h) - 5*k(h). Factor a(p).
-5*(p + 2)**2
Factor 2/5*r**2 - 52 + 6/5*r.
2*(r - 10)*(r + 13)/5
Let j(n) = n**3 + 19*n**2 + 15*n + 289. Let g be j(-19). Factor -48/5*h**2 + 64/5*h - 2/5*h**g - 32/5 + 16/5*h**3.
-2*(h - 2)**4/5
Let r = -66 + 28. Let m be r/(-4) + 9/(-6). Factor 4*h**2 - 4*h**4 - m*h + 8*h**3 + 4*h**4 - 6 + 2*h**4.
2*(h - 1)*(h + 1)**2*(h + 3)
Let a(u) be the second derivative of -u**5/80 - u**4/32 + 16*u**2 - 7*u. Let l(b) be the first derivative of a(b). Factor l(o).
-3*o*(o + 1)/4
Let t(n) be the third derivative of -n**6/540 + n**4/9 - 16*n**3/27 - 241*n**2. Let t(s) = 0. What is s?
-4, 2
Let i(f) be the first derivative of f**5/25 + f**4/2 - f**3/5 - 14*f**2 + 196*f/5 + 915. Find x such that i(x) = 0.
-7, 2
Let h(n) be the second derivative of -n**4/18 - 5*n**3/9 + 22*n**2 - 28*n. Factor h(q).
-2*(q - 6)*(q + 11)/3
Let d(b) = -3*b - 15. Let m be d(-7). Let o be 24 - (-4 + (m - 2)). Let 23*l**4 - 9*l**3 - 6*l**2 + o*l**4 - 50*l**4 = 0. What is l?
-2, -1, 0
Let m be -155 + 169 + 12*((-8)/(-4))/(-2). What is b in -25/6*b + 2 - 1/6*b**3 + 7/3*b**m = 0?
1, 12
Factor -121*x**2 + 61*x**2 + 65*x**2 + 35280 + 222*x + 618*x.
5*(x + 84)**2
Let p(q) be the first derivative of 1/1800*q**6 + 1/150*q**5 - 36 - 14/3*q**3 + 1/30*q**4 + 0*q + 0*q**2. Let t(m) be the third derivative of p(m). Factor t(c).
(c + 2)**2/5
Let h(z) be the second derivative of -z**6/60 + 3*z**5/10 + 27*z**4/8 + 17*z**3/3 + 106*z + 1. Factor h(r).
-r*(r - 17)*(r + 1)*(r + 4)/2
Let z(c) be the second derivative of 3/4*c**4 - 3/20*c**5 + 0 + 0*c**3 + 0*c**2 - 132*c. Find w such that z(w) = 0.
0, 3
Solve 11552/3*v**3 + 2/3*v**5 - 272/3*v**4 - 38400*v**2 - 516096*v - 1179648 = 0.
-4, 48
Let f = 421 - 420. Let x(n) = -n**3 + n**2 + n. Let b(i) = -5*i**3 + 3*i**2 + 4*i. Suppose l - 5*l = 16. Let v(t) = f*b(t) + l*x(t). Factor v(u).
-u**2*(u + 1)
Let q(j) be the first derivative of 6*j**2 + 56 + 148/21*j**3 - 10/7*j**5 + 2/7*j**6 - 18/7*j - 4/7*j**4. Solve q(l) = 0 for l.
-1, 1/6, 3
Let y = 596669 + -2386675/4. Factor -1/4*c**4 - 1/4*c + y*c**2 + 0 + 1/4*c**3.
-c*(c - 1)**2*(c + 1)/4
Suppose -2*n + 7*n - 25 = 0, -2*k + 68 = 2*n. Let j = k - 26. Suppose -42 + 5 - 155 + 48*h - j*h**2 = 0. What is h?
8
Let l(z) be the first derivative of -6*z**5/55 + 3777*z**4/11 - 3160074*z**3/11 - 19051188*z**2/11 - 38162904*z/11 - 3606. Find n, given that l(n) = 0.
-2, 1261
Let c(v) be the first derivative of -2/9*v**6 + 4/5*v**5 + 4/3*v**2 - 4/3*v**3 + 155 - 1/3*v**4 + 0*v. Solve c(r) = 0.
-1, 0, 1, 2
Let c be (-3*2/(-8))/(1/4). Suppose 0 = -5*r + c*a - 0*a + 5, -4*r - 2*a + 26 = 0. Let -5*l**2 + l + 4*l**2 + 3*l**2 - r*l**2 + l**3 = 0. What is l?
0, 1
Let r be (-6)/(-57) - 288888/114. Let o = r - -12768/5. Factor 72/5 - 168/5*l + o*l**2.
2*(7*l - 6)**2/5
Factor 21*o**2 + 1906*o**3 + 80*o + o**4 - 144 + 11*o**2 - 1926*o**3.
(o - 18)*(o - 2)**2*(o + 2)
Suppose -39 = -5*j - 4*z, -86*z + 6 = -2*j - 84*z. Suppose -69/2*o**j + 36*o**4 + 0 - 45/2*o**2 + 24*o**5 - 3*o = 0. What is o?
-2, -1/4, 0, 1
Let b(d) be the first derivative of -9/4*d**4 + 0*d**2 + 0*d + 228/5*d**5 - 15/2*d**6 + 107 - 10*d**3. Solve b(o) = 0 for o.
-1/3, 0, 2/5, 5
Let x(b) be the third derivative of -1/8*b**4 - 1/40*b**5 + b**2 + 0*b - 14 + 0*b**3. Factor x(m).
-3*m*(m + 2)/2
Factor 0*y - 1/5*y**5 + 154/5*y**3 + 15*y**4 + 0 + 0*y**2.
-y**3*(y - 77)*(y + 2)/5
Let m = 1 - -4. Let k(n) = -n**2 - 19*n + 46. Let i be k(-21). Factor m*r**2 + 4*r - 4*r - r - 2 - i*r**2.
(r - 2)*(r + 1)
Suppose -6*d - 201 + 231 = 0. Suppose -4*u = -8, 3*m + 0*u + d*u - 25 = 0. Let 0 + 0*j**3 - 4/5*j**4 + 2/5*j**m + 4/5*j**2 - 2/5*j = 0. What is j?
-1, 0, 1
Factor 2 + 2/7*z**4 + 12/7*z**3 - 16/7*z**2 - 12/7*z.
2*(z - 1)**2*(z + 1)*(z + 7)/7
Factor -486*g**3 + 171*g**3 + 160*g**3 + 160*g**3 - 2355*g**2 + 369735*g - 19349465.
5*(g - 157)**3
Let f(d) be the second derivative of 3*d**6/20 - 37*d**5/40 - 169*d**4/12 - 155*d**3/3 - 82*d**2 - 27*d + 4. Determine h, given that f(h) = 0.
-2, -1, 82/9
Let o(t) be the first derivative of 0*t - 1/45*t**5 + 1/36*t**4 + 0*t**3 + 0*t**2 - 79. Suppose o(z) = 0. What is z?
0, 1
Suppose 4*k = 3*k - b + 9, 4*k = 5*b. Let o(m) = 8 - 26*m**2 - 13 + k + 2*m**3. Let c(x) = x**3 - 25*x**2. Let q(y) = 5*c(y) - 4*o(y). Solve q(l) = 0.
-7, 0
Suppose 24 = 22*j - 20. Suppose -19 + 9 - 8*w + j*w**2 - 3 - 17*w = 0. What is w?
-1/2, 13
Suppose 13*k - 19*k + 108 = 0. Suppose 19 + k = 2*l + 3*i, 5*l - 40 = 3*i. Suppose 6*f**2 - 15*f**4 - l*f**4 - f**4 + 0*f**2 - 21*f**3 = 0. Calculate f.
-1, 0, 2/9
Let r be (-1)/((-2 - 2) + 165/45). Suppose 5*g - 73*g**r + 137*g**3 - g - 72*g**3 + 4*g**5 = 0. What is g?
-1, 0, 1
Let p(x) = -x**2 - 14*x - 109. Let o be 9/(-15) - 720/(-75). Let d(j) = 3*j**2 + 30*j + 219. Let g(i) = o*p(i) + 4*d(i). Factor g(v).
3*(v - 7)*(v + 5)
Let r = -1/682 + 817/92070. Let q(a) be the second derivative of -r*a**6 + 0 + 1372/27*a**3 - 2401/9*a**2 + 14/45*a**5 - 49/9*a**4 - 18*a. Factor q(m).
-2*(m - 7)**4/9
Let r(h) be the first derivative of h**8/5040 + h**7/2520 + h**3/3 - 9*h**2/2 - 29. Let t(o) be the third derivative of r(o). Factor t(c).
c**3*(c + 1)/3
Solve 0 + 14/5*r + 1/5*r**3 + 9/5*r**2 = 0 for r.
-7, -2, 0
Suppose 2*f = 3*f - 4. Let g be (8 - (-148)/(-16))*72/(-30). What is q in -2*q**4 - 5*q**g + 6*q**f - 8*q**4 + 2*q**2 + 3*q**5 = 0?
-1, 0, 1/3, 2
Factor -2/3 - 29/9*r**2 + 89/9*r.
-(r - 3)*(29*r - 2)/9
Let d(b) be the second derivative of -49/2*b**2 - 7/3*b**3 + 0 - 1/12*b**4 + 5*b. Let d(l) = 0. Calculate l.
-7
Let d(s) be the second derivative of s**4/16 + 245*s**3/8 + 183*s**2/2 + 26*s + 25. Factor d(k).
3*(k + 1)*(k + 244)/4
Let m(s) be the second derivative of s**5/60 + 487*s**4/36 - 983*s**3/6 + 1479*s**2/2 + 12289*s. Factor m(v).
(v - 3)**2*(v + 493)/3
Factor -28 - 1/8*c + 1/8*c**3 + 28*c**2.
(c - 1)*(c + 1)*(c + 224)/8
Factor 8 + 7/2*r**2 + 29*r.
(r + 8)*(7*r + 2)/2
Let r(n) = -n**3 - 4*n**2 + 10*n - 8. Let k be r(-7). Let c = 72 - k. Factor -19*p**3 - 14*p**3 + 9*p**2 + 49*p**3 - 19*p**c.
-3*p**2*(p - 3)
Suppose -151*a + 10 = -146*a. Suppose -35*v**5 - 260*v**3 - 45*v + 250*v**4 - 300*v**3 + 40*v**2 + 350*v**a = 0. Calculate v.
0, 1/7, 1, 3
Let d(k) be the second derivative of -k**7/63 + k**6/45 + k**5/10 - 5*k**4/18 + 2*k**3/9 - k + 30. Let d(w) = 0. What is w?
-2, 0, 1
Determine v, given that 44/9*v + 16/9*v**3 - 62/9*v**2 + 2/9*v**4 + 0 = 0.
-11, 0, 1, 2
Let n(l) = -8*l**4 + 214*l**3 + 2004*l**2 + 2914*l - 15686. Let d(b) = -6*b**4 + 213*b**3 + 2004*b**2 + 2923*b - 15685. Let g(p) = 6*d(p) - 5*n(p). Factor g(a).
4*(a - 2)*(a + 7)**2*(a + 40)
What is i in 2/9*i**2 - 628/9*i + 49298/9 = 0?
157
Determine d, given that -3/7*d**3 - 18 + 9*d**2 - 1/7*d**4 + 67/7*d = 0.
-9, -2, 1, 7
Let f = 112 - 109. Find j such that 5*j**2 - 3*j + 7 + f*j**4 + 5*j**2 - 19*j**2 + 3*j**3 - 1 = 0.
-2, -1, 1
Factor -512095750/11 - 2/11*k**3 - 2419350/11*k - 3810/11*k**2.
-2*(k + 635)**3/11
Suppose -j = -m - 21, -5*j + 4*j - 3*m = -1. Suppose 36 + 166*u - 6*u**2 - 8*u**3 + 42*u**2 + j*u**2 - 246*u = 0. What is u?
1, 9/2
Let w(b) be the second derivative of -19*b - 58/9*b**3 + 0 + 1/18*b**4 + 841/3*b**2. Suppose w(k) = 0. Calculate k.
29
Let w(u) be the third derivative of -u**7/3360 - 13*u**6/480 - 169*u**5/160 + 111*u**4/8 + u**2 - 86*u. Let p(z) be the second derivative of w(z). Factor p(r).
-3*(r + 13)**2/4
Let o(b) = b**3 - 24*b**2 + b - 1. Let p(g) = -10*g**5 - 92*g**4 - 12*g**3 + 1052*g**2 + 26*g - 1010. Let k(j) = -2*o(j) + p(j). Suppose k(z) = 0. What is z?
-6, -1, 1, 14/5
Let q(d) = -7*d**3 - 65*d**2 + 142*d - 130. Let y(h) = -13*h**3 - 130*h**2 + 294*h - 261. Let p(a) = 11*q(a) - 6*y(a). Factor p(z).
(z - 2)*(z - 1)*(z + 68)
Let p(o) = -5*o**2 + o + 3. Suppose 23*h = 26*h - 63. Let i = -19 + h. Let z(u) = u**3 + u + 1. Let r(f) = i*p(f) - 6*z(f). Suppose r(a) = 0. What is a?
-1, -2/3, 0
Suppose -8*y - 13 + 53 = 0. Solve 0 - 3*d**5 + 12*d + 2*d**2 + 6*d**5 - 2*d**y - 7*d**3 - 8 = 0 for d.
-2, 1, 2
Let y(t) be the second derivative of -t**5/20 - 19*t**4/12 - 35*t**3/6 - 17*t**2/2 - 906*t. Let y(x) = 0. What is x?
-17, -1
Let u = 576 - 572. Factor -260*t**u - 780 - 11701 + 53460*t - 19710*t**2 - 4325*t**3 + 166*t**5 - 16679 - 171*t**5.
-5*(t - 1)**2*(t + 18)**3
Let n(p) be the second derivative of -2/3*p**3