
Let h(l) be the third derivative of l**5/60 - 13*l**4/4 - 80*l**3/3 - 95*l**2 + 7. Factor h(p).
(p - 80)*(p + 2)
Let m = 6388 - 6388. Let t(b) be the second derivative of m - 1/100*b**5 - 1/30*b**3 - 31*b + 0*b**2 - 1/30*b**4. Let t(j) = 0. Calculate j.
-1, 0
Let d(q) be the second derivative of 0*q**2 + 0 - 7*q - 3/7*q**3 + 1/28*q**4. Suppose d(f) = 0. Calculate f.
0, 6
Let a = -162 + 164. Determine s, given that -131*s + 71*s - 16*s**3 + 12*s**a - 12*s**4 + 78*s - 2*s**5 = 0.
-3, -1, 0, 1
Let a(d) be the first derivative of -221 + 0*d**3 + 3*d**2 - 3/2*d**4 - 3*d + 3/5*d**5. Suppose a(o) = 0. Calculate o.
-1, 1
Let d be (-293)/5 + 5685 + -5626. Suppose d*r**4 - 264/5*r + 144/5 + 148/5*r**2 - 6*r**3 = 0. What is r?
1, 2, 6
Let x = -4488389/345 - -39032/3. Let h = 22/23 + x. Determine g so that -6/5*g**3 - 3/5*g**4 + 12/5 + h*g**2 + 24/5*g = 0.
-2, -1, 2
Factor 0 + 183/4*a**3 + 0*a + 9/2*a**2.
3*a**2*(61*a + 6)/4
Let g(v) be the second derivative of v**6/300 + 9*v**5/200 - v**4/12 + 1137*v. Suppose g(f) = 0. What is f?
-10, 0, 1
Let c(a) be the first derivative of 2/3*a**6 + 0*a - 4*a**5 + 52/3*a**3 - 3*a**4 + 152 + 20*a**2. Factor c(n).
4*n*(n - 5)*(n - 2)*(n + 1)**2
Let s(h) be the second derivative of -h**7/504 + 121*h**6/180 + 613*h**5/120 + 277*h**4/18 + 1727*h**3/72 + 247*h**2/12 - 9758*h. Let s(w) = 0. Calculate w.
-2, -1, 247
Suppose a + 0*a - 6 = 0. Suppose a*f = 2*f + 20. Determine u so that 1181*u - 5*u**3 + 5*u**f - 1181*u = 0.
-1, 0, 1
Let s = 103 - 101. Suppose -l - 2*a = -12, -16*l + 2*a - s = -12*l. Factor 2/3*d**l - 8/3 + 8/3*d - 2/3*d**3.
-2*(d - 2)*(d - 1)*(d + 2)/3
Let d be (-6694)/(-3) + 26/117*3. Suppose -d = 9*x - 2268. Solve 1/7*u**x - 1/7*u**2 - 1/7*u**3 + 1/7*u + 0 = 0.
-1, 0, 1
Let k(t) = -t**3 + 19*t**2 + 25*t - 79. Let n be k(20). Factor -8*l**4 - n*l**3 + 36*l - 3277*l**2 + 3193*l**2 + 23*l**4.
3*l*(l - 3)*(l + 2)*(5*l - 2)
Let d(k) be the first derivative of -13 - 3*k**3 - 6497*k + 165 + 2*k**3 + 5525*k - 54*k**2. Factor d(v).
-3*(v + 18)**2
Determine y, given that 3/2*y**3 - 2001/2*y + 1995 - 996*y**2 = 0.
-2, 1, 665
Let d(b) be the first derivative of b**6/3240 - 2*b**5/135 - 119*b**3/3 - 250. Let z(p) be the third derivative of d(p). Let z(k) = 0. What is k?
0, 16
Suppose -266 - 292 = -18*g. Factor -165*s - 3*s**4 + 9*s**2 + 4*s**3 - 13*s**3 + g*s**3 - s**3 - 150.
-3*(s - 5)**2*(s + 1)*(s + 2)
Let j(h) be the first derivative of 2349/2*h**2 - 1/2*h**6 + 674*h**3 - 1173/2*h**4 + 33*h**5 - 2187*h - 27. Let j(k) = 0. Calculate k.
-1, 1, 27
Determine c so that -2555 + 62*c**2 - 96*c**2 + 29*c**2 + 2084*c + 476*c = 0.
1, 511
Let o(a) = 33*a**3 + 15*a**2 - 86*a - 393. Let d(s) = 8*s**3 + 4*s**2 - 22*s - 96. Let i(p) = 25*d(p) - 6*o(p). Solve i(y) = 0 for y.
-7, -1, 3
Let l(u) be the second derivative of -20/3*u**3 - 1/6*u**6 - 35/6*u**4 - 7/4*u**5 + 0 - 28*u + 0*u**2. Factor l(i).
-5*i*(i + 1)*(i + 2)*(i + 4)
Let c(r) be the first derivative of -r**5/60 - r**4/36 + r**3/9 - 211*r - 245. Let a(k) be the first derivative of c(k). Factor a(l).
-l*(l - 1)*(l + 2)/3
Let m(a) be the first derivative of 3*a**5/5 - 159*a**4/2 - 324*a**3 - 489*a**2 - 327*a + 599. Suppose m(v) = 0. Calculate v.
-1, 109
Let g(j) be the second derivative of -j**4/18 + 434*j**3/9 - 433*j**2/3 - 4168*j. Solve g(b) = 0.
1, 433
Let h = 23463 + -23460. Let j(i) be the third derivative of 0*i - 3/40*i**4 + 1/300*i**5 + 16*i**2 + 0*i**h + 0. Factor j(a).
a*(a - 9)/5
Factor -106/9*t + 140 + 2/9*t**2.
2*(t - 35)*(t - 18)/9
Let l(m) be the first derivative of 1/24*m**4 + 169 + 0*m + 1/9*m**3 - 1/4*m**2. What is u in l(u) = 0?
-3, 0, 1
Let v(g) be the second derivative of -3*g**5/100 + g**4/4 + 30*g**3 + 1013*g + 4. Find b such that v(b) = 0.
-15, 0, 20
Solve 1755*r**3 - 32*r**4 - r**5 + 26*r**2 - 1720*r**3 + 40*r**2 = 0 for r.
-33, -1, 0, 2
Let d(a) be the third derivative of -a**6/300 + 2*a**5/75 + 41*a**4/60 + 12*a**3/5 - 7*a**2 + 248. Suppose d(k) = 0. Calculate k.
-4, -1, 9
Let f(u) = -u**2 - u + 38 - 25 - 12. Let o(y) = -2*y**2 + 22*y + 89. Let r(w) = f(w) + o(w). Suppose r(a) = 0. Calculate a.
-3, 10
Let z(v) be the first derivative of -5/6*v**3 - 88 - 245/2*v + 35/2*v**2. Let z(b) = 0. What is b?
7
Factor -124/3 + 994/3*q + 14/3*q**3 - 884/3*q**2.
2*(q - 62)*(q - 1)*(7*q - 1)/3
Let 11/4*z**3 + 1/4*z**4 - 5/2 + 9/4*z**2 - 11/4*z = 0. What is z?
-10, -1, 1
Let b be 207/(-15) - -13 - (-212)/240. Let l(p) be the second derivative of 1/3*p**3 + 7*p + 3/2*p**2 + 0 - b*p**4. Let l(o) = 0. What is o?
-1, 3
Let d(u) = 4*u**3 + 56*u**2 + 2*u + 28. Let y be d(-14). Let o be 0/2*(-5)/(-1 - 9). Factor -2/3*i**4 + 0 + y*i - 1/3*i**3 + o*i**2 - 1/3*i**5.
-i**3*(i + 1)**2/3
Suppose -76 = -3*r - 6*h + 2*h, -4*r + 3*h = -143. Suppose -34*g = -r*g - 6. Factor 80*p - 16 - 16 - 25*p**3 - 59*p**g + 136*p**2.
-4*(p - 2)*(3*p + 2)*(7*p - 2)
Factor -259 + 3*f**2 + 154 + 93*f + 609.
3*(f + 7)*(f + 24)
Let c(l) be the second derivative of l**4/18 - 25*l**3/9 - 224*l**2/3 - 10618*l. Factor c(q).
2*(q - 32)*(q + 7)/3
Let o = 52138/166005 - -1/4743. Let b = o - -247/105. Find m, given that 4/3*m**2 - 4 - b*m = 0.
-1, 3
Let 333*u**2 + 43*u - 5 - 7 - 334*u**2 - 36*u = 0. What is u?
3, 4
Let c = -113066 - -452275/4. Suppose -c + 23/4*s - 13/4*s**2 + 1/4*s**3 = 0. Calculate s.
1, 11
Let x(a) = 4*a**3 + 38*a**2 + 76*a. Let d(r) = -8*r**3 - 77*r**2 - 154*r. Let i(b) = -2*b + 51. Let y be i(23). Let z(g) = y*x(g) + 2*d(g). Factor z(c).
4*c*(c + 3)*(c + 6)
Suppose -732 = -32*i + 6*i - 35*i. Let t(s) be the first derivative of 4/3*s**6 - 6 - 128/3*s**3 - 52/5*s**5 - i*s + 30*s**4 + 32*s**2. Factor t(m).
4*(m - 3)*(m - 1)**3*(2*m - 1)
Let y(c) be the second derivative of 3 - 1/20*c**5 - 2*c - 2/15*c**3 + 0*c**2 - 1/150*c**6 - 2/15*c**4. Let y(x) = 0. What is x?
-2, -1, 0
Let u(d) = -7*d + 77. Let s be u(13). Let a be ((-12)/s)/((-873)/(-2716)). Solve -16/3*y**2 + 0 + 4*y**3 + a*y**4 - 4/3*y**5 - 16/3*y = 0 for y.
-1, 0, 2
Let z be (-3)/(2 + (-33)/12 - 21516/(-29744)). Factor -26/3*d - z - 1/6*d**2.
-(d + 26)**2/6
Let v(x) = 3*x**3 + 5*x**2 - 12. Let r be v(-4). Let q = 1118/9 + r. Factor -2/9*k + 8/9*k**5 - 22/9*k**4 + 2*k**3 + 0 - q*k**2.
2*k*(k - 1)**3*(4*k + 1)/9
Let v(w) be the second derivative of w**7/70 + w**6/5 - 21*w**5/100 - 16*w**4/5 + 6*w**3 + 3*w - 2181. Let v(q) = 0. What is q?
-10, -3, 0, 1, 2
Suppose -5*a = 25, 4*g - a + 2*a - 323 = 0. Find s, given that -g*s**2 + 88*s**2 + 7*s - 2*s**3 + s = 0.
-1, 0, 4
Suppose 15*s - 1846 = 104*s - 2113. Let 5*r + 16/7*r**2 + 18/7 - 1/7*r**s = 0. What is r?
-1, 18
Suppose 240*v**2 + 0 - 429/7*v**3 + 192/7*v + 27/7*v**4 = 0. Calculate v.
-1/9, 0, 8
Suppose j - h = 115, 10*j - 551 = 5*j - h. Suppose 5*f - j = -4*x, -4*f = -4*x - 0*f + 120. Factor 4 + 60*u - 126*u - x*u**2 - 21*u**3 + 62*u.
-(u + 1)*(3*u + 2)*(7*u - 2)
Factor -1156/3 + 67/3*w**2 + 1088/3*w + 1/3*w**3.
(w - 1)*(w + 34)**2/3
Let m(z) = -z**3 - 2*z**2 + 13*z + 8. Let n be m(-5). Let b = n + -14. Factor -35*q**2 + 35*q**2 + b*q**4 - 12*q**3 + 16*q.
4*q*(q - 2)**2*(q + 1)
Let x be ((-20)/6 + 6)*-6. Let v be (x - -1)*6/(-45). Factor -1 - j - 1/4*j**v.
-(j + 2)**2/4
Let z(o) be the third derivative of 0 - 83/20*o**6 - 225/8*o**4 - 21*o**5 + 2/5*o**7 + 248*o**2 + 0*o - 1/112*o**8 + 0*o**3. Factor z(l).
-3*l*(l - 15)**2*(l + 1)**2
Let m(v) be the third derivative of 215*v**2 - 4/33*v**4 - 1/330*v**5 + 0 + 0*v - 16/11*v**3. Find f such that m(f) = 0.
-12, -4
Let s(y) be the second derivative of -y**4/4 + 929*y**3 - 2589123*y**2/2 + 3*y + 1118. Factor s(r).
-3*(r - 929)**2
Let w(b) = -b**3 - b. Let l = 233 + -234. Let x(q) = 6*q**3 - 2*q**2 + 5*q. Let z(i) = l*x(i) - 5*w(i). What is y in z(y) = 0?
0, 2
Let m(n) be the third derivative of n**6/30 - 2*n**5/3 + 2*n**4 + 48*n**3 + 2668*n**2. Find y, given that m(y) = 0.
-2, 6
Suppose 9 = 14*n - 15*n. Let m be 30/(-40) - n/12*1. Factor 5/3*a**4 + 0*a + m + 0*a**2 + 5*a**3.
5*a**3*(a + 3)/3
Let t(b) = -9*b**4 - 298*b**3 + 17*b**2 + 836*b - 586. Let s(y) = 6*y**4 + 199*y**3 - 11*y**2 - 557*y + 391. Let i(a) = -10*s(a) - 7*t(a). Solve i(m) = 0 for m.
-32, -2, 1
Let v be -8*(87/(-168) - (-54)/378). Solve -4/5 - 4*w**v + 38/5*w + 22/5*w**2 = 0.
-1, 1/10, 2
Let z(p) be the first derivative of p**4/4 - 65*p**3/21 - 26*p**2/7 + 20*p/7 + 88