rmine h, given that t(h) = 0.
-1/2
Let o(b) be the first derivative of -2 + 0*b + 0*b**4 + 0*b**2 - 2/25*b**5 + 2/15*b**3. Factor o(n).
-2*n**2*(n - 1)*(n + 1)/5
Suppose 1/4*x**2 - 7*x - 29/4 = 0. Calculate x.
-1, 29
Let 0*q**3 + 20/3*q**2 - 20/3*q**4 + 0 + 2*q**5 - 2*q = 0. Calculate q.
-1, 0, 1/3, 1, 3
Suppose 25*l + 4 - 4 = 0. Factor 0*q**3 + 0 + 2/15*q**4 + l*q - 2/15*q**2.
2*q**2*(q - 1)*(q + 1)/15
Let y(k) be the first derivative of 1/5*k**2 + 7*k + 7 + 1/30*k**4 + 2/15*k**3. Let j(m) be the first derivative of y(m). Determine n, given that j(n) = 0.
-1
Let c(y) = 8*y**4 - 2*y**3 + 5. Let k(d) = 9*d**4 - 3*d**3 + 6. Let z(a) = 6*c(a) - 5*k(a). Determine l so that z(l) = 0.
-1, 0
Let y(a) = -a**2 + a + 1. Let k(u) be the second derivative of -17*u**4/12 - 2*u**3 + 2*u**2 + 9*u. Let r(g) = 5*k(g) - 40*y(g). Let r(m) = 0. Calculate m.
-2, -2/9
Let s(l) be the first derivative of 0*l**3 + 0*l + 12 + 0*l**2 - l**5 - 5/4*l**4. Suppose s(f) = 0. Calculate f.
-1, 0
Suppose -3*f + 5*w = -6 - 5, -2*f = 5*w + 1. Let s = 20 + -16. Factor -s + 5*a**f + 7*a - 2 + 3 + 5.
(a + 1)*(5*a + 2)
Suppose 23*t = 21*t - 4*s + 34, -6*t = -4*s + 10. Determine p so that -39/2*p**2 + 45/2*p - t = 0.
2/13, 1
Let u(d) be the third derivative of -d**8/560 + 3*d**7/350 + 3*d**6/100 - 2*d**5/25 - 2*d**2 - 34. Solve u(x) = 0.
-2, 0, 1, 4
Suppose 0 = -5*r - k + 16, -8 = -3*r - 3*k + 4*k. Factor -8 + 2*w**2 - 10*w + 4*w**r + 11 + 3 - 2*w**3.
2*(w - 1)**2*(w + 3)
Let p(v) be the second derivative of -v**4/54 - 11*v**3/27 + 4*v**2/3 - 107*v. Let p(x) = 0. What is x?
-12, 1
Suppose 9/4 + 3/4*c**3 - 9/4*c**2 - 3/4*c = 0. Calculate c.
-1, 1, 3
Suppose -1 = -z + 1. Let t be ((-18)/7)/(183/(-854)). Factor -9*y + 3*y + t*y**2 - 10*y**z.
2*y*(y - 3)
Let i = -1251 - -62551/50. Let v(w) be the second derivative of -3*w - i*w**5 + 0 + 1/5*w**2 - 1/30*w**4 + 1/15*w**3. Factor v(f).
-2*(f - 1)*(f + 1)**2/5
Let z be (6*-163)/(-5*1) - 2. Let m = z - 193. Let -m*l**2 - 2/5 + 1/5*l**3 + 1/5*l**4 - l = 0. What is l?
-1, 2
Let q = -11135 + 11138. Find l such that -4/23*l**q + 2/23*l**2 + 0 + 4/23*l - 2/23*l**4 = 0.
-2, -1, 0, 1
Let u(d) be the second derivative of 0*d**2 + 1/15*d**4 + 13*d + 0*d**3 + 0 - 3/50*d**5. Solve u(g) = 0 for g.
0, 2/3
Factor -204*x**2 + 150*x**2 + 140*x - 191*x**2 - 20.
-5*(7*x - 2)**2
Let u(v) be the first derivative of v**5/140 + v**4/56 + v**2/2 - 11*v + 6. Let g(k) be the second derivative of u(k). Factor g(x).
3*x*(x + 1)/7
Let d(b) be the first derivative of -10 - 2/33*b**3 + 4/11*b + 1/11*b**2. Solve d(f) = 0 for f.
-1, 2
Let m(z) = -10*z**3 - 13*z**2 + 10*z + 22. Let h(g) = -g**3 + g + 1. Let j(t) = -18*h(t) + 2*m(t). Factor j(s).
-2*(s - 1)*(s + 1)*(s + 13)
Let h = 21 + -17. Suppose h*b = 5 + 15. Factor 2/3*j + 4/3*j**4 - 2/3*j**b + 0 + 0*j**3 - 4/3*j**2.
-2*j*(j - 1)**3*(j + 1)/3
Suppose 290*k + 40 = 298*k. Let x(y) be the first derivative of 0*y**4 + 0*y + k + 0*y**2 - 1/15*y**5 + 1/9*y**3. Determine m so that x(m) = 0.
-1, 0, 1
Let o(r) be the first derivative of 13 - 3/20*r**4 + 1/3*r**3 + 3/10*r**2 - 4/25*r**5 - 1/5*r. Determine n so that o(n) = 0.
-1, 1/4, 1
Let h(m) be the third derivative of m**6/270 - m**5/9 + 25*m**4/18 + 3*m**3 - 17*m**2. Let i(y) be the first derivative of h(y). Factor i(k).
4*(k - 5)**2/3
Factor -67*i - 172 - 260 + 4*i - 21*i**3 - 35*i**3 + 228*i**2 + 4*i**4 - 81*i.
4*(i - 6)**2*(i - 3)*(i + 1)
Solve -3/2*g**2 - 1/4*g**4 - g + 5/4*g**3 + 2 = 0 for g.
-1, 2
Suppose -54/5 + 528/5*z**4 - 123/5*z**3 + 63*z - 192/5*z**5 - 474/5*z**2 = 0. Calculate z.
-1, 3/8, 1, 2
Let i(t) be the third derivative of t**8/112 + t**7/7 + 37*t**6/40 + 16*t**5/5 + 13*t**4/2 + 8*t**3 - t**2 - 69. Solve i(w) = 0 for w.
-4, -2, -1
Let i(f) be the third derivative of -f**6/1080 - f**5/120 - f**4/36 - 13*f**3/6 + f**2. Let t(y) be the first derivative of i(y). Factor t(r).
-(r + 1)*(r + 2)/3
Let l(q) = -q**3 - q**2. Let x(m) = m**4 + 7*m**3 + 6*m**2. Let w(t) = 18*l(t) + 2*x(t). Factor w(g).
2*g**2*(g - 3)*(g + 1)
Let q(n) = n**3 - 20*n**2 + 37*n - 24. Let z be q(18). Let o be 24/15*z/(-18). Find t such that 8/15*t + 2/15*t**2 - o*t**3 - 2/15 = 0.
-1, 1/4, 1
Let y(n) = 11*n**5 - 29*n**4 + 60*n**3 - 14*n**2. Let v(p) = 6*p**5 - 14*p**4 + 30*p**3 - 6*p**2. Let s(d) = -7*v(d) + 4*y(d). Suppose s(c) = 0. Calculate c.
0, 1, 7
Suppose -2/13*t**3 - 1058/13 - 1150/13*t - 94/13*t**2 = 0. What is t?
-23, -1
Let l(j) be the first derivative of j**6/12 - j**5/10 - j**4/4 + j**3/3 + j**2/4 - j/2 + 39. Factor l(c).
(c - 1)**3*(c + 1)**2/2
Let s(c) be the first derivative of -c**5/5 + 3*c**4/2 + c**3/3 - c**2/2 - 5*c - 5. Let i(b) = -b**4 + b**3 + b**2 - 1. Let w(q) = -5*i(q) + s(q). Factor w(x).
x*(x - 1)*(x + 1)*(4*x + 1)
Suppose -5*q - 4*n = -6, -368*n - 14 = -5*q - 364*n. What is g in 2/5*g**5 + 0*g**3 + 0*g**q - 6/5*g**4 + 0 + 0*g = 0?
0, 3
Let p = 354 - 345. Let x be (40/(-30))/((-15)/p). Factor -12/5*n**3 + 12/5*n + 0 - 4/5*n**2 + x*n**4.
4*n*(n - 3)*(n - 1)*(n + 1)/5
Let a be 1/(2 + (-9)/3) + 2. Factor -a + 20*w + 51 - 7*w**2 + 9*w**2.
2*(w + 5)**2
Let r(o) = 2*o - 8. Let b = -49 - -53. Let l be r(b). Determine z, given that 2/7*z**3 + 1/7*z**4 - 1/7*z**2 - 2/7*z + l = 0.
-2, -1, 0, 1
What is d in -224 + 375*d - 4*d**2 + 268*d - 523*d = 0?
2, 28
Suppose -2*a + 3*m + 29 = 0, 3*a - 21*m = -22*m + 27. Factor -5/3*i**2 + 0 - a*i + 5/3*i**3.
5*i*(i - 3)*(i + 2)/3
Let g = 4472/3735 + 2/747. Factor 3/5*w**5 + 9/5*w + 0*w**4 + g - 12/5*w**3 - 6/5*w**2.
3*(w - 2)*(w - 1)*(w + 1)**3/5
Suppose 3*d + 14 = -91. Let j = -33 - d. Solve -21 + 4*t**j + 57 + 0*t**2 - 24*t = 0.
3
Let g = 4023/46 + -1770/23. Suppose -4*j**4 - 11*j**2 - 4*j + 0 - 1/2*j**5 - g*j**3 = 0. Calculate j.
-4, -2, -1, 0
Let r = -1188 + 1191. Let d(q) be the second derivative of 0 + 0*q**2 + 1/6*q**4 - 1/10*q**5 + 0*q**r + 5*q. Factor d(s).
-2*s**2*(s - 1)
Let k = 2/9295 - -74346/65065. Factor k - 2/7*f**3 + 2/7*f - 8/7*f**2.
-2*(f - 1)*(f + 1)*(f + 4)/7
Let m(t) = 6*t**4 + 39*t**3 - 147*t - 111. Let k(h) = h**5 - 5*h**4 - 39*h**3 + h**2 + 146*h + 110. Let u(p) = -3*k(p) - 2*m(p). Let u(d) = 0. What is d?
-2, -1, 3
Let c = 113/520 - 6/65. Let q(f) be the first derivative of -5/6*f**3 - 7/4*f**2 - 2 - c*f**4 - 3/2*f. Factor q(p).
-(p + 1)**2*(p + 3)/2
Let a(n) be the first derivative of -n**3/3 - 3*n**2/2 - 2*n - 17. Let y be a(-2). What is x in y + 1/5*x**4 + 2/5*x**3 + 0*x + 1/5*x**2 = 0?
-1, 0
Let d(w) be the second derivative of -w**7/294 + 17*w**6/210 - 47*w**5/70 + 95*w**4/42 - 23*w**3/6 + 7*w**2/2 + 82*w. Determine r so that d(r) = 0.
1, 7
Factor -19*h**3 + 42*h**3 - 35*h**3 + 3*h**4.
3*h**3*(h - 4)
Let a(f) = f**2 - 2*f. Let x be (-4 - (-2 + 1)) + 5/1. Let i be a(x). Solve -2/3*o**2 + 2/3*o + i = 0 for o.
0, 1
Let i(a) be the first derivative of -2*a**4/3 + 2*a**3/9 + 10*a**2/3 - 30*a + 28. Let g(x) be the first derivative of i(x). Factor g(q).
-4*(q - 1)*(6*q + 5)/3
Let g(h) = h**3 - 13*h**2 + 13*h - 10. Let r(j) = j + 1. Let l be r(11). Let i be g(l). Solve 0*c**i - 2/7*c**5 + 0 + 2/7*c**3 + 0*c + 0*c**4 = 0.
-1, 0, 1
Factor -8/9 + 8/9*s**3 + 2/9*s**4 + 2/3*s**2 - 8/9*s.
2*(s - 1)*(s + 1)*(s + 2)**2/9
Let n = -10656 + 1236155/116. Let j = n - 1/116. Solve f + j + 1/2*f**2 = 0.
-1
Determine g, given that 0*g**4 - 14*g**3 + 6*g**4 + 0*g**4 + 11*g**3 + 10*g**2 - 7*g**4 = 0.
-5, 0, 2
Suppose 4*n - 15 = f, 0 = -234*n + 232*n + 3*f + 5. Factor n*d - 8 - 1/2*d**2.
-(d - 4)**2/2
Let v(g) be the first derivative of g**6/180 + g**5/60 - g**4/6 + 10*g**3/3 + 10. Let t(n) be the third derivative of v(n). Factor t(h).
2*(h - 1)*(h + 2)
Let f(v) = 2*v**3 - 5*v**2 + 10*v - 37. Let x be f(3). Suppose 57/2*g**x - 21/2*g**3 - 6 - 12*g = 0. Calculate g.
-2/7, 1, 2
Let h = 31 - 28. Let m(n) be the first derivative of -3/4*n**4 + h*n - n**3 - 4 + 3/2*n**2. Factor m(k).
-3*(k - 1)*(k + 1)**2
Let z(p) be the second derivative of p**7/210 - 15*p**2/2 - 3*p. Let n(a) be the first derivative of z(a). Let n(l) = 0. What is l?
0
Let k be (2/(-4) + 15/10)*97. Determine l, given that -52 - 21 + 28*l + 4*l**2 + k = 0.
-6, -1
Factor 82*i + 1800 + 10*i**2 - 26*i**2 - 1842 - 22*i**2 - 2*i**3.
-2*(i - 1)**2*(i + 21)
Let y(f) be the second derivative of f**6/10 - 9*f**5/20 - 9*f**4/4 + 23*f**3/2 - 18*f**2 - f - 43. Factor y(j).
3*(j -