tive of h**7/840 + h**6/80 + 3*h**5/80 + h**4/24 + 41*h**2 + 2*h - 48. Let z(g) be the first derivative of n(g). Factor z(b).
b*(b + 1)**2*(b + 4)/4
Determine n so that -197*n**3 - 218*n**3 - 12 + 478*n + 1888*n**2 + 12 + 287*n**3 + 30 = 0.
-1/8, 15
Let n be (50/(-20))/((-20)/16). Let 3*w + 4*w**3 + 210 + 2*w**4 - 208 - n*w**5 - 5*w - 4*w**2 = 0. What is w?
-1, 1
Factor 1/8*u**2 - 19/8 + 9/4*u.
(u - 1)*(u + 19)/8
Let h be 0/(12/(-4) - -2). Suppose -13*i = 23 - 5 - 18. Find g such that h + i*g + 3/8*g**2 - 3/8*g**4 + 0*g**3 = 0.
-1, 0, 1
Let b be (-18)/4 + (51 - 36 - (4 + 3)). Factor -b*w**4 - 3*w**2 + 0 - 23/2*w**3 + 0*w.
-w**2*(w + 3)*(7*w + 2)/2
Let h(o) be the third derivative of o**7/1155 + 3*o**6/110 - 23*o**5/66 + 16*o**2 + 113*o. Determine i so that h(i) = 0.
-23, 0, 5
Factor 35*h**2 + 20*h + 2*h**3 - 940 - 240 - 7*h**3 + 18*h**2 + 242*h**2.
-5*(h - 59)*(h - 2)*(h + 2)
Let w = -559 - -557. Let c be (-728)/(-338) + w/13. Suppose 2/5*f**4 - c*f**3 + 12/5*f**2 - 16/5 + 8/5*f = 0. Calculate f.
-1, 2
Let t(u) be the first derivative of -1/20*u**4 - 36*u - 9/5*u**2 + 1/2*u**3 + 26. Let i(q) be the first derivative of t(q). Factor i(j).
-3*(j - 3)*(j - 2)/5
Let b(z) = z - 2. Let g be b(5). Let h = 5799/3806 - 45/1903. Factor -h*t**2 + 2 + 0*t + 1/2*t**g.
(t - 2)**2*(t + 1)/2
Let h be ((-12040)/504 + 56)/((-2)/(-6)). Factor h - 101/3*y**2 + y**3 + 833/3*y.
(y - 17)**2*(3*y + 1)/3
Let c(j) be the first derivative of -2/3*j**6 + 119 - 80*j**2 - 64*j + 4*j**5 - 100/3*j**3 + 5*j**4. Find v, given that c(v) = 0.
-1, 4
Let v(b) = b**2 - 2*b - 79. Let z be v(11). Let r be (-39)/(-260) + 2/z. Solve r*c**4 + 1/2*c**2 - 5/2*c**5 + 0 + 7/4*c**3 + 0*c = 0 for c.
-1/2, -2/5, 0, 1
Let b(a) = -170*a**2 - 60*a + 30. Let k(f) = 7*f**2 + 2*f - 1. Let m(x) = b(x) + 25*k(x). Factor m(t).
5*(t - 1)**2
Let y(h) be the first derivative of 0*h - 26 + 4/3*h**3 - 14*h**2. Solve y(n) = 0 for n.
0, 7
Let p(n) = 5*n**4 + 396*n**3 - 7*n**2 - 1390*n - 944. Let v(j) = 2*j**4 + 129*j**3 - 3*j**2 - 463*j - 315. Let y(z) = -3*p(z) + 8*v(z). Factor y(x).
(x - 156)*(x - 2)*(x + 1)**2
Suppose -4/9*i**3 + 4/9*i**2 + 224/9*i + 64 = 0. What is i?
-4, 9
Let o = -1264659 - -1264661. Factor -2/11*w**o - 11250/11 - 300/11*w.
-2*(w + 75)**2/11
Let 10/9*w**2 - 4/3*w + 0 - 2/9*w**3 = 0. Calculate w.
0, 2, 3
Suppose -76*u + 1227 = 333*u. Let h(s) be the second derivative of 1/240*s**5 + 21*s - 1/24*s**4 + 5/72*s**u + 0 + 0*s**2. Let h(r) = 0. What is r?
0, 1, 5
Let x(u) be the third derivative of u**8/224 - u**7/70 - u**6/80 + u**5/20 + 28*u**2 + 21*u. Determine s, given that x(s) = 0.
-1, 0, 1, 2
Let z(p) be the third derivative of -1/160*p**6 + 0*p**4 + 3*p**2 + 7*p - 1/80*p**5 + 1/448*p**8 + 0 + 1/280*p**7 + 0*p**3. Determine k, given that z(k) = 0.
-1, 0, 1
Let c(u) be the third derivative of -1/30*u**6 - 1/315*u**7 + 31*u**2 - 1/6*u**4 + 0*u + 0*u**3 + 0 - 11/90*u**5. Determine x, given that c(x) = 0.
-3, -2, -1, 0
Factor 475 + 1122*d - 1766*d**2 - 174 + 699 + 3*d**4 - 1122*d**3 + 125 + 638*d**2.
3*(d - 375)*(d - 1)*(d + 1)**2
Let a(w) be the first derivative of -55/4*w**4 - w**5 - 2 + 20*w**3 + 0*w + 0*w**2. Let a(d) = 0. Calculate d.
-12, 0, 1
Let j(v) be the second derivative of v**5/90 - v**4/4 - 22*v**3/9 - 15*v**2 - 7*v - 1. Let s(y) be the first derivative of j(y). Factor s(a).
2*(a - 11)*(a + 2)/3
Factor 3830*s**3 - 529*s**2 - 876 - 1748*s - 339*s**2 - 3826*s**3.
4*(s - 219)*(s + 1)**2
Let y(p) be the second derivative of 1/54*p**4 + 27*p - 10/9*p**2 - 1 - 1/3*p**3. Factor y(s).
2*(s - 10)*(s + 1)/9
Suppose 1630 = 2*j + 498. Suppose 5*x + 2*v - j = 312, 0 = -x + 2*v + 166. Factor -4*f**5 - x*f**2 - 125*f**3 - f**5 - 40*f**4 + 20*f**2 - 140*f - 40 - 36*f**2.
-5*(f + 1)**2*(f + 2)**3
Suppose -1 = -5*m + 14. Suppose -5*x = -2*q - 2*q - 356, x - 56 = -m*q. Factor 3*p**2 + x - 68 + 9*p.
3*p*(p + 3)
Let f(k) = -4*k**2 + 3*k - 2. Let x(o) = 2*o**3 - 250*o**2 - 2166*o - 4380. Let a(y) = 4*f(y) + 2*x(y). Suppose a(t) = 0. Calculate t.
-4, 137
Let q = 5863 - 5847. Let i(n) be the first derivative of 4/3*n**3 - q + 36*n + 12*n**2. Factor i(y).
4*(y + 3)**2
Let j(f) be the first derivative of -f**6/6 + 16*f**5/5 - 16*f**4 + 106*f**3/3 - 79*f**2/2 + 22*f + 1793. Let j(r) = 0. What is r?
1, 2, 11
Let a = 383/53 - 45589/6360. Let x(v) be the third derivative of 0 + 0*v - 1/420*v**7 + 0*v**3 - 44*v**2 - 1/8*v**4 + a*v**5 + 0*v**6. Factor x(m).
-m*(m - 2)*(m - 1)*(m + 3)/2
What is t in 40*t - 95*t - 35*t + 425*t**3 - 335*t + 415*t**2 + 5*t**4 - 420 = 0?
-84, -1, 1
Let q(y) be the second derivative of -5*y**4/12 - 255*y**3/2 - 380*y**2 + 2*y - 346. Factor q(g).
-5*(g + 1)*(g + 152)
What is l in -712*l - 484 - 1348*l + 199*l - 538*l + 225*l + 18*l**2 = 0?
-2/9, 121
Let c(u) be the third derivative of 25*u + 0 - 1/90*u**5 + 6*u**2 - 2/9*u**4 + 16/3*u**3. Let c(h) = 0. What is h?
-12, 4
Let g = 128 + -126. Determine o, given that 21*o**2 - 9*o**4 - 108*o**2 - 15 + 68*o**3 + 10*o**3 + 98*o - 97*o**g = 0.
1/3, 3, 5
Suppose -7*u + 2*u = -375. Let s = u + -73. Suppose 0*a**s + a**2 - 20*a**3 + a**4 + 18*a**3 = 0. Calculate a.
0, 1
Let z(q) be the first derivative of -1/14*q**6 - 47/7*q**3 + 192/7*q + 64 - 237/28*q**4 + 120/7*q**2 - 51/35*q**5. Find u, given that z(u) = 0.
-8, -1, 1
Suppose z - 2*k = -21 + 13, k = 5*z + 4. Let a(l) be the first derivative of -1/2*l**2 + 0*l**3 + 1/4*l**4 + z*l - 2. Factor a(i).
i*(i - 1)*(i + 1)
Let z = -1657/3 + 553. Suppose -6 + 3 = 2*a - 3*i, i = 4*a - 9. Factor 2/3*k**2 + 0*k**4 - 1/3*k**5 - z + 4/3*k**a - k.
-(k - 2)*(k - 1)*(k + 1)**3/3
Let u(g) be the first derivative of -8/11*g - 5/11*g**2 - 2/33*g**3 + 111. Factor u(i).
-2*(i + 1)*(i + 4)/11
Let d(n) be the third derivative of n**8/168 - 41*n**6/60 - 12*n**5/5 + 28*n**4/3 + 5294*n**2. Let d(p) = 0. Calculate p.
-4, 0, 1, 7
Let i(o) be the second derivative of -o**5/20 - 7*o**4/3 + 21*o**3/2 + 45*o**2 + 1638*o. Factor i(b).
-(b - 3)*(b + 1)*(b + 30)
Let k = 2115/356 + -1581/356. Find o such that k*o + 7/4 - 1/4*o**2 = 0.
-1, 7
Suppose -2/11*r**2 - 4992800/11 - 6320/11*r = 0. What is r?
-1580
Determine b so that -5*b**3 - 486*b - 23*b**3 + 124*b**2 + 558*b**4 + 84*b**2 + 192 - 562*b**4 + 118*b = 0.
-12, 1, 2
Let j(r) = -2*r**2 - 3*r + 2. Let v(l) = -35*l**2 - 15130*l + 11355285. Let y(s) = -20*j(s) + v(s). Find k, given that y(k) = 0.
1507
Suppose 8*d = 18*d - 3*k + 22, 3*k = 5*d + 32. Find w such that -w**d + 1/2*w**3 + 1 - 1/2*w = 0.
-1, 1, 2
Let x(v) be the first derivative of -5*v**4/4 + 20*v**3/3 + 30*v**2 + 505. Let x(g) = 0. What is g?
-2, 0, 6
Let z(s) = 178*s**3 - 10797*s**2 + 226266*s - 410759. Let g(d) = -d**4 + d**3 - d + 1. Let b(p) = g(p) + z(p). Factor b(a).
-(a - 59)**3*(a - 2)
Suppose 0 = 36*w + 22*w. Factor 1/2*q**4 + 1/4*q**5 + w - 1/4*q + 0*q**3 - 1/2*q**2.
q*(q - 1)*(q + 1)**3/4
Determine k, given that -76*k**3 - 249661577*k**4 + 249661601*k**4 - 30*k**2 + 4*k**5 - 66*k**2 = 0.
-8, -1, 0, 3
Factor 11244/7*l**2 + 1694 + 304/7*l**3 - 3344*l + 2/7*l**4.
2*(l - 1)**2*(l + 77)**2/7
Let a(i) be the first derivative of 24*i - 5*i**3 + 3/4*i**4 + 3*i**2 + 45. What is y in a(y) = 0?
-1, 2, 4
Let g(l) = -8*l**4 - l**3 - l - 1. Let o(h) = -93*h**4 - 3*h**3 - 12*h**2 - 12*h - 12. Let i(q) = -12*g(q) + o(q). Factor i(n).
3*n**2*(n - 1)*(n + 4)
Determine x, given that 1730*x + 616 + 482*x**3 + 4*x**4 + 820*x**2 - 374*x**3 - 398*x = 0.
-14, -11, -1
Suppose 0 = 4*l - s + 6 - 8, 0 = -l + 3*s + 6. Let z be 2*(l + 0 + -2 + 3). Solve -69*m + 75*m + 7*m**2 + 14*m**z = 0.
-2/7, 0
Let s(k) = k**2 + 2*k. Let h(x) be the second derivative of -x**3/6 + 3*x. Suppose 166*o = 65*o - 202. Let i(z) = o*h(z) - s(z). Suppose i(b) = 0. Calculate b.
0
Suppose 21*v**5 + 18*v + 416*v**2 + 11*v**5 + 56*v**4 + 238*v + 240*v**3 - 28*v**5 = 0. Calculate v.
-8, -2, 0
Let f(v) = 15*v**2 - 15*v - 16. Let w be f(-1). Factor 0*r**2 - 4776*r + 3*r**2 + 4803*r + w - 5 + 15.
3*(r + 1)*(r + 8)
Let d(j) = -75*j**2 + 240*j + 625. Let i(v) = -41*v**2 + 121*v + 312. Let k(f) = 6*d(f) - 11*i(f). Factor k(u).
(u + 3)*(u + 106)
Let r(f) be the second derivative of 2*f**7/21 - 4*f**6 + 52*f**5/5 + 40*f**4 - 448*f**3/3 - 5326*f. Let r(l) = 0. What is l?
-2, 0, 2, 28
Let k(u) = 2*u**2 + 2. Let y(r) = 2*r**3 - 434*r**2 - 2. Let q(j) = -k(j) - y(j). 