econd derivative of 5/78*k**4 - 3/13*k**3 + k + 23 - 2/13*k**2. Factor m(i).
2*(i - 2)*(5*i + 1)/13
Let d(o) = 35*o - 837. Let g be d(24). Let z(f) be the first derivative of 8/7*f**2 + 2/21*f**g + 5 + 32/7*f. Factor z(n).
2*(n + 4)**2/7
Let r = 670 - 558. Determine x, given that 518*x**2 + 951 - 161*x + 4*x**4 - 1295*x - 275 + 10*x**2 - r*x**3 + 360*x**2 = 0.
1, 13
Suppose 4*b + l + 18 - 26 = 0, 0 = -5*l + 40. Let 2/7*k**5 + b - 24/7*k**4 + 512/7*k + 8/7*k**3 + 384/7*k**2 = 0. Calculate k.
-2, 0, 8
Let j(a) be the second derivative of 2*a**7/7 + 81*a**6/10 + 177*a**5/5 + 131*a**4/2 + 60*a**3 + 51*a**2/2 - 138*a + 4. Let j(m) = 0. What is m?
-17, -1, -1/4
Let c = -291 - -290. Let a(g) = -g + 1. Let j(y) = -24*y**2 + 23*y + 1. Let i(w) = c*j(w) - a(w). Factor i(x).
2*(x - 1)*(12*x + 1)
Suppose 5*d = 2828 + 937. Factor 0*w**2 + d*w - 758*w + 9*w**2 - 2 - 13*w**2 - w**3.
-(w + 1)**2*(w + 2)
Let f(d) be the third derivative of -d**6/60 - 41*d**5/30 + 372*d**2. Factor f(x).
-2*x**2*(x + 41)
Let f(x) be the first derivative of -x**6/36 + 3*x**5/8 - 25*x**4/12 - 104*x**3/3 + 87. Let t(p) be the third derivative of f(p). Suppose t(y) = 0. What is y?
2, 5/2
Suppose -278*n + 97 + 1015 = 0. Let y(f) be the third derivative of 1/120*f**5 + 5/96*f**n + 0*f - 1/12*f**3 - 17*f**2 + 0 - 1/96*f**6. Factor y(r).
-(r - 1)*(r + 1)*(5*r - 2)/4
Let x be (897/54 + -17)*6/(-70). Let r(k) be the third derivative of 0 - x*k**5 - 36*k**2 + 0*k**3 - 1/10*k**4 + 0*k. Factor r(n).
-2*n*(5*n + 6)/5
Let w(b) = -3819*b - 38188. Let l be w(-10). Suppose 4/5*x**3 - 4/5*x - 8*x**l + 8 = 0. What is x?
-1, 1, 10
Let d(l) be the first derivative of -13*l**6/60 + 32*l**5/25 - 11*l**4/20 - 6*l**3 + 27*l**2/20 + 54*l/5 - 808. Let d(i) = 0. What is i?
-1, 12/13, 3
Let i(c) be the first derivative of 110 + 136/3*c**3 + 12/5*c**5 + 32*c - 56*c**2 - 17*c**4. Factor i(z).
4*(z - 2)**2*(z - 1)*(3*z - 2)
Let n be ((-4389)/(-3762))/((-56)/(-72)). Factor n*h**2 + 9/2 + 6*h.
3*(h + 1)*(h + 3)/2
Let o(w) be the second derivative of 1/42*w**4 - 2*w + 1 + 26/21*w**3 + 0*w**2. Find g such that o(g) = 0.
-26, 0
Let z(n) be the third derivative of n**8/84 + 2*n**7/15 - 11*n**6/30 - 19*n**5/15 + 19*n**4/3 - 32*n**3/3 + n**2 + 16*n + 98. Solve z(c) = 0.
-8, -2, 1
Let x be (-2424)/(-1) - (1 - 16/(-4)). Let t = x - 12092/5. Suppose 0*l**3 - 6/5*l**4 + 0*l + 0*l**2 - t*l**5 + 0 = 0. Calculate l.
-2, 0
Let b(l) be the first derivative of -4*l**4/5 - 3308*l**3/15 + 2078*l**2/5 - 832*l/5 + 126. Let b(d) = 0. What is d?
-208, 1/4, 1
Factor 10722 + 8*t**2 - 486 + 1205*t - 4336 - 3*t**2.
5*(t + 5)*(t + 236)
Let p(u) = 8*u**2 - 19*u + 53. Let y(f) be the second derivative of -1/2*f**2 + 0 - 1/6*f**3 - 1/12*f**4 - 17*f. Let n(l) = p(l) + 5*y(l). Factor n(h).
3*(h - 4)**2
Let u = 145099/54393 + -17/18131. Factor 0 - u*i - 4*i**2 - 4/3*i**3.
-4*i*(i + 1)*(i + 2)/3
Suppose -123/4*q + 3/4*q**4 - 117/4*q**2 - 21/2 - 33/4*q**3 = 0. Calculate q.
-1, 14
Let p = 4777 - 4772. Let s(u) be the third derivative of 0*u + 0*u**4 + 0 + 5/6*u**3 - 1/12*u**p + 19*u**2. Find i, given that s(i) = 0.
-1, 1
Let j(x) be the second derivative of x**6/45 + 2*x**5/15 + 5*x**4/18 + 2*x**3/9 + 3*x + 621. Suppose j(w) = 0. What is w?
-2, -1, 0
Let i(p) = -47*p**2 - 1962*p + 958449. Let g(c) = -35*c**2 - 1961*c + 958447. Let z(j) = 4*g(j) - 3*i(j). Let z(f) = 0. What is f?
979
Let z(p) be the first derivative of 36*p + 2/9*p**3 + 1/6*p**2 + 1/12*p**4 - 25. Let m(w) be the first derivative of z(w). Factor m(r).
(r + 1)*(3*r + 1)/3
Let a(t) = t**4 + 8*t**3 - 10*t**2 + t. Suppose 21*m - 58 - 68 = 0. Let o(h) = -h**4 + h. Let v(l) = m*o(l) + 2*a(l). Factor v(d).
-4*d*(d - 2)*(d - 1)**2
Let n(y) be the first derivative of 2/5*y**2 - 12 + 0*y + 1/10*y**4 + 2/5*y**3. Solve n(a) = 0.
-2, -1, 0
Let a(o) be the third derivative of o**6/420 + 143*o**5/210 + 5183*o**4/84 + 5041*o**3/21 - 1144*o**2. What is p in a(p) = 0?
-71, -1
Let g(z) = -198 + 4 + 20*z + 57. Let l be g(7). Factor 0 + s**5 + 3/2*s**4 + 0*s**2 + 1/2*s**l + 0*s.
s**3*(s + 1)*(2*s + 1)/2
Let z be 2258/(-2)*(-12)/((-8)/(-4)). Factor 76*a**2 + 6694*a - z*a - 4*a**2 - 28*a**3 + 4*a**4 + 32.
4*(a - 2)**3*(a - 1)
Let n(j) = 12*j**5 - 165*j**4 + 990*j**3 - 1416*j**2 + 633*j - 9. Let x(y) = y**5 + y**4 + 3*y**3 + y - 1. Let q(w) = -n(w) + 9*x(w). What is m in q(m) = 0?
0, 1, 4, 52
Let m be (-221 + 217)/(-2 + 0). Let c(b) be the first derivative of -10*b + 15/2*b**m + 12 - 5/3*b**3. Factor c(k).
-5*(k - 2)*(k - 1)
Let q = 10301/5 + -1782/5. Let f = 1704 - q. Factor -f*c**3 + 1/5*c + 3/5*c**2 - 3/5.
-(c - 3)*(c - 1)*(c + 1)/5
Factor -4/5*c**2 - 553536/5 + 2976/5*c.
-4*(c - 372)**2/5
Let l = -20893/4 + 5224. Let j(t) be the first derivative of -l*t**4 + 6*t - 12 + 0*t**3 + 9/2*t**2. Factor j(c).
-3*(c - 2)*(c + 1)**2
Let b be 141/((-241110)/(-2318)) - (-1)/5. Let -b*u**2 + 10/3*u**3 - 2*u**4 + 0 + 2/9*u = 0. Calculate u.
0, 1/3, 1
Let w(r) be the second derivative of r**6/120 + 19*r**5/80 + 125*r**4/48 + 329*r**3/24 + 147*r**2/4 + 457*r + 2. Factor w(x).
(x + 2)*(x + 3)*(x + 7)**2/4
Let c = 17735 + -10247. Suppose c = 2*d + 6*d. Find n such that -3456 + 16*n**4 - d*n**2 - 9*n**4 + 4320*n - 9*n**4 + 74*n**3 = 0.
1, 12
Let w(k) = 2*k**2 + 4*k - 70. Let f be w(5). Let h(o) be the third derivative of 1/24*o**4 - 1/3*o**3 + 0*o + f - 17*o**2 + 1/60*o**5. Factor h(l).
(l - 1)*(l + 2)
Let x(f) be the third derivative of f**5/330 - 2*f**4/11 - 112*f**3/33 + 667*f**2. Factor x(s).
2*(s - 28)*(s + 4)/11
Let u = 281 + -210. Let m be u + -73 + (-40)/(-18). Factor -m*v**2 + 0 - 2/3*v.
-2*v*(v + 3)/9
Let j(a) be the third derivative of 5*a**8/1848 + 58*a**7/1155 + 19*a**6/165 - 52*a**5/33 + 16*a**4/11 - 110*a**2 + 4*a. Solve j(l) = 0 for l.
-8, -6, 0, 2/5, 2
Let n(k) = -23*k**3 - 3573*k**2 + 156*k - 13. Let o(y) = -11*y**3 - 1786*y**2 + 72*y - 6. Let c(b) = -6*n(b) + 13*o(b). Factor c(m).
-5*m**2*(m + 356)
Let w(c) be the third derivative of -c**5/30 + 7*c**4/3 - 44*c**3 - 8161*c**2. Let w(h) = 0. Calculate h.
6, 22
Let x(o) be the third derivative of o**6/72 + 521*o**5/60 + 69*o**4/2 - 622*o**3/9 + 4*o**2 + 128*o. Let x(d) = 0. What is d?
-311, -2, 2/5
Let b be (3 + -7 + 0)*(-770)/56. Factor 2*a - 45*a**2 + 24*a**2 + 4 + b*a + 14.
-3*(a - 3)*(7*a + 2)
Let s(w) = -10*w**2 + 1555*w - 11980. Let d(p) = p**2 - 173*p + 1332. Let x(z) = -35*d(z) - 4*s(z). Determine k so that x(k) = 0.
13, 20
Let n(p) be the third derivative of 0 - 1/315*p**7 - 8/15*p**5 - p**4 - 13/180*p**6 + 55*p**2 + 0*p**3 - 2*p. Find f, given that n(f) = 0.
-6, -1, 0
Let n(v) = -v**3 - 12*v**2 - 15*v + 35. Let c be n(-12). Suppose -219*m**3 + 16*m - 10*m**2 + c*m**3 - 32 - 4*m**4 + 34*m**2 = 0. Calculate m.
-2, 1, 2
Let p(b) be the first derivative of -35*b**4/4 + 160*b**3 - 1435*b**2/2 - 450*b - 430. Solve p(g) = 0.
-2/7, 5, 9
Let u = -1119 + 13429/12. Let n(w) be the third derivative of -u*w**4 + 1/105*w**7 + 0 + 1/10*w**5 + 0*w**3 + 0*w - 16*w**2 - 1/20*w**6. Factor n(k).
2*k*(k - 1)**3
Let a(x) be the first derivative of -34 + 0*x**2 + 0*x - 1/40*x**4 + 2/15*x**3. Solve a(j) = 0.
0, 4
Suppose -463 - 119 + 86 = -248*y. Find l such that 0*l**3 + 0*l + 0 - 2/5*l**5 + 0*l**y + 2*l**4 = 0.
0, 5
Let v(i) be the first derivative of 0*i**2 + 57/4*i**4 + 34*i**3 + 20 + 0*i + 3/5*i**5. Factor v(w).
3*w**2*(w + 2)*(w + 17)
Let m(z) be the third derivative of 0 + 0*z + 5/4*z**4 - 75/2*z**3 - 1/60*z**5 + 13*z**2. Find t, given that m(t) = 0.
15
Determine h so that 156/7*h + 232/7*h**3 - 32/7*h**4 - 4/7*h**5 - 352/7*h**2 + 0 = 0.
-13, 0, 1, 3
Let m = -5/23 + 121/345. Let n = -3/706963 + 5655713/2120889. Factor n*v + m*v**2 + 40/3.
2*(v + 10)**2/15
Let o = -38 - -178. Suppose 3*r = o - 47. Suppose 53 - 5 + 34*a**3 + 27*a**2 - r*a**3 + 72*a = 0. Calculate a.
-4, -1
Let g(x) be the second derivative of -x**4/12 - 805*x**3/3 - 648025*x**2/2 - x + 742. Let g(c) = 0. What is c?
-805
Let s be -1 - (-28)/36 - (-55910)/90. Let i = s + -8071/13. Let -i*r**4 + 10/13*r**3 + 6/13*r - 14/13*r**2 + 0 = 0. What is r?
0, 1, 3
Let d(t) be the first derivative of 0*t - 1/3*t**2 - 10 - 1/15*t**5 + 0*t**4 + 1/3*t**3. Factor d(s).
-s*(s - 1)**2*(s + 2)/3
Let s = 270691 + -270683. Suppose 1/3*t**2 + s - 11/3*t = 0. Calculate t.
3, 8
Solve 50/3*j**2 - 256/3*j - 728/3 - 2/3*j