et l(p) be the second derivative of 17*p**7/6300 + 19*p**6/1800 + p**5/150 - p**4/2 - 6*p - 1. Let s(v) be the third derivative of l(v). Factor s(i).
2*(i + 1)*(17*i + 2)/5
Let r(d) be the second derivative of -9*d**5/40 + 13*d**4/8 - 7*d**3/2 + 92*d + 1. Factor r(a).
-3*a*(a - 2)*(3*a - 7)/2
Solve -117*i**2 + 335*i - 45*i**4 + 205*i**3 - 228*i**2 - 80*i - 70 = 0.
1, 14/9
Let w be (1/2)/((22/68)/11). Suppose -12*r - 20 = -w*r. Factor -12*n**2 + 0*n + 5*n - 32*n**3 + 3*n - 12*n**r.
-4*n*(n + 1)*(n + 2)*(3*n - 1)
Let b(m) be the first derivative of -m**6/16 - 3*m**5/10 + 105*m**4/32 + 75*m**3/4 + 8796. Solve b(w) = 0 for w.
-5, 0, 6
Factor -15/2*y**2 - 1479/2*y + 297.
-3*(y + 99)*(5*y - 2)/2
Let r = -102 - -106. Let 12*a**3 - a**4 - 32*a**3 - 14*a**3 - a**r = 0. Calculate a.
-17, 0
Let l(i) be the first derivative of 0*i**2 + 0*i**3 + 2*i**4 + 1 + 1/5*i**5 + 0*i. Determine u so that l(u) = 0.
-8, 0
Factor 207/4 - 75/4*f**2 - 3/4*f**3 - 129/4*f.
-3*(f - 1)*(f + 3)*(f + 23)/4
Let s(w) = -2*w**2 - 37*w - 75. Let d be s(-16). Factor -16 + d + 14 - 3*m**2 + m**3 + 0*m - m.
(m - 3)*(m - 1)*(m + 1)
Let u(o) = 30 + 4*o - 8 - 26*o**3 - 14*o**4 - 8 + 3*o**2 - 3. Let a(w) = -5*w**4 - 9*w**3 + w**2 + w + 4. Let j(n) = 11*a(n) - 4*u(n). Factor j(x).
x*(x - 1)*(x + 1)*(x + 5)
Let n be (((-2760)/108)/(-46))/((-10)/(-12))*3. Find w such that -1/4*w**n - 3*w - 9 = 0.
-6
Let -10/7*d**2 - 58/21*d**3 + 0*d + 0 + 2/21*d**5 - 26/21*d**4 = 0. What is d?
-1, 0, 15
Let s be (20/(-65))/(6/(14 - 92)). Let -282/7*y**2 - 36/7 - 24/7*y**5 + 54/7*y**3 + 30*y + 78/7*y**s = 0. Calculate y.
-2, 1/4, 1, 3
Determine g so that -2/5*g**5 + 1028/5*g**3 + 1664/5 - 1256/5*g**2 - 198/5*g**4 - 816/5*g = 0.
-104, -1, 2
Suppose 19*a + 11*a - 90 = 0. Suppose -4*q + 102 - 90 = -a*s, 5*q + 8 = -2*s. Suppose 0*r**2 + 9/4*r**4 + q + 3/4*r**3 + 0*r - 3*r**5 = 0. What is r?
-1/4, 0, 1
Factor 1193*y**2 + 1179*y**2 + 3072 - 81*y**3 + 3*y**4 + 1492*y**2 - 3564*y**2 + 3456*y.
3*(y - 16)**2*(y + 1)*(y + 4)
Let b(t) = -300*t**4 + 261*t**3 - 48*t**2 + 63*t. Let x(u) = 75*u**4 - 65*u**3 + 12*u**2 - 15*u. Let p(h) = 5*b(h) + 21*x(h). Factor p(n).
3*n**2*(5*n - 2)**2
Let r(k) be the first derivative of -5*k**4/4 + 5*k**3 + 225*k**2/2 + 405*k + 259. Determine h, given that r(h) = 0.
-3, 9
Let r = 277345/504 + -3852/7. Let d(i) be the third derivative of 1/30*i**6 - r*i**8 + 0*i + 1/12*i**4 + 16*i**2 + 4/45*i**5 + 0 + 0*i**7 + 0*i**3. Factor d(u).
-2*u*(u - 3)*(u + 1)**3/3
Let s(n) be the first derivative of -2*n**5/35 + 3*n**4/7 + 74*n**3/7 + 344*n**2/7 + 480*n/7 - 3548. What is d in s(d) = 0?
-4, -1, 15
Factor -1115*t**3 + 120*t**2 + 1105*t**3 - 110*t - 79*t**2 + 184*t**2.
-5*t*(t - 22)*(2*t - 1)
Let j = -54 + 68. Suppose -y + 4*b + j = 0, -b - 10 = 4*b. Factor -14*v**2 + 49*v**2 - 4*v + 5*v**3 - 30*v**3 - y*v.
-5*v*(v - 1)*(5*v - 2)
Suppose -33 + 21 = -2*i. Suppose -6*o + i = -6. Solve -186*d**o - 153*d**3 - 60*d**4 + 9 - 9*d**5 - 26 - 110*d + 2*d - 7 = 0.
-2, -1, -2/3
Suppose 7 = 6*s + 43. Let b(p) = -p - 3. Let j be b(s). Determine n so that j*n**4 + n**2 + 2*n**2 + 8*n**2 - 2*n**2 - 12*n**3 + 12*n - 12 = 0.
-1, 1, 2
Let u(j) = -j - 45. Let a be u(-34). Let f be a/2145*5*6*-1. Factor -f*d + 2/13 - 4/13*d**2.
-2*(d + 1)*(2*d - 1)/13
Let s(t) be the second derivative of t**6/15 + 11*t**5/10 + 7*t**4/6 - 37*t**3 - 108*t**2 + 33*t - 16. Find g, given that s(g) = 0.
-9, -4, -1, 3
Factor -8 + 3*v - 3/4*v**3 + 23/4*v**2.
-(v - 8)*(v - 1)*(3*v + 4)/4
Let q(t) be the second derivative of -7*t**5/80 - 12*t**4 - 41*t**3/6 - 2*t + 2416. Factor q(p).
-p*(p + 82)*(7*p + 2)/4
Solve 104 + 536*x**2 - 1061/2*x**3 + 25/2*x**5 - 640*x**4 + 518*x = 0 for x.
-1, -2/5, 1, 52
Let l be (-136)/(-288)*116 + (-2)/(-9). Suppose 55 = -o + l. Factor o - 8/15*f**3 + 4/15*f + 14/15*f**2.
-2*f*(f - 2)*(4*f + 1)/15
Suppose 0 = 4*y + 4*y + 5632. Let b = y - -707. Factor 15/8*c - 9/8 - 7/8*c**2 + 1/8*c**b.
(c - 3)**2*(c - 1)/8
Let 4*n**4 + 39*n - 44/3 - 88/3*n**2 + 2/3*n**3 + 1/3*n**5 = 0. What is n?
-11, -4, 1
Let j(x) be the first derivative of x**3/9 + 11*x**2/3 + 7*x + 906. Factor j(u).
(u + 1)*(u + 21)/3
Let y(v) be the third derivative of -5*v**9/3024 + v**8/84 - v**7/42 + 43*v**3/2 + 88*v**2. Let u(k) be the first derivative of y(k). Let u(g) = 0. Calculate g.
0, 2
Let v(p) be the second derivative of -702*p**6/35 - 4518*p**5/35 - 172*p**4/3 + 176*p**3/21 + 64*p**2/7 - 596*p - 4. Let v(y) = 0. What is y?
-4, -2/9, 2/13
Let s(x) = x**2 + 1. Let d(j) be the second derivative of -j**5/20 - 3*j**4/4 - 2*j**3/3 + 5*j**2 + 32*j + 1. Let v(q) = -2*d(q) - 4*s(q). Factor v(a).
2*(a - 1)*(a + 2)*(a + 6)
Let p(m) be the third derivative of -5*m**8/336 + 3*m**7/14 - 5*m**6/12 - 5*m**5 + 35*m**4/3 + 80*m**3 + 1044*m**2. Solve p(f) = 0 for f.
-2, -1, 2, 4, 6
Let a be -3 + (-11 - (-20)/(-5)). Let j be (-11)/(-6) + -3*1/a. Factor -1737 - 6*b**4 - 72*b**j + 28*b**3 + 80*b + 1705 + 2*b**4.
-4*(b - 2)**3*(b - 1)
Let j(m) be the third derivative of m**6/180 + 11*m**5/30 + 9*m**4/2 + 2312*m**2 - m. Factor j(i).
2*i*(i + 6)*(i + 27)/3
Let z(r) = -15*r - 12*r**2 + 13*r**2 + 22*r - 4. Let k be z(-8). Determine p so that 209*p**3 + 3*p**2 - 2*p**4 - 201*p**3 + p**2 - 8*p - 2*p**k = 0.
-1, 0, 1, 2
Let n(f) = 19*f**3 + 448*f**2 - 2801*f + 1054. Let u(k) = -39*k**3 - 897*k**2 + 5601*k - 2109. Let z(x) = 9*n(x) + 4*u(x). Solve z(m) = 0.
-35, 2/5, 5
Suppose 0 = 5*p - 16 + 1. Suppose 0 = j - m - 2*m - 153, 0 = -p*j - 3*m + 447. Factor -j*x + 1125 + 32*x**2 + 34*x**2 - 61*x**2.
5*(x - 15)**2
Let x(g) be the second derivative of -5*g**3/6 - 3*g**2/2 + 19*g. Let z be x(-1). Factor -5 + 1 - 27*t**3 - 1 - 36*t - 3 - 54*t**z.
-(3*t + 2)**3
Let a(g) = 2*g**3 - 17*g**2 + 1049*g + 528. Let k(d) = -d**3 + 5*d**2 - 350*d - 176. Let u(h) = -3*a(h) - 8*k(h). Find q such that u(q) = 0.
-16, -1/2, 11
Let k = 14330/3 - 4728. Let c = k - 658/15. Solve 6/5 + 12/5*x**4 - 3*x - 9/5*x**5 + c*x**3 - 18/5*x**2 = 0.
-1, 1/3, 1, 2
Factor -11968/9*h + 11560/3 + 518/9*h**2 + 98/9*h**3.
2*(h + 15)*(7*h - 34)**2/9
Let t(f) be the first derivative of f**4/18 + 208*f**3/27 + 103*f**2/9 + 398. Factor t(p).
2*p*(p + 1)*(p + 103)/9
Let z = -632334/5 - -126468. Suppose -6/5*b**4 + z*b**2 + 0*b + 9/5*b**5 - 9/5*b**3 + 0 = 0. Calculate b.
-1, 0, 2/3, 1
Suppose 69 = 5*z + 24. Suppose z*u - 737 = -143. Solve -u*o + 18*o - 148*o**2 + 144*o**2 - 144 = 0.
-6
Let f(j) be the third derivative of -j**5/30 - 35*j**4/24 + 19*j**3/2 - 40*j**2 + 7*j. Solve f(u) = 0 for u.
-19, 3/2
Find s such that 160/7*s**2 - 88/7*s**3 + 0 + 4/7*s**4 + 0*s = 0.
0, 2, 20
Let g(n) be the third derivative of 0*n - 7/6*n**4 + 8/3*n**3 - 6*n**2 + 7/30*n**5 - 1/60*n**6 - 2. Factor g(b).
-2*(b - 4)*(b - 2)*(b - 1)
Factor 450*j**2 + 84*j**3 + 65*j - 65*j - 169*j**3 + 5*j**4 - 20*j**3.
5*j**2*(j - 15)*(j - 6)
Let r = 31 - 28. Suppose 0 = -r*a + 12 - 6. Determine v so that -7*v**2 + 14*v + 2*v**3 + 4*v**2 + 6 + 13*v**a = 0.
-3, -1
Let n be (-35)/14*4/(-6). Let o(v) be the first derivative of -15/2*v**2 + 5 + 2*v**5 - 5*v + 15/4*v**4 - n*v**3. Factor o(i).
5*(i - 1)*(i + 1)**2*(2*i + 1)
Factor -10727 + 57*b**3 - 1503*b**2 + 189000*b - 176773 - 30*b**3 - 24*b**3.
3*(b - 250)**2*(b - 1)
Let s(w) = -w**2 + 75*w + 88. Let v be s(76). Let l(a) be the first derivative of 20/3*a**3 - 2*a**2 - 21/4*a**4 + 0*a + v. Factor l(h).
-h*(3*h - 2)*(7*h - 2)
Let g(l) = -20*l**2 - 216*l - 1951. Let m = -8 + 15. Let u(h) = -14*h**2 - 144*h - 1301. Let s(y) = m*u(y) - 5*g(y). Determine k, given that s(k) = 0.
-18
Suppose 0 = 356*b - 553*b. Let p(a) be the second derivative of 0*a**4 + 1/60*a**6 + b - 1/40*a**5 - 25*a + 0*a**3 + 0*a**2. Factor p(r).
r**3*(r - 1)/2
Let c(o) = -9*o + 121. Let s be c(13). Find h, given that -5*h**s - 34*h**3 + 46*h + 74*h**3 + 16*h + 95*h**2 - 12*h = 0.
-1, 0, 10
Let j = -274619/12370 + 1/2474. Let f = 114/5 + j. Solve -2/5*q**2 - 2/5*q**4 + 1/10*q**5 + f*q**3 + 1/10*q + 0 = 0 for q.
0, 1
Suppose -2/9*i**5 - 8*i - 10/9*i**4 + 0 + 74/9*i**3 + 10/9*i**2 = 0. What is i?
-9, -1, 0, 1, 4
Let y(z) be the first derivative of z**5 + 145*z**4/4 - 105*z**3 - 145*z**2/2 + 310*z - 58. Determine k, given that y(k) = 0.
-31, -1, 1, 2
Let x = 1752 + -1748. Let z(h) be the third derivative of -1/40*h**6 - 3*h**2 + 0*h**3 + 0*h + 1/20*h**5