w - 2*w. Let h be 20/w*9/8. Factor h*c**2 - 1/4*c - 1/2.
(c - 2)*(c + 1)/4
Let c(x) be the second derivative of x**7/4620 - x**6/1980 - x**5/110 + 4*x**3 - 20*x. Let i(r) be the second derivative of c(r). Factor i(h).
2*h*(h - 3)*(h + 2)/11
Suppose 4*d - h + 15 = 0, 3*d - 7 = -4*h - 23. Let a be (6/d)/((-9)/96). Solve -3*t**3 - 21*t**2 + 14*t**2 + a*t**2 = 0 for t.
0, 3
Suppose 11*c - 55 = 11. Factor -c*o - 3/4*o**2 - 12.
-3*(o + 4)**2/4
Let m be ((-8)/7)/(112/(-196)). Solve -18 - 2/9*k**m + 4*k = 0 for k.
9
Let i = -8 - -5. Let q(u) be the first derivative of 2*u**3 + 5*u**2 + 8. Let s(k) = 6*k**2 + 10*k + 1. Let j(h) = i*q(h) + 4*s(h). Factor j(t).
2*(t + 1)*(3*t + 2)
Let r(o) = o**2 + 3*o - 20. Let g(k) = 2*k**2 + 3*k - 39. Let n(j) = 4*g(j) - 10*r(j). Determine f, given that n(f) = 0.
-11, 2
Suppose -75*t - 36 = -80*t - 3*p, -4*t + 5*p = -14. Let u(g) be the second derivative of 0*g**2 + 0 + 0*g**5 + 1/105*g**t - 1/42*g**4 + 0*g**3 - g. Factor u(z).
2*z**2*(z - 1)*(z + 1)/7
Determine a so that 60 - 5*a**4 - 2*a**3 + 336*a - 196*a - 4*a**2 + 11*a**3 + 99*a**2 + a**3 = 0.
-2, -1, 6
Let y(g) = g**2 - 12*g + 16. Let o be y(11). Factor 16*p + 2*p**2 + o*p**3 - 7*p**3 - 20 - 4.
-2*(p - 2)**2*(p + 3)
Let u(j) = 12*j + 172. Let l be u(-14). Let m(y) be the second derivative of 0*y**2 - 1/2*y**3 - 8*y - 1/4*y**l + 0. Factor m(x).
-3*x*(x + 1)
Let i be (-35742)/(-1260) + (-4)/(-30). Factor -48*l - 15/4*l**3 + 24 - i*l**2.
-3*(l + 4)**2*(5*l - 2)/4
Factor 4/5*m**5 - 4/5*m**4 - 2/5*m**2 + 0 - 7/5*m**3 + 0*m.
m**2*(m - 2)*(2*m + 1)**2/5
Let 57/4*r - 15/2 - 21/4*r**2 = 0. What is r?
5/7, 2
Determine g, given that -204*g**3 + 10*g**4 - 38803*g + 441*g**2 + 300 + 5*g**4 + 39763*g = 0.
-1, -2/5, 5, 10
Let -2/7*u**3 + 222/7*u**2 + 0 - 220/7*u = 0. What is u?
0, 1, 110
Factor -1332/19*p + 162/19 - 16/19*p**3 + 290/19*p**2.
-2*(p - 9)**2*(8*p - 1)/19
Suppose -3 = -o - 2*o. Let g be (-3)/(-6)*(-2 + 10*o). Factor 8/5*f**3 - 8/5*f**g + 4/5 + 2/5*f**5 - 2*f + 4/5*f**2.
2*(f - 2)*(f - 1)**3*(f + 1)/5
Let v be (90/36)/(-5) + 0 + 1/2. Find l such that -56/5*l**3 - 114/5*l**2 + 8/5 + v*l = 0.
-2, -2/7, 1/4
Suppose 3*n + l + 4 = 5*n, -4*n + 4*l = -8. Let f be -2*(-9)/6 + n. Suppose -2*a**2 - 5*a**5 + 6*a**f + a - 2*a**3 + 2*a**2 = 0. What is a?
-1, 0, 1
Let c(b) be the first derivative of -2*b**5/5 + 5*b**4/12 + 2*b**3/3 - 5*b**2/6 + 395. What is r in c(r) = 0?
-1, 0, 5/6, 1
Let d(f) = -17*f**3 - 7 + 5*f + 0 + 12*f**3 - 2 + 11*f**2. Let n(z) = -6*z**3 + 12*z**2 + 6*z - 9. Let u(x) = 3*d(x) - 2*n(x). Factor u(l).
-3*(l - 3)*(l - 1)*(l + 1)
Let l(k) be the third derivative of -k**6/150 - 7*k**5/300 + 31*k**4/60 - k**3/2 - 405*k**2. Let l(n) = 0. Calculate n.
-5, 1/4, 3
Find o, given that -405*o**2 - 34*o**4 - 5*o**5 + 4*o**4 + 385*o**2 - 45*o**3 = 0.
-4, -1, 0
Let -5/2*o**3 + 10*o + 20 - 5*o**2 = 0. What is o?
-2, 2
Let b(f) = 33*f - 193. Let s be b(6). Let z(w) be the third derivative of -1/240*w**6 - 1/40*w**s + 0 + 1/4*w**3 + 9*w**2 + 0*w + 1/48*w**4. Factor z(c).
-(c - 1)*(c + 1)*(c + 3)/2
Let p = -25 + 28. Determine a, given that -9*a - 2*a**4 - 23*a**3 + 29*a**p + a = 0.
-1, 0, 2
Let z(c) be the first derivative of -c**4/10 + 4*c**3/15 - c**2/5 + 19. Solve z(k) = 0 for k.
0, 1
Let d(s) be the third derivative of -s**6/30 + s**5/3 + s**4 - 34*s**2. Factor d(r).
-4*r*(r - 6)*(r + 1)
Suppose s - 5*j + 25 = 0, -3*j + 15 = 3*s + 2*s. Suppose 0*m + 15*m = 2*m. Let 2/11*b**5 + s*b + m*b**4 - 2/11*b**3 + 0 + 0*b**2 = 0. Calculate b.
-1, 0, 1
Let g(d) be the second derivative of 3*d**5/32 + d**4/8 + 3*d - 7. Suppose g(y) = 0. Calculate y.
-4/5, 0
Let -4/7*x**3 - 8/7 + 0*x**2 + 12/7*x = 0. What is x?
-2, 1
Let p(h) = -2*h**4 + 22*h**3 + 28*h**2 - 20*h - 20. Let u(t) = 5*t**4 - 67*t**3 - 84*t**2 + 60*t + 58. Let o(f) = 7*p(f) + 2*u(f). Let o(d) = 0. Calculate d.
-1, 1, 6
Find m such that 14*m**4 - 15*m**3 + 73*m - 185*m**2 + 45 + 17*m**4 + 62*m - 7*m**4 - 4*m**4 = 0.
-3, -1/4, 1, 3
Let c(q) be the second derivative of -7*q**7/300 - 7*q**6/225 - q**5/75 - q**3/6 + 3*q. Let a(s) be the second derivative of c(s). Solve a(o) = 0.
-2/7, 0
Let f(k) = k + 7. Let a be f(13). Let -8 - 5*u**2 + 33 - u + u + a*u = 0. What is u?
-1, 5
Let z(y) be the second derivative of y**5/40 + 7*y**4/24 - 49*y**3/12 - 343*y**2/4 + 420*y. Find r such that z(r) = 0.
-7, 7
Let q = -8765 - -26297/3. Suppose 1/3*j**3 + 0 + q*j - j**2 = 0. What is j?
0, 1, 2
Solve 0*u - 1/4*u**4 - 9/2*u**2 + 0 - 19/4*u**3 = 0 for u.
-18, -1, 0
Let l(u) be the first derivative of -u**4 - 32*u**3/3 - 14*u**2 + 96. Suppose l(y) = 0. What is y?
-7, -1, 0
Let v(l) be the first derivative of l**4/3 - 44*l**3/9 - 8*l**2 + 87. What is w in v(w) = 0?
-1, 0, 12
Let x = -381/8 - -7319/152. Let b = 874384/19 - 46020. Solve 2/19*o - b + 16/19*o**2 + x*o**3 = 0.
-1, 2/5
Suppose 3 = -4*d - 9. Let i be (-4)/d - (-2)/6. What is u in u**3 - 1/3*u**5 + 0 + 1/3*u**4 - i*u**2 + 2/3*u = 0?
-2, 0, 1
Let c(p) be the second derivative of p**5/120 + p**4/8 - p**3/36 - 3*p**2/4 + 2*p - 7. Factor c(u).
(u - 1)*(u + 1)*(u + 9)/6
Let x = 4 + -1. Suppose 12 = x*v + 6. Find b, given that 12/7 + 3/7*b**v + 12/7*b = 0.
-2
Find z, given that 10/11*z + 0 + 2/11*z**3 + 12/11*z**2 = 0.
-5, -1, 0
Let o(c) be the second derivative of c**6/80 + 3*c**5/20 - 9*c**4/32 - 152*c. Factor o(q).
3*q**2*(q - 1)*(q + 9)/8
Let g(b) be the second derivative of -b**4/4 + 23*b**3 - 1587*b**2/2 - 4*b + 3. Let g(o) = 0. What is o?
23
Suppose -16*d + 4 = -14*d. Let y(f) be the third derivative of 0*f + 1/120*f**5 - 3*f**d + 0 + 0*f**3 + 1/48*f**4. Factor y(i).
i*(i + 1)/2
Let q = -1510/3 - -4532/9. Suppose 5*b - 4*b - 3 = 0. Factor -4/9*r + 2/9*r**4 + 4/9*r**b - q*r**2 + 0.
2*r*(r - 1)*(r + 1)*(r + 2)/9
Let h(v) be the third derivative of -v**7/840 - v**6/120 + v**4/12 - 5*v**3/6 + 30*v**2. Let n(w) be the second derivative of h(w). Factor n(r).
-3*r*(r + 2)
Let h = -99/20 - -103/20. Solve -1/5*l**3 + h*l**2 + 2/5*l + 0 = 0 for l.
-1, 0, 2
Let w(u) = -u**2 - 11*u - 63. Let r be w(-7). Let b be (-2 - 1)*14/r. Factor -2/5*c**3 + 2/5 - b*c + 6/5*c**2.
-2*(c - 1)**3/5
Let l = -38982 - -38986. Let 3/10*r**2 + 0 + 0*r + 1/2*r**l - 7/10*r**3 - 1/10*r**5 = 0. Calculate r.
0, 1, 3
Let j(p) be the third derivative of -1/60*p**6 - 1/672*p**8 + 0 - 1/60*p**5 + 0*p - 13*p**2 + 1/105*p**7 + 5/48*p**4 - 1/6*p**3. Factor j(k).
-(k - 2)*(k - 1)**3*(k + 1)/2
Suppose 4*i = 5*c + 31, -3 = 4*i + 5*c - 4. Let g = 9 - i. What is w in -2*w - 11*w**4 - 8*w**4 + 12*w**3 + 3*w**4 + w**5 + 5*w**g = 0?
-1/3, 0, 1
Let r(i) = -2*i**3 + i**2 - 3*i + 2. Let x(j) = 6*j**3 - 2*j**2 + 10*j - 7. Let c(p) = -14*r(p) - 4*x(p). Factor c(l).
2*l*(l - 1)*(2*l - 1)
Suppose 5*x = -5*g + 40, 86*x - 82*x - 2*g = -16. Factor x*i + 1/2*i**2 + 0 + 1/2*i**3.
i**2*(i + 1)/2
Let t be (-20)/(-35) - (-24)/7. Suppose 0 = 4*u + 16, -t*n + 20 = -3*u - 0*u. Factor -2*r**4 + 17*r**3 - 27*r**3 - 2*r**n - 6*r**4.
-2*r**2*(r + 1)*(4*r + 1)
Let k = -524 - -528. Let p(m) be the second derivative of 0 - 1/8*m**k - 1/40*m**5 - 7*m + 0*m**2 - 1/6*m**3. Factor p(w).
-w*(w + 1)*(w + 2)/2
Solve -18/7 + 12/7*y - 2/7*y**2 = 0 for y.
3
What is h in 13827 - 3*h**3 + 9839 - 368*h**2 - 7300*h - h**3 - 784*h - 5994 = 0?
-47, 2
Let p(m) be the first derivative of 5*m**4/2 + 56*m**3/3 + 28*m**2 - 32*m - 36. Determine i, given that p(i) = 0.
-4, -2, 2/5
Let t = -217 + 213. Let c be (2 - 2) + (-16)/t - 1. Factor -3/5*b**2 + 0 + 1/5*b**c + 2/5*b.
b*(b - 2)*(b - 1)/5
Let x(q) be the second derivative of -q**5/240 + q**4/36 - q**3/18 - 88*q. Factor x(t).
-t*(t - 2)**2/12
Factor -135*r**3 - 96*r**2 + 156*r - 12*r**2 - 32 + 39*r**3 + 33*r**3 + 47*r**3.
-4*(r - 1)*(r + 8)*(4*r - 1)
Let b(z) be the second derivative of -z**5/30 - 2*z**2 - 2*z. Let w(q) be the first derivative of b(q). Factor w(f).
-2*f**2
Let q(j) be the second derivative of j**4/8 - 15*j**3 + 675*j**2 + 93*j. Factor q(f).
3*(f - 30)**2/2
Let r(i) be the third derivative of -i**6/420 - i**5/42 + i**4/14 + 3*i**2 + i. Factor r(v).
-2*v*(v - 1)*(v + 6)/7
Let r be (-152)/(-45) - (-2)/9. Let q = 16357/9090 + 1/1818. Let -36/5*j**2 - q*j**4 - r*j - 3/5 - 6*j**3 = 0. Calculate j.
-1, -1/3
Factor 4/3*z**3 + 4/3*z**2 - 2*z**4 + 2/3 - 2*z + 2/3*z**5.
2*(z - 1)**4*(z + 1)/3
Factor -20*m + 112/3 + 2/3*m*