he second derivative of -p**6/210 + 17*p**5/140 - 5*p**4/14 - 585*p - 2. Determine m so that i(m) = 0.
0, 2, 15
Let f(k) be the first derivative of -2*k**3/21 + 6*k**2 + 470*k/7 - 3775. Solve f(c) = 0 for c.
-5, 47
Let b(u) be the third derivative of 3*u - 29/96*u**4 + 1/240*u**5 + 0 + 7/6*u**3 + 79*u**2. Factor b(g).
(g - 28)*(g - 1)/4
Suppose -2*q - 2 = -2*t, 9*q - 7*t + 11*t - 30 = 0. What is v in 0 - 6/5*v - 3/5*v**q = 0?
-2, 0
Suppose -12*w = -588 - 1428. Factor -2*f**2 - 355 - 831 + 668 - 1537 - 1473 + w*f.
-2*(f - 42)**2
Factor 52*q**4 - 2*q**5 + 0*q**5 - 72*q**3 - 964*q - 1536 + 178566*q**2 + 2948*q - 179222*q**2.
-2*(q - 24)*(q - 2)**3*(q + 4)
Let t be 9 - -5 - -999*(-25)/1800. Let 0 - 9/4*z**2 - t*z**3 + 0*z = 0. What is z?
-18, 0
Let q = -144 + 147. Suppose 5*f + 4*p + 12 = 0, -11*f + 6*f = -q*p - 9. Factor -20/3*n**3 + f*n + 10/3*n**2 + 25/6*n**4 - 5/6*n**5 + 0.
-5*n**2*(n - 2)**2*(n - 1)/6
Let f = 2/356391 - -11298914/118797. Let n = 11146/117 - f. Find s, given that -4/13*s + n*s**2 + 0 + 2/13*s**3 = 0.
-2, 0, 1
Let w be (-1670)/(-105)*-16 - (-2)/14. Let p = -254 - w. Factor -1/3*u + p*u**4 + 0 + 1/3*u**3 - 1/3*u**2.
u*(u - 1)*(u + 1)**2/3
Let w(i) = -23*i + 6. Let s be w(-1). Factor -6 + 2*u**4 - 21 + s - 4*u**2.
2*(u - 1)**2*(u + 1)**2
Let g(q) be the third derivative of -q**7/560 + q**6/320 + 5*q**5/2 - 25*q**4/4 + 158*q**2 + 2*q - 1. Determine b, given that g(b) = 0.
-20, 0, 1, 20
Suppose -18*v = -17*v - 15. Suppose -3*d + v + 18 = 0. Factor 16*u**2 + 7*u**2 - d*u**2 - 16*u + 8*u**3 - 4*u**4 - 16.
-4*(u - 2)**2*(u + 1)**2
Let s(x) be the first derivative of -3*x - 1/4*x**3 + 0*x**2 + 13 - 1/16*x**4. Let h(a) be the first derivative of s(a). Factor h(r).
-3*r*(r + 2)/4
Let c(n) be the second derivative of n**5/100 - n**4/5 + 7*n**3/6 - 12*n**2/5 + 162*n. Factor c(t).
(t - 8)*(t - 3)*(t - 1)/5
Let g(w) be the third derivative of 29*w**2 - 100/3*w**3 - 4/5*w**5 + 15/2*w**4 + 1/30*w**6 + 0 + 0*w. Factor g(o).
4*(o - 5)**2*(o - 2)
Suppose 24 + 5 = m. Let b = m + -26. Factor 2*d**b - 14*d + 0*d**3 + 324 - 312.
2*(d - 2)*(d - 1)*(d + 3)
Let j(n) = 31*n**3 - 224*n**2 - 721*n. Let a(l) = -2*l**3 + 14*l**2 + 45*l. Let x(t) = -94*a(t) - 6*j(t). Factor x(m).
2*m*(m + 6)*(m + 8)
Let y(q) = q**2 + 11*q - 22. Let u(i) = -15 + 6 + 11. Let b(t) = -5*u(t) - y(t). Factor b(o).
-(o - 1)*(o + 12)
Let o(w) be the first derivative of -3*w**4/4 - 61*w**3 + 3*w**2/2 + 183*w - 2013. Find n, given that o(n) = 0.
-61, -1, 1
Let a be (-8)/9 - 16/(-16). Let o = 1343 + -1341. Let 1/9 + a*b**o + 2/9*b = 0. Calculate b.
-1
Let a(g) be the third derivative of g**5/48 - 325*g**4/96 - 335*g**3/12 - 150*g**2 - 4*g. Let a(i) = 0. What is i?
-2, 67
Suppose 3*r = 3*x - 147, x + 5*r = -0*x + 37. What is s in -18*s - 2*s**3 + 172*s**2 - 20*s - x*s**2 - 29*s**2 - 56*s**2 = 0?
0, 1, 19
Factor -27/10*u**2 + 1/10*u**3 - 1/10*u + 27/10.
(u - 27)*(u - 1)*(u + 1)/10
Factor -44*y - 434653*y**3 - 3*y**2 - 27*y - y**2 - 66 + 434654*y**3.
(y - 11)*(y + 1)*(y + 6)
Let d(b) be the first derivative of -20/7*b**2 + 6*b - 2/21*b**3 - 31. What is r in d(r) = 0?
-21, 1
Factor 3/2*v**4 + 0*v - 63*v**2 - 3/2*v**3 + 0.
3*v**2*(v - 7)*(v + 6)/2
Suppose 16 = -2*w - 4*t, 4*w + 5 - 23 = 2*t. Suppose -2*c = -p + 9 - 1, -c = w. Factor 3/7*b**5 + 0*b + 3/7*b**3 + 0 + 0*b**2 + 6/7*b**p.
3*b**3*(b + 1)**2/7
Let v(l) be the first derivative of 3*l**4/4 + 323*l**3 + 39840*l**2 + 230400*l + 1356. Let v(c) = 0. Calculate c.
-160, -3
Let h(g) be the first derivative of -g**5/25 + 24*g**4/5 - 19*g**3/3 - 4155. Determine r so that h(r) = 0.
0, 1, 95
Let d be 3*(-7)/21 + 1. Find s such that -11 - 6*s - 61 + d*s - 11*s - 7*s - 2*s**2 = 0.
-6
Suppose -124131*m + 124210*m = 316. Solve 2 + 52/5*v + 6/5*v**m + 44/5*v**3 + 16*v**2 = 0.
-5, -1, -1/3
Let u(y) be the second derivative of -y**8/420 + 2*y**7/105 - 7*y**6/150 + y**5/25 - 61*y**2 + y - 26. Let h(s) be the first derivative of u(s). Factor h(q).
-4*q**2*(q - 3)*(q - 1)**2/5
Suppose -948*i + 933*i = 0. Let q(n) be the third derivative of 0*n**4 - 1/240*n**6 + 0*n**3 + 0 - 1/420*n**7 - 16*n**2 + i*n + 1/60*n**5. Factor q(w).
-w**2*(w - 1)*(w + 2)/2
Let i(x) = x**2 + 10*x + 16. Let a be i(-8). Suppose a = -3*h + 4 + 8. Factor -4*d**4 - 11*d**3 + h*d**5 + 612*d**2 - 5*d**3 - 596*d**2.
4*d**2*(d - 2)*(d - 1)*(d + 2)
Let c(m) be the third derivative of m**5/60 + 13*m**4 - 318*m**3 + 79*m**2 + 35*m. Factor c(h).
(h - 6)*(h + 318)
Let f = 1909399 + -1909399. Let n = -25/4 + 7. Let -3/4*h**2 - n*h + f = 0. What is h?
-1, 0
Let q(c) be the third derivative of -2 + 0*c**4 + 0*c**3 + 5/42*c**7 - 1/24*c**6 + 0*c**5 + 0*c - 222*c**2 - 5/84*c**8. Let q(p) = 0. Calculate p.
0, 1/4, 1
Let p(w) be the first derivative of 163 - 13/3*w**2 + 10/3*w - 8/15*w**4 + 112/45*w**3. Factor p(r).
-2*(r - 1)*(4*r - 5)**2/15
Find c, given that -63/8*c**3 + 1/2*c**4 - 25/4 + 61/2*c**2 - 135/8*c = 0.
-1/4, 1, 5, 10
Factor -996979*w + 13486*w**3 - 137465*w + 13494*w**3 + 323208 + 13473*w**3 + 11264*w**2 - 40481*w**3.
-4*(w - 201)**2*(7*w - 2)
Let y = 2/27031 + 81023/946085. Let k(u) be the first derivative of -9/7*u - 12/7*u**2 + 0*u**4 + 3 - 6/7*u**3 + y*u**5. Factor k(g).
3*(g - 3)*(g + 1)**3/7
Let h = 7571924/701105 + 2/140221. Let -1/5*c**3 + 5832/5 + h*c**2 - 972/5*c = 0. What is c?
18
Factor 34*r**2 + 200/3 - 904/9*r - 2/9*r**3.
-2*(r - 150)*(r - 2)*(r - 1)/9
Let v = 97374 - 97370. Determine p, given that -2*p**3 + 3/2*p + 1/2*p**5 + 0 + p**v - p**2 = 0.
-3, -1, 0, 1
Let s(z) be the third derivative of -z**7/1890 - z**6/108 - 31*z**5/540 - 5*z**4/36 - 477*z**2. Suppose s(o) = 0. Calculate o.
-5, -3, -2, 0
Let d be 14/4*28/49. Suppose h - 12 = -t, 3*h - 29 = -0*t - d*t. Factor -t + 138*s**2 - 8*s - 9 - 134*s**2 + 2*s**3.
2*(s - 2)*(s + 2)**2
Suppose -4*j + 80 - 52 = 0. Let -3 - 2*t**2 + 7*t + j - 9*t = 0. What is t?
-2, 1
Let g = 7026 + -7016. Let d(o) be the third derivative of 1/10*o**3 - g*o**2 - 1/200*o**6 + 1/40*o**4 + 0*o + 0 - 1/100*o**5. Determine w, given that d(w) = 0.
-1, 1
Let f be (162/27 + -5)/(14/158). Factor 18/7*d + 54/7*d**3 + d**4 + 0 - f*d**2.
d*(d - 1)*(d + 9)*(7*d - 2)/7
Let l(k) be the first derivative of -k**4/24 + 434*k**3/9 - 865*k**2/3 + 576*k - 5779. Factor l(w).
-(w - 864)*(w - 2)**2/6
Find g such that -2/5*g**2 - 74498/5 + 772/5*g = 0.
193
Let o(r) = -2*r**3 - 27*r**2 - 72*r + 24. Let i be o(-10). Suppose 10*h = -i*h. Factor h*n - 3/10*n**3 - 1/10*n**2 + 0.
-n**2*(3*n + 1)/10
Determine c so that 144*c**2 - 20*c**2 + 670*c - 14*c**2 - 105*c**2 + 3225 = 0.
-129, -5
Factor -2/7*s - 158/7 + 2/7*s**3 + 158/7*s**2.
2*(s - 1)*(s + 1)*(s + 79)/7
Let m(r) be the third derivative of r**5/60 - 34*r**4/3 + 9248*r**3/3 - 241*r**2 - 2*r. Factor m(q).
(q - 136)**2
Let r = 966 + -968. Let s be 8/r - 32/((-88)/11). Factor 1/7*t - 5/7*t**3 + s + 3/7*t**4 + 1/7*t**2.
t*(t - 1)**2*(3*t + 1)/7
Let h(n) be the first derivative of n**3 - 9*n**2/2 - 10*n - 67. Let i be h(-1). Solve 0 + 12/5*z**4 + 2/5*z**5 + 26/5*z**3 + 8/5*z + 24/5*z**i = 0 for z.
-2, -1, 0
Let q be (((-8)/(-6))/1)/((-14)/126). Let v be (q/42 - 65/(-7))*2. Let -30*m**2 - 7*m - 24 - 48*m + v*m**3 - 9*m = 0. What is m?
-2/3, 3
Let -21*j**4 + 334*j**3 - 104*j**2 - 703 - 23*j**4 - 193 - 2019*j**5 + 2017*j**5 - 1376*j = 0. What is j?
-28, -1, 4
Let c(w) be the second derivative of 31/33*w**3 + 0 + 99*w + 5/22*w**5 + 6/11*w**2 + 25/33*w**4. Determine p, given that c(p) = 0.
-1, -3/5, -2/5
Let v be 1/(20/(-30))*(-28)/21*(-14)/(-140). Find r, given that 8 - v*r**2 - 18/5*r = 0.
-20, 2
Let w = -142792 + 142805. Factor -w*j**2 + 39/2*j**3 - 2*j**4 + 0 - 9/2*j.
-j*(j - 9)*(j - 1)*(4*j + 1)/2
Factor 24030*s**2 - 664 + 78 - 275 - 24029*s**2 + 284*s.
(s - 3)*(s + 287)
Suppose -84*b - 321517 + 321685 = 0. What is q in 0 + 12/5*q + 2/5*q**b - 2/5*q**3 = 0?
-2, 0, 3
Let g(z) be the first derivative of -56 + 15/16*z**4 - 27*z + 17/4*z**3 - 63/2*z**2. Factor g(f).
3*(f - 3)*(f + 6)*(5*f + 2)/4
Let j(w) be the third derivative of w**5/40 - 267*w**4/4 + 71289*w**3 + 3*w**2 + 141*w. Factor j(t).
3*(t - 534)**2/2
Let g(j) = 5*j**3 - 3*j**2 + 2*j + 2. Let a be g(2). Let t be a/12 + (-4)/(-24). Determine i, given that 10*i**2 - 8*i - 10*i**2 + 2*i**t + 0*i**3 = 0.
-2, 0, 2
Solve 1/2*k**5 + 9/2*k + 3/2*k**4 - 5*k**3 - 5/2 + k**2