - 34*m**7/15 + 43*m**6/10 + 1091*m**5/15 + 662*m**4/3 + 320*m**3 - 47*m**2 - 18. Solve l(y) = 0.
-120, -1, 4
Let -4/7*d**4 - 4*d**3 + 48/7*d + 0 - 16/7*d**2 = 0. Calculate d.
-6, -2, 0, 1
Solve -32/3 - 400/3*w - 200*w**3 - 1346/3*w**2 - 24*w**4 = 0.
-4, -1/6
Let t(g) be the third derivative of -g**7/42 + 41*g**6/8 - 157*g**5/4 - 2975*g**4/24 - 8144*g**2. Factor t(y).
-5*y*(y - 119)*(y - 5)*(y + 1)
Let s(g) be the first derivative of 4*g**5/5 - 11*g**4 - 160*g**3 - 216*g**2 - 3028. Determine n, given that s(n) = 0.
-6, -1, 0, 18
Let k(c) be the second derivative of 0 + 5/12*c**4 + 153*c - 140/3*c**3 + 1960*c**2. Find h such that k(h) = 0.
28
Let a(n) = -13*n**2 - 63*n - 212. Let m(u) = -2*u**2 - 2. Let i(h) = -2*a(h) + 14*m(h). Find z such that i(z) = 0.
-3, 66
Factor -2*b**2 - 3*b**2 - 96*b + 456 - 389*b + 2*b**2 + 32*b.
-3*(b - 1)*(b + 152)
Suppose -u + 1 = -1. Let k be 9 - (u - 2) - 4. Let 4*j**3 + 5*j - 2*j + 8*j**k - 5*j - 10*j**5 = 0. What is j?
-1, 0, 1
Let s be 2*5/(-10)*-12. Let z(w) = -4*w + 1. Let o(q) = -q**2 + 24*q + 5. Let c(v) = s*z(v) + 3*o(v). Factor c(t).
-3*(t - 9)*(t + 1)
Factor -22/5*r + 12 + 2/5*r**2.
2*(r - 6)*(r - 5)/5
Let v(g) be the third derivative of g**5/60 + 9*g**4/8 - 15*g**3 + 272*g**2 - 7*g. Factor v(y).
(y - 3)*(y + 30)
Suppose 11*g = 4 + 20 - 2. Let y(a) be the first derivative of 21/2*a**4 - 14 - 16*a - 36*a**g - 44/3*a**3. Suppose y(m) = 0. What is m?
-2/3, -2/7, 2
Factor 4389025/2*f**2 + 1/2*f**4 + 0*f + 2095*f**3 + 0.
f**2*(f + 2095)**2/2
Let i(y) be the second derivative of 1/4*y**5 - 10/3*y**4 + 6*y - 25*y**2 + 3 - 95/6*y**3. Factor i(h).
5*(h - 10)*(h + 1)**2
Let j(h) be the third derivative of h**7/70 - 31*h**6/40 + 137*h**5/10 - 189*h**4/2 + 324*h**3 + 7*h**2 + 14*h - 8. Factor j(b).
3*(b - 18)*(b - 9)*(b - 2)**2
Let i(j) be the first derivative of 2*j**6/21 - 4*j**5/5 + 9*j**4/7 + 4*j**3/3 - 20*j**2/7 + 2283. Let i(p) = 0. Calculate p.
-1, 0, 1, 2, 5
Let a(l) be the third derivative of -l**7/2520 - l**6/90 - l**5/8 - 3*l**4/4 - 289*l**3/6 + 5*l**2 + 16. Let b(w) be the first derivative of a(w). Factor b(f).
-(f + 3)**2*(f + 6)/3
Let a(p) be the third derivative of p**7/42 - 49*p**6/12 + 527*p**5/4 - 7775*p**4/6 - 19750*p**3/3 + 6962*p**2. Determine v, given that a(v) = 0.
-1, 10, 79
Determine u, given that -42*u - 2/3*u**2 - 1900/3 = 0.
-38, -25
Suppose 0 = -17*i + 23*i - 24. Determine k so that -2*k**3 + 27*k**2 - 4*k - 16*k**5 - 16*k**4 - 30*k**4 - 9*k**4 - 17*k**i - 23*k**3 = 0.
-4, -1, 0, 1/4
Let y(a) be the first derivative of -8*a**6/3 - 32*a**5/5 + 91*a**4 + 980*a**3/3 + 2225. Factor y(f).
-4*f**2*(f - 5)*(2*f + 7)**2
Factor 5/3*z**3 + 280/3*z + 50*z**2 + 0.
5*z*(z + 2)*(z + 28)/3
Let z(l) be the third derivative of 2*l**2 + 0*l + 11/1890*l**7 + 1/540*l**5 + 0*l**3 + 1/120*l**6 + 1/756*l**8 - 1/216*l**4 + 1. Let z(x) = 0. What is x?
-1, 0, 1/4
Let h(u) be the second derivative of 64*u + 0 + 0*u**2 + 81/190*u**5 + 6/19*u**4 + 4/57*u**3. Determine g so that h(g) = 0.
-2/9, 0
Let l be 8/(-42)*((-63)/6)/7. Let j be (6/8)/((-116)/(-32) + -1). Factor 4/7*v - l*v**2 - j.
-2*(v - 1)**2/7
Let v(j) = 5*j**2 + 4*j + 4. Let t = -40 + 38. Let s be v(t). Determine d, given that -s + 0*d - 12*d - 20 + 0*d - d**2 = 0.
-6
Suppose 8*g**2 + 30*g**3 - 4*g**5 - 103 + 43 - 76 + 242*g**3 + 128*g**4 - 268*g = 0. What is g?
-1, 1, 34
Suppose 0*h - 3*q = 4*h - 63, 57 = 4*h + 5*q. Let k be 6/39 + 37/13. Find r such that -r - 2*r - 3*r**4 - h*r**3 - 9*r**2 + 9*r**k + 0*r = 0.
-1, 0
Let z be 0*(-3)/(-18) + 2. Factor 6876 - 3*h**2 + 432*h + 7*h**z + 695 + 6232 - 2139.
4*(h + 54)**2
Let r be (-6)/(-69)*23*(3 - 2). Factor 0 - 2/3*m**2 - 4/3*m**4 - r*m**3 + 0*m.
-2*m**2*(m + 1)*(2*m + 1)/3
Let t(l) = 49*l - 345. Let n be t(7). Let i be ((-2)/(-5))/((-21)/(-105)) - n. What is y in 2/3*y**2 - 4/3*y**3 - 3 - 1/3*y**i + 4*y = 0?
-3, 1
What is n in 1348*n + 19*n**3 - 16*n**3 + 185*n**2 - 1805 + 267*n + 2*n**3 = 0?
-19, 1
Let -60/7*o**2 + 0*o - 312/7*o**4 + 0 + 46*o**3 + 50/7*o**5 = 0. What is o?
0, 6/25, 1, 5
Factor 18/7*w**2 - 2/7*w**3 + 0 + 18/7*w - 2/7*w**4.
-2*w*(w - 3)*(w + 1)*(w + 3)/7
Let m(b) = b**4 + b**2 + b. Let a(z) = -5*z**5 + 5*z**4 + 65*z**3 - 45*z**2 - 190*z - 100. Let n(k) = -a(k) - 10*m(k). Find s such that n(s) = 0.
-2, -1, 2, 5
Let y(j) be the third derivative of j**5/70 + 13*j**4/4 - 480*j**3/7 - 117*j**2 + 20*j + 1. Factor y(t).
6*(t - 5)*(t + 96)/7
Let y be ((-14)/119 - 75/85) + (-12)/(-9). Let l(z) be the first derivative of 1/5*z**5 + 0*z + 1/2*z**2 - y*z**3 - 1/4*z**4 + 12. Let l(c) = 0. Calculate c.
-1, 0, 1
Let l(v) be the first derivative of 0*v**3 - 17*v + 0*v**5 + 0*v**4 - 4 + 1/10*v**6 + 0*v**2. Let m(n) be the first derivative of l(n). Factor m(t).
3*t**4
Let d(i) = -i - 1. Let v(f) = -12*f**2 + 12. Suppose -174 = -17*x - 38. Let y(w) = x*d(w) + v(w). Factor y(n).
-4*(n + 1)*(3*n - 1)
Let c(d) be the second derivative of -d**6/40 + d**5/2 - 13*d**4/8 - 12*d**3 - 77*d**2/2 - 121*d. Let w(g) be the first derivative of c(g). Factor w(m).
-3*(m - 8)*(m - 3)*(m + 1)
Let p(r) be the second derivative of -1/100*r**5 + 1/10*r**3 + 3*r - 9/5*r**2 - 3 + 1/15*r**4. Factor p(m).
-(m - 3)**2*(m + 2)/5
Suppose -62 = 235*c - 266*c. Let l(j) be the second derivative of 1/18*j**4 + 32*j + 49/3*j**c + 0 - 14/9*j**3. Suppose l(u) = 0. What is u?
7
Let x = 9 - 3. Let c be x/2 + -1 + 0. Factor 15*l**2 - c*l**4 + 84*l**3 + 6*l - 72*l**3 + 5*l**4.
3*l*(l + 1)**2*(l + 2)
Let n(p) be the second derivative of p**7/14 - 48*p**6/5 + 4743*p**5/10 - 9610*p**4 + 89373*p**3/2 + 408*p - 7. Let n(l) = 0. What is l?
0, 3, 31
Let g(n) be the first derivative of -5*n**4/4 - 325*n**3/3 + 690*n**2 + 5102. Factor g(l).
-5*l*(l - 4)*(l + 69)
Factor 3/4*y**5 + 633/2*y**2 + 207/2*y**4 + 0 - 423/4*y - 315*y**3.
3*y*(y - 1)**3*(y + 141)/4
Let c(l) be the first derivative of -l**6/12 + 247*l**5/30 - 1705*l**4/8 + 287*l**3/6 + 8405*l**2/6 - 7211. Determine t, given that c(t) = 0.
-5/3, 0, 2, 41
Let r(t) be the third derivative of -t**8/80640 + t**7/10080 - 28*t**5/15 + 233*t**2. Let q(f) be the third derivative of r(f). What is i in q(i) = 0?
0, 2
Determine k so that -30*k - 313 - 312 - k**2 + k**2 - 3*k**2 + 658 = 0.
-11, 1
Let i(c) be the second derivative of -3*c**6/55 + 3*c**5/22 + 5*c**4/11 - 20*c**3/11 + 24*c**2/11 + 1804*c. Suppose i(z) = 0. Calculate z.
-2, 2/3, 1, 2
Let z(r) be the first derivative of -r**4/15 + 116*r**3/15 + 118*r**2/5 - 3*r - 47. Let f(s) be the first derivative of z(s). Determine k, given that f(k) = 0.
-1, 59
Solve 2*t**4 - 3/2 - 13/2*t**3 + 13/2*t - 1/2*t**2 = 0.
-1, 1/4, 1, 3
Let j be (-23214)/(-30) + (-6)/(-5). Find s, given that 22*s**3 - 1385*s**2 - 66*s**4 + 3*s**5 + 200*s**3 + 18*s**3 + 3888*s + 312*s**3 - j*s**2 - 2592 = 0.
2, 6
Let s(d) be the first derivative of 47*d**4 - 1152*d**2 + 4/5*d**5 + 0*d - 170 + 704*d**3. Suppose s(p) = 0. Calculate p.
-24, 0, 1
Let q = -3888 + 3895. Let c(y) be the second derivative of 0*y**2 + 1/48*y**3 + 1/336*y**q + 0 + 13*y - 1/60*y**6 + 3/80*y**5 - 1/24*y**4. Factor c(d).
d*(d - 1)**4/8
Let h(l) be the first derivative of l**5/40 - 7*l**4/32 - l**3/24 + 7*l**2/16 + 1641. Factor h(m).
m*(m - 7)*(m - 1)*(m + 1)/8
Let b be (-18)/((-19440)/(-28))*(-3)/14. Let f(w) be the third derivative of 0 - 1/450*w**5 - 3*w**2 + b*w**4 + 2/45*w**3 + 0*w. Suppose f(z) = 0. Calculate z.
-1, 2
Let b(r) = 3*r**3 + 176*r**2 - 693*r + 827. Let v(l) = -l**3 - 87*l**2 + 346*l - 414. Let c(u) = 6*b(u) + 13*v(u). Solve c(q) = 0 for q.
2, 6, 7
Let h = 1119/815 + -126/163. Let c(b) be the second derivative of -34/3*b**4 + 8/15*b**6 - 48*b**2 - 5*b - 2/21*b**7 + 0 + 104/3*b**3 + h*b**5. Factor c(k).
-4*(k - 2)**3*(k - 1)*(k + 3)
Factor 141/8*y**2 + 9/2 + 75/2*y.
3*(y + 2)*(47*y + 6)/8
Factor -189*j**3 - 1/5*j**5 + 66/5*j**4 + 0 - 980*j**2 + 0*j.
-j**2*(j - 35)**2*(j + 4)/5
Let u = -25423/22 + 12794/11. Factor 3/4*o**2 - u*o + 27/4.
3*(o - 9)*(o - 1)/4
Let i(k) be the third derivative of -29/36*k**4 - k**3 - 49/135*k**5 + 92*k**2 + 0 - 1/315*k**7 + 1/1512*k**8 - 7/90*k**6 + 0*k. Factor i(a).
2*