t derivative of 0*d - d**3 - 60 + 27/2*d**2. Suppose m(q) = 0. Calculate q.
0, 9
Let d be (8/(-10))/((-6)/15). Suppose -d*u + 10*u = 16. Factor 2*w**2 - u - w - w**3 - 6*w + 8*w.
-(w - 2)*(w - 1)*(w + 1)
Let c(t) be the third derivative of 0*t + 0*t**3 + 0*t**6 + 0*t**4 + 2/315*t**7 - 1/63*t**8 + 0 + 0*t**5 + 56*t**2. Solve c(h) = 0.
0, 1/4
Factor 36*p**3 + 1599*p**2 + 472*p + 679*p**2 - 253*p**2 + 107*p**2.
4*p*(p + 59)*(9*p + 2)
Let a(y) be the first derivative of -y**4/20 + 67*y**3/15 + 7*y**2 - 136*y/5 + 14285. Let a(s) = 0. Calculate s.
-2, 1, 68
Let t(b) be the second derivative of 6/7*b**3 + 0 - 1/28*b**4 - 50*b + 0*b**2. Factor t(r).
-3*r*(r - 12)/7
Let g(d) be the second derivative of d**7/14 + 28*d**6/15 + 43*d**5/4 + 45*d**4/2 + 26*d**3/3 - 28*d**2 - 1018*d. Solve g(t) = 0 for t.
-14, -2, -1, 1/3
Let a be (84/196 - (-6)/(-14))*(-1 + 2). Factor 0*n**3 - 3/7*n**4 + 9/7*n**2 + a + 6/7*n.
-3*n*(n - 2)*(n + 1)**2/7
Factor -5/4*r**3 + 16810 + 415/2*r**2 - 8815*r.
-5*(r - 82)**2*(r - 2)/4
Let x(c) be the first derivative of 9*c**4/2 + 112*c**3/3 + 12*c**2 - 267. Suppose x(n) = 0. Calculate n.
-6, -2/9, 0
Let j(o) be the second derivative of -25/2*o**3 + 5*o + 1/4*o**5 - 5/3*o**4 + 45*o**2 - 15. Factor j(k).
5*(k - 6)*(k - 1)*(k + 3)
Let j(i) = i**3 + 2*i - 1. Let b(a) = 2*a**4 - a**3 - 2*a**2 + 34*a - 11. Let f(r) = -2*b(r) + 22*j(r). Factor f(k).
-4*k*(k - 6)*(k - 1)*(k + 1)
Let t(n) = -n**2 + 11*n + 19. Let u be t(0). Suppose -36 - 9*y + u*y + 14*y - 3*y**2 = 0. Calculate y.
2, 6
Let z(r) be the first derivative of r**4/16 - r**3/2 - 163*r**2/8 - 102*r - 2218. Factor z(u).
(u - 17)*(u + 3)*(u + 8)/4
Let h be 4/6*(2 - 20). Let d be (h/16)/((-210)/80). Factor 1/7*c - 3/7*c**3 + 0*c**2 + 0 - d*c**4.
-c*(c + 1)**2*(2*c - 1)/7
Let l(z) be the third derivative of -z**6/180 + 2539*z**5/135 - 59737*z**4/3 + 53016*z**3 + 2*z**2 - 3*z + 267. Factor l(x).
-2*(x - 846)**2*(3*x - 2)/9
Let g(m) = -m**2 - 184*m + 3202. Let h be g(16). Determine t, given that 1/4*t**h + 4 - 17/4*t = 0.
1, 16
Let m(f) be the third derivative of 0*f + 10*f**3 - 2*f**2 + 16 + 1/12*f**5 + 5/3*f**4. Factor m(q).
5*(q + 2)*(q + 6)
Let g(f) be the third derivative of -f**5/60 + 17*f**4/8 - 24*f**3 + f**2 - 420. Suppose g(d) = 0. Calculate d.
3, 48
Let s(i) = -2*i - 38. Let v be s(-19). Suppose -r + 2*q + 1 = v, r - 11 = 3*q - 6*q. Solve 3*m**4 + r*m**3 - 43*m**3 + 20*m**3 = 0.
0, 6
Let u(t) be the third derivative of 10*t**2 + 0*t**3 + 0*t - 1/90*t**5 + 0 + 1/48*t**4. Factor u(o).
-o*(4*o - 3)/6
Let k be (-1154)/(-8) + (-3)/10*490/(-21). Suppose -30*z**4 + 140*z**5 + 65/2*z**2 - 5/2 - k*z**3 + 45/4*z = 0. What is z?
-1, -2/7, 1/4, 1
Suppose 8*q - 576 = 304. Find w such that q*w + 3*w**4 - 211*w + 101*w = 0.
0
Let p(k) = -3*k**2 - 495*k + 8762. Let c(g) = 85*g**2 + 13365*g - 236585. Let d(n) = -2*c(n) - 55*p(n). Factor d(b).
-5*(b - 76)*(b - 23)
Let v(n) be the first derivative of -2/85*n**5 - 1/17*n**4 + 4/17*n**2 - 8/17*n + 2/17*n**3 + 194. Factor v(p).
-2*(p - 1)**2*(p + 2)**2/17
Let i(y) be the third derivative of 0 + 0*y + 110*y**2 + y**4 + 38/9*y**3 - 1/45*y**5. Suppose i(x) = 0. Calculate x.
-1, 19
Suppose -4*a + 261 = -3*w, a - 16 = w + 49. Suppose 0 = -6*p + a + 42. Factor -10*f**4 - 13*f**3 + 23*f**4 - p*f**4 + 0*f**2 + 6*f**2.
-f**2*(f + 3)*(5*f - 2)
Let k(t) = -3*t**3 + 6*t**2 - 8*t + 23. Let u be k(5). Let x = -238 - u. Let -1/8*c**2 + 0 - 1/8*c + 1/8*c**3 + 1/8*c**x = 0. Calculate c.
-1, 0, 1
Let f(o) = 35*o**4 - 60*o**3 - 35*o**2 + 60*o + 5. Let i(x) = -x**5 + x**4 + x**3 - x**2 - 1. Let z(v) = -f(v) - 5*i(v). What is d in z(d) = 0?
-1, 0, 1, 2, 6
Let h = 7739 + -270863/35. Let f(z) be the second derivative of 0*z**6 - 8*z + 0*z**2 + 0*z**4 + 0 + 2/147*z**7 + 2/21*z**3 - h*z**5. Factor f(n).
4*n*(n - 1)**2*(n + 1)**2/7
Let j = -32 - -44. Suppose 19*f - j = 15*f. Factor 10 + 10*q**2 + 45*q**f - 30*q**3 + 0 - 35*q.
5*(q - 1)*(q + 2)*(3*q - 1)
Let k(h) be the third derivative of h**6/60 - 7*h**5/120 - 49*h**4/24 - 2*h**3 + 4124*h**2. Factor k(f).
(f - 6)*(f + 4)*(4*f + 1)/2
Let s be ((-80)/(-24) - 390/117)/(-3). Factor 4/3*u**2 + 20/9*u**3 - 4/9*u**5 + 0*u + s + 4/9*u**4.
-4*u**2*(u - 3)*(u + 1)**2/9
Let a = 2205 + -2200. Let t(k) be the first derivative of -3/5*k**a - 4*k**3 + 0*k + 0*k**2 - 3*k**4 + 1. Factor t(u).
-3*u**2*(u + 2)**2
Let g(h) be the second derivative of -h**7/54 - 17*h**6/90 + 49*h**5/60 + 319*h**4/108 - 50*h**3/9 - 6*h**2 + 3*h + 310. Suppose g(o) = 0. Calculate o.
-9, -2, -2/7, 1, 3
Let d(x) be the third derivative of -37*x + 4/15*x**5 - x**2 + 5/3*x**4 + 16/3*x**3 + 0 + 1/60*x**6. Factor d(q).
2*(q + 2)**2*(q + 4)
Factor 69/5*f - 6/5*f**3 + 9/5*f**2 - 36/5.
-3*(f - 4)*(f + 3)*(2*f - 1)/5
Let f be ((-4)/(-11) - 0) + (-2900)/(-1100). Let m(k) be the second derivative of -2/9*k**4 + 0*k**2 - 12*k + 0 + 4/9*k**f + 1/30*k**5. Factor m(a).
2*a*(a - 2)**2/3
Let o(h) be the first derivative of 2*h**3 + 1/10*h**6 - 3/5*h**5 + 1/2*h**4 + 19*h + 36 - 9/2*h**2. Let n(j) be the first derivative of o(j). Factor n(u).
3*(u - 3)*(u - 1)**2*(u + 1)
Suppose -32 + 312 = 140*g. Factor 3/7*h**g - 6/7 + 3/7*h.
3*(h - 1)*(h + 2)/7
Let l = 483 - 467. Suppose 2 + l + 4*h**2 - 6*h**2 = 0. What is h?
-3, 3
Let o be 36/(-8)*(-8)/12. Suppose o*d - 13 = -4. Solve 23 - 25*r - 11*r**3 - 33 - 9*r**d - 25*r**3 + 80*r**2 = 0 for r.
-2/9, 1
Factor -257 + 60 + 4*n**3 + 256 + 133 - 80*n - 16*n**2.
4*(n - 6)*(n - 2)*(n + 4)
Let -4/5*y**5 + 0 + 16/5*y**4 - 48/5*y - 16/5*y**2 + 52/5*y**3 = 0. Calculate y.
-2, -1, 0, 1, 6
Suppose 2*z - 58 = -3*m - 1873, 0 = -z - 3. Let w = m + 608. Factor 0*i**3 + 3/4*i**4 - 3/8*i + 0 + 3/8*i**w - 3/4*i**2.
3*i*(i - 1)*(i + 1)**3/8
Let -2959*d**3 - d**4 - 4*d + 12 + 1453*d**3 - 9*d**2 + 1512*d**3 = 0. Calculate d.
-1, 2, 3
Let a be (-2)/(-40)*(-5)/(-2). Let u(z) be the first derivative of a*z**4 - 1/2*z + 1/6*z**3 + 19 - 1/4*z**2. Factor u(o).
(o - 1)*(o + 1)**2/2
Let j(v) = -v + 9. Let c be j(1). Let m be (c/(-6))/(46/(-9) - -5). Factor -3*y**5 - m*y**4 + 7*y**5 + 815*y**2 + 8*y**3 - 815*y**2.
4*y**3*(y - 2)*(y - 1)
Factor -469*r**3 + 4*r + 6*r + 234*r**3 - 60*r + 237*r**3.
2*r*(r - 5)*(r + 5)
Let g(y) be the second derivative of 1/11*y**3 - 1/66*y**4 + 23/2*y**2 + 0 + 12*y - 1/330*y**5. Let i(h) be the first derivative of g(h). Factor i(a).
-2*(a - 1)*(a + 3)/11
Let d(f) be the second derivative of -2*f**6/15 + 53*f**5/5 + f**4/3 - 106*f**3/3 - 1042*f. Let d(o) = 0. What is o?
-1, 0, 1, 53
Find l such that -70 + 70 - 3*l**3 - 285*l + 249*l**2 - 303*l + 102*l = 0.
0, 2, 81
Let m be (-40)/(-6)*2/15*(352 + -350). What is s in 0 - 16/9*s + 4/9*s**3 - m*s**2 + 4/9*s**4 = 0?
-2, -1, 0, 2
Determine p so that 37676/7*p**3 + 6/7*p**5 - 926/7*p**4 - 150156/7*p**2 - 33750/7 + 147150/7*p = 0.
1/3, 1, 3, 75
Suppose -7*m - 9 = -10*m. Factor -19*u**m - 10*u + 38*u**3 + 5*u**5 - 40*u**2 - 34*u**3 + 15*u**2 + 5*u**4.
5*u*(u - 2)*(u + 1)**3
Let m be 2857/(-5985) - 1/(-7) - -2. Let l = m - -1/855. Find c, given that 0*c + l - 5/3*c**2 = 0.
-1, 1
Factor -335*w + 178 + 427*w + 628 + 331 + 2*w**2 - 97.
2*(w + 20)*(w + 26)
Let m(t) be the second derivative of 1/36*t**4 + 5/18*t**3 + 2/3*t**2 + 2*t + 4. Factor m(i).
(i + 1)*(i + 4)/3
Let m(r) be the second derivative of -3*r**5/20 + 73*r**4/4 + r + 6003. Suppose m(y) = 0. What is y?
0, 73
Let j(h) be the second derivative of -1/4*h**5 + 125/6*h**3 + 0 + 0*h**2 + 47*h + 10*h**4. Let j(z) = 0. Calculate z.
-1, 0, 25
Suppose -180 = -25*u + 45. Find r such that -2*r**3 + 12 + 8 - 8*r**2 - 5*r + 5*r**3 - u*r - r**3 = 0.
-2, 1, 5
Let g = -190 + 192. Suppose -24*u**3 - 288*u + 22*u**3 + 0*u**3 + 48*u**g = 0. What is u?
0, 12
Let r(z) = 4*z**2 - 4*z + 39. Let x(p) = -7*p**2 + 7*p - 65. Let h(d) = 5*r(d) + 3*x(d). Find w, given that h(w) = 0.
0, 1
Let c(y) be the first derivative of y**6/27 + 4*y**5/15 - 5*y**4/9 - 32*y**3/27 + 11*y**2/3 - 28*y/9 - 1037. Determine j, given that c(j) = 0.
-7, -2, 1
Let m(r) be the second derivative of r**5/20 - 59*r**4/4 - 89*r**3/3 + 13*r + 3. Determine i so that m(i) = 0.
-1, 0, 178
Let d be (-2)/3 - (-10 + 65 - 59). Factor 14/3*n**3 - 32/3*n - 8/3 - d*n**2.
2*(n - 2)*(n + 1)*(7*n + 2)/3
Let j(b) be the third derivative of -b**7/735 - 13*b**6/420 - 3*b**5/14 + 25*b**4/84 + 250*b**3/21 + 7*b**2