, 2
Factor 151*q**3 - 304*q**3 + 154*q**3 + 8*q - 9*q**2.
q*(q - 8)*(q - 1)
Let g(s) = -9*s**3 + 4*s**2 + 5*s - 4. Let d = -24 - -35. Let c(r) = 4*r + 4*r + 11*r**2 - d - 26*r**3 + 7*r. Let a(n) = 4*c(n) - 11*g(n). Factor a(q).
-5*q*(q - 1)*(q + 1)
Let c(h) be the second derivative of -h**6/2160 - h**5/90 - h**4/9 + 5*h**3/2 - 17*h. Let f(p) be the second derivative of c(p). Factor f(b).
-(b + 4)**2/6
Let d(p) be the third derivative of -841*p**5/45 - 58*p**4/9 - 8*p**3/9 + 124*p**2. Solve d(v) = 0 for v.
-2/29
Let f(m) be the third derivative of -m**6/80 + 13*m**5/60 + 3*m**4/16 + 10*m**2 - 7*m. Factor f(a).
-a*(a - 9)*(3*a + 1)/2
Find b such that -26/9 + 1/9*b**2 + 11/9*b = 0.
-13, 2
Let q(v) be the second derivative of 0 + 2*v**3 + 1/2*v**6 + 0*v**2 - 9*v + 9/20*v**5 - 3*v**4. Suppose q(w) = 0. What is w?
-2, 0, 2/5, 1
Let x(i) be the second derivative of 0*i**2 - 1/35*i**6 + 4*i + 1/14*i**3 + 0*i**5 + 0 - 1/98*i**7 + 1/14*i**4. Suppose x(h) = 0. What is h?
-1, 0, 1
Let o(n) be the first derivative of -n**3 + 291*n**2 - 28227*n + 90. Suppose o(y) = 0. What is y?
97
Let i(r) be the third derivative of -r**6/420 + r**5/42 + 17*r**4/84 - r**3 + 987*r**2. Factor i(f).
-2*(f - 7)*(f - 1)*(f + 3)/7
Let j(a) be the second derivative of -a**5/35 + 37*a**4/21 - 142*a**3/21 + 10*a**2 - 2*a + 258. Find x such that j(x) = 0.
1, 35
Let r(v) be the third derivative of 1/3*v**4 + 19*v**2 + 1/5*v**5 + 0 + 0*v + 0*v**3 + 1/30*v**6. Factor r(u).
4*u*(u + 1)*(u + 2)
Suppose -5*m + 2*m - 14 = -o, 0 = 3*o + m - 2. Factor 1/10*p**o + 1/5*p + 0.
p*(p + 2)/10
Suppose -3*p + 1 + 11 = -3*n, 0 = 2*p + 4*n - 14. Determine i so that i**p - 4*i**3 - 2*i**4 + 3*i**3 + 2*i**4 = 0.
-1, 0, 1
Let s(k) = 3*k**3 - k**2 + k + 1. Let m(f) = -7*f**3 - 5*f**2 - f + 9. Let d(o) = -2*m(o) - 6*s(o). Find q, given that d(q) = 0.
-1, 2, 3
Let i(f) be the third derivative of -1/240*f**5 - 9*f**2 + 0*f - 1/8*f**3 - 1/480*f**6 + 0 + 5/96*f**4. Factor i(p).
-(p - 1)**2*(p + 3)/4
Suppose 450 = 7*y - 5*y. Let z = -897/4 + y. Factor 0 + z*b**2 + 0*b.
3*b**2/4
Let g(m) be the first derivative of 11 + 4*m + m**2 - m**3 + 1/21*m**7 + 1/5*m**5 - 1/5*m**6 + 1/3*m**4. Let y(n) be the first derivative of g(n). Factor y(o).
2*(o - 1)**4*(o + 1)
Let j be (1505/(-175))/(4/70). Let t = 151 + j. What is u in 1/2*u + 1/2*u**4 + 0 - t*u**2 - 1/2*u**3 = 0?
-1, 0, 1
Let n(g) = -8*g**4 + 224*g**3 - 1568*g**2 + 5*g + 15. Let x(v) = -12*v**4 + 336*v**3 - 2352*v**2 + 8*v + 24. Let l(a) = -8*n(a) + 5*x(a). Factor l(w).
4*w**2*(w - 14)**2
Let a = 43 + -12. Factor -4*s**3 + 0*s**3 + 27*s**4 - a*s**4.
-4*s**3*(s + 1)
Let f(u) be the second derivative of -u**6/10 - 21*u**5/10 - 49*u**4/4 + 54*u. What is j in f(j) = 0?
-7, 0
Let v(l) = 115*l - 686. Let w be v(6). Suppose 2/9*f**2 + 0 - 2/9*f**w - 4/9*f**3 + 4/9*f = 0. What is f?
-2, -1, 0, 1
Let a(g) be the first derivative of -g**5/630 - 5*g**4/126 - 25*g**3/63 - g**2/2 + 8. Let s(n) be the second derivative of a(n). Solve s(k) = 0 for k.
-5
Let s(o) be the first derivative of 1/3*o + 1/18*o**6 + 1/6*o**2 - 2/9*o**3 + 1/15*o**5 - 1/6*o**4 + 3. Factor s(d).
(d - 1)**2*(d + 1)**3/3
Let u(j) = -j**2 + 6*j - 3. Let b be u(5). Let a be (b/(-24))/((-1)/4). Determine z, given that -4/3 - 4/3*z - a*z**2 = 0.
-2
Let x(z) be the second derivative of -z**4/18 - 160*z**3/9 - 6400*z**2/3 - 248*z. Factor x(n).
-2*(n + 80)**2/3
Let z(n) = 8*n**3 - 42*n**2 + 76*n - 2. Let p(w) = 11*w**3 - 42*w**2 + 76*w - 3. Let j(r) = -2*p(r) + 3*z(r). Let j(l) = 0. What is l?
0, 2, 19
Let y = 12567 - 62598/5. Let i = y - 47. Solve 2/5*n**3 + i*n + 4/5*n**2 + 0 = 0 for n.
-1, 0
Let f(v) = -6*v**3 + 12*v**2 - 2*v - 4. Let w(a) = -a**3 + a**2 - a + 1. Suppose 4*j - 4 = 0, -3*g + 5*j - 5 - 3 = 0. Let k(b) = g*f(b) - 2*w(b). Factor k(s).
2*(s - 1)**2*(4*s + 1)
Let l = 13595/4 - 3398. Factor -1/2 + 5/4*q**2 - l*q.
(q - 1)*(5*q + 2)/4
Let a(i) = -20*i**2 + 43*i - 92. Suppose -7*t = -11*t + 44. Suppose d + 22 = t. Let y(l) = -7*l**2 + 14*l - 31. Let q(c) = d*y(c) + 4*a(c). Factor q(k).
-3*(k - 3)**2
Let k(m) be the third derivative of 1/360*m**6 - 6*m**2 + 0 - 1/1890*m**7 + 0*m + 1/27*m**3 - 1/72*m**4 - 1/540*m**5. Determine u, given that k(u) = 0.
-1, 1, 2
Let s be (-9 - 12/(-3)) + 7. Factor 7 + 6*q**3 - s*q**4 - 2*q**2 - 5*q - 3 - q.
-2*(q - 2)*(q - 1)**2*(q + 1)
Find g such that -76 - 336*g**2 + g**3 + 111*g**2 - 151*g + 151*g**2 = 0.
-1, 76
Let q be ((-2)/(-6))/((-5)/360*-6). Let x be (30/q)/(-5)*144/(-135). Suppose 12/5*n**4 + 2/5*n + 0 + 2/5*n**3 - x*n**2 = 0. Calculate n.
-1, 0, 1/3, 1/2
Let a(f) = f**2 + f + 1. Let j(h) = -11*h**2 - 36*h + 74. Let u(r) = 6*a(r) + j(r). Find v, given that u(v) = 0.
-8, 2
Let r(a) be the first derivative of a**5 + 45*a**4/2 + 95*a**3 - 650*a**2 - 1500*a - 119. Let r(t) = 0. What is t?
-10, -1, 3
Suppose 0*f**4 - f**4 - 3*f + 1100*f**2 - 1099*f**2 + 4*f**3 - f = 0. What is f?
-1, 0, 1, 4
Let w(h) be the first derivative of -75*h**4/4 + 530*h**3 - 1827*h**2/2 + 540*h - 232. Factor w(r).
-3*(r - 20)*(5*r - 3)**2
Let t(g) be the third derivative of g**5/30 - 59*g**4/24 + 11*g**3/2 + 27*g**2. Let r be t(29). Factor 1/4*b**5 + 0*b**2 + 0 + 0*b + 9/4*b**3 + 3/2*b**r.
b**3*(b + 3)**2/4
What is p in -2312/7*p + 0 - 2/7*p**3 + 136/7*p**2 = 0?
0, 34
Let o(s) be the third derivative of 0*s - 1/2*s**3 + 0 + 7/40*s**5 + 5/16*s**4 + 5*s**2. Factor o(p).
3*(p + 1)*(7*p - 2)/2
Determine k so that -3*k**5 - 919*k**2 + 455*k**2 + 9*k**3 + 458*k**2 = 0.
-2, 0, 1
Let h be (-5)/(-3)*(-21)/(28/(-4)). Factor 5*d**h - 11*d**4 + 0*d**2 - 8*d**2 + 28*d**2 - 4*d**4.
5*d**2*(d - 2)**2*(d + 1)
Let t = 3673/4 + -918. What is f in 3/4*f**2 + 1/4*f**3 - 1/4*f**4 - 1/2 - t*f = 0?
-1, 1, 2
Find z, given that -10*z**2 + 2*z**3 + 80*z - 16*z**2 - 43 - 82 + 53 = 0.
2, 9
Let j(t) = -7*t**5 - 6*t**4 + 10*t**2 - t - 4. Let i(r) = -r**5 + 428*r**4 + r**2 - 428*r**4 - r - 1. Let o(f) = 4*i(f) - j(f). Factor o(l).
3*l*(l - 1)*(l + 1)**3
Let b(c) = 9*c**2 - 27*c + 42. Let k(i) = i**2 - i + 2. Let s(f) = -b(f) + 12*k(f). Determine w so that s(w) = 0.
-6, 1
Let z(p) be the first derivative of 1/15*p**3 - 11 + 0*p - 1/20*p**2. Suppose z(s) = 0. Calculate s.
0, 1/2
Let v(h) be the second derivative of 0 + 0*h**2 - 1/18*h**4 - 11*h - 2/9*h**3. Suppose v(y) = 0. Calculate y.
-2, 0
Let z(f) be the first derivative of f**9/25704 - f**8/4760 - 3*f**7/2380 - f**6/612 - 12*f**3 - 31. Let t(m) be the third derivative of z(m). Factor t(o).
2*o**2*(o - 5)*(o + 1)**2/17
Suppose 0*m + 4*m = 4*s + 140, 2*m - 2 = 0. Let t = s + 36. Factor 2/3 - 2/3*w**t + 0*w.
-2*(w - 1)*(w + 1)/3
Let b(c) be the first derivative of c**3 + 6*c**2 - 15*c + 20. What is d in b(d) = 0?
-5, 1
Let p be 2/8 - -5*(-3)/(-12). Let r be (-18)/(-6) - 0/2. Factor 9/2*b**4 - 3/2 - r*b**2 - p*b**5 - 3*b**3 + 9/2*b.
-3*(b - 1)**4*(b + 1)/2
Suppose 4*p - 5*p + 10 = 5*k, 0 = 5*p + 3*k - 6. Factor -27/4 + 1/4*v**4 + 9/2*v**2 - 2*v**3 + p*v.
(v - 3)**3*(v + 1)/4
Let i(m) be the second derivative of -6*m + 0 - 1/16*m**3 + 0*m**2 - 1/16*m**4. Suppose i(t) = 0. Calculate t.
-1/2, 0
Let z(f) = 5*f**3 - 7*f**2 - f + 11. Let c(j) = 12*j - 13*j**2 + 6*j**3 - 28*j + 5*j**3 + 23 + 15*j. Let s(v) = 2*c(v) - 5*z(v). Factor s(b).
-3*(b - 3)*(b - 1)*(b + 1)
Let j(d) be the third derivative of -d**5/330 - 5*d**4/132 + 2*d**3/11 - 2*d**2 - 58*d. Factor j(v).
-2*(v - 1)*(v + 6)/11
Let j = -126 + 133. Let w be (j/(42/(-4)))/(0 + -2). Factor 2/3 + w*q**2 + q.
(q + 1)*(q + 2)/3
Suppose 36/7*g + 72/7 - 32/7*g**2 + 4/7*g**3 = 0. Calculate g.
-1, 3, 6
Factor 6/11 - 52/11*r**2 + 46/11*r.
-2*(r - 1)*(26*r + 3)/11
Suppose -12/5*j**3 - 138/5*j**2 - 252/5*j + 162/5 = 0. Calculate j.
-9, -3, 1/2
Let o = -399 - -403. Let b(l) be the third derivative of -2/105*l**7 - 1/3*l**o - 13*l**2 + 0 + 0*l**3 + 0*l**6 + 0*l + 1/5*l**5. Factor b(i).
-4*i*(i - 1)**2*(i + 2)
Let c(u) = 3*u - 3. Let b(l) = l - 1. Let v(o) = -10*b(o) + 4*c(o). Let d be v(3). Factor 9*a**3 + a**4 + 7*a**4 + 3*a**2 + a**d + 3*a**5.
3*a**2*(a + 1)**3
Let z = 38 - 36. Factor 2*m**z + 3*m**2 + 94*m - 74*m + 15.
5*(m + 1)*(m + 3)
Let j(v) be the third derivative of -v**6/200 - 6*v**5/25 - 23*v**4/40 + 89*v**2. Let j(w) = 0. What is w?
-23, -1, 0
Let u(m) be the first derivative of m**5/210 - m**3/21 - 7*m**2 - 12. Let q(l) be 