p**2*(p + 1)**2*(p + 2)
Let i(b) = -18*b**2 + 6 - 62*b**3 - 18*b**2 - 20*b**4 - 27*b + 21*b + 2. Let f(l) = -l**3 - l. Let q(h) = -10*f(h) + i(h). Let q(d) = 0. What is d?
-1, 2/5
Let q be -2 + 1 + 3 - -4. Suppose -4*j + q*j - 14 = 0. Factor 0*s**4 - s**5 + 2*s**4 + 7*s**2 - j*s**2.
-s**4*(s - 2)
Let a(z) be the first derivative of -9*z**4/8 + 13*z**3/2 + 29*z**2/4 + 5*z/2 + 4. Suppose a(o) = 0. Calculate o.
-1/3, 5
Suppose -s + 6*s = -g + 1, 2*s - 4*g - 18 = 0. Suppose -u = -1 - s. Factor -4*c**2 + 3*c**u + 5*c**2.
4*c**2
Let c(w) be the third derivative of w**6/1200 - w**5/300 - w**4/80 - 7*w**2. Factor c(s).
s*(s - 3)*(s + 1)/10
Let -12/5*z + 12/5 + 3/5*z**3 - 3/5*z**2 = 0. What is z?
-2, 1, 2
Find j, given that j - 5/2*j**3 + 3/2*j**2 + 0 = 0.
-2/5, 0, 1
Suppose r - 3*j = 6, 0 = 2*r + j - 4 + 6. Factor -245*t**2 + 2*t**4 - 4*t + r*t**3 + 243*t**2 + 4*t**3.
2*t*(t - 1)*(t + 1)*(t + 2)
Let r(z) = 3*z**3 - 76*z**2 + 596*z - 8. Let c(n) = -n**3 + 25*n**2 - 199*n + 3. Let v(m) = -8*c(m) - 3*r(m). Factor v(o).
-o*(o - 14)**2
Suppose b + 0*k = -5*k, -2*b + 12 = -2*k. Factor 2/17*p**4 - 2/17*p**3 + 2/17*p**b + 0*p - 2/17*p**2 + 0.
2*p**2*(p - 1)*(p + 1)**2/17
Let v(l) be the second derivative of 0 - 1/30*l**5 + 2*l + 1/6*l**4 + 0*l**3 + 5/2*l**2. Let g(r) be the first derivative of v(r). Find i, given that g(i) = 0.
0, 2
Let f(s) = 100*s. Let u be f(1). Determine h, given that 2*h**2 + 358*h - h**2 - 338*h + u = 0.
-10
Let z(s) be the first derivative of s**7/525 + s**6/150 - s**5/150 - s**4/30 - 7*s**2/2 + 2. Let x(f) be the second derivative of z(f). Factor x(o).
2*o*(o - 1)*(o + 1)*(o + 2)/5
Let n be 888/660 + 6/(-11). Suppose n*j + 0 - 2/5*j**2 = 0. What is j?
0, 2
Let w(h) = h**3 + 7*h**2 + h + 9. Let g be w(-7). Let a(d) be the first derivative of 3/2*d + 2*d**3 - 5 - 15/4*d**g. Solve a(l) = 0.
1/4, 1
Let t(p) = 2 - p + 0 - p**3 - 1. Let x(i) = 5*i**3 + 2*i**2 + 5*i - 6. Let a(w) = 6*t(w) + x(w). Find o, given that a(o) = 0.
0, 1
Suppose 0 = 5*r + 2*y + y - 37, -5*r + 41 = -y. Suppose r*d = 3*d + 20. Factor 0*p - 2/3*p**3 + 0 + 0*p**2 - 2/3*p**5 - 4/3*p**d.
-2*p**3*(p + 1)**2/3
Suppose 0 = -3*k + 2*r + 17, 0 = 2*r - 8 + 16. Let o(f) be the first derivative of 5 + 1/36*f**6 - 1/9*f**k - 1/24*f**4 + 0*f**2 + 0*f + 1/15*f**5. Factor o(x).
x**2*(x - 1)*(x + 1)*(x + 2)/6
Let a(w) = -3*w**3 - 12*w**2 + 9*w + 6. Let g(d) = -3*d**2 + 4*d**2 + 14 - 15. Let y(o) = -a(o) - 12*g(o). What is t in y(t) = 0?
-2, 1
Find p such that -92/9*p - 64/3 + 2/9*p**2 = 0.
-2, 48
Let q(o) be the third derivative of o**8/47040 - o**7/5880 - 11*o**5/60 - 8*o**2. Let v(j) be the third derivative of q(j). Factor v(g).
3*g*(g - 2)/7
Let d = 12 + -25. Let c be d/(-20) + (-30)/120. Find y such that -c*y**2 + 2/5*y + 4/5 = 0.
-1, 2
Let w(f) = -17*f**3 + 117*f**2 + 350*f + 100. Let o(k) = k**3 - k**2 - 5*k. Let b(r) = 2*o(r) + w(r). Factor b(t).
-5*(t - 10)*(t + 2)*(3*t + 1)
Factor 2/15*u**2 + 0 - 4/15*u.
2*u*(u - 2)/15
Suppose 4 + 20 = 6*t. Determine l, given that 3*l**t - 17*l**3 + 8*l**3 - 2*l**4 - 4*l**4 - 6*l**2 = 0.
-2, -1, 0
Let y be (2/(-36))/((-774)/567 - 200/(-175)). Let u be ((-3)/16)/((-1)/4). Factor y + p + u*p**2.
(p + 1)*(3*p + 1)/4
Suppose 2*s + 7*g - 2*g = 2, 5 = 5*s - g. Let c(o) be the first derivative of s + 0*o**2 + 9/5*o**5 + 0*o + 12/7*o**4 + 9/14*o**6 + 4/7*o**3. Factor c(h).
3*h**2*(h + 1)*(3*h + 2)**2/7
Let u(c) be the third derivative of 0 + 0*c - 1/150*c**6 + 0*c**7 + 1/60*c**4 + 0*c**5 + 0*c**3 + 23*c**2 + 1/840*c**8. Factor u(y).
2*y*(y - 1)**2*(y + 1)**2/5
Suppose 16/3*k**2 + 4/3*k**3 - 116/3*k + 32 = 0. What is k?
-8, 1, 3
Determine j so that 1/2*j**3 + 5043/2*j + 123/2*j**2 + 68921/2 = 0.
-41
Let y(s) be the third derivative of 0*s**4 + 0*s + 0 - 1/24*s**6 + 0*s**3 + 1/6*s**5 - 1/42*s**7 - 13*s**2. Factor y(v).
-5*v**2*(v - 1)*(v + 2)
Let l(q) be the first derivative of 4*q**5/5 - 5*q**4 - 4*q**3/3 + 10*q**2 - 77. Find v, given that l(v) = 0.
-1, 0, 1, 5
Let o(r) = -2*r**3 + 8*r**2 + 8*r + 14. Let c be o(5). Let l be (-33)/(-36) + (-4)/6. Factor 0*h**c + 0 + 0*h**2 - 1/4*h**3 + 0*h + l*h**5.
h**3*(h - 1)*(h + 1)/4
Let b(s) = -26*s - 232. Let q be b(-9). Let -11/2*p + 1/2 + 121/8*p**q = 0. What is p?
2/11
Let m = 7548/95 + -894/19. Let j be ((-48)/(-10))/(1/3). Determine g so that -8/5 - m*g**2 - j*g = 0.
-2/9
What is g in 6/7*g**2 - 72*g + 1512 = 0?
42
Let c(j) be the second derivative of 2*j**7/7 - 3*j**6/10 - 39*j**5/20 + 17*j**4/4 - 3*j**3/2 - 3*j**2 - 19*j + 15. Factor c(p).
3*(p - 1)**3*(p + 2)*(4*p + 1)
Let q(v) be the third derivative of -1/150*v**5 + 0*v - 23*v**2 - 1/20*v**4 + 0 + 4/15*v**3. Let q(x) = 0. What is x?
-4, 1
Let z(j) = j**2 - 4*j - 7. Let b be z(5). Let s be 22/44 - b/(-4). Determine l, given that 2/3*l**2 + s*l + 0 - 4/3*l**3 = 0.
0, 1/2
Let o(s) be the first derivative of 3*s**4/4 + 18*s**3 + 315*s**2/2 + 600*s + 199. Factor o(b).
3*(b + 5)**2*(b + 8)
Suppose -5*q + 40 = -5*k, q + 1 = -2*k - 3. Let i be ((-27)/(-18))/((-3)/k). Suppose -4 + 0*x**2 + 6*x**2 - 2*x**3 - i + 2*x = 0. What is x?
-1, 1, 3
Let v(u) be the second derivative of 0*u**2 + 0*u**3 - 9/80*u**5 - 1/8*u**4 - 1/40*u**6 + 2*u + 0. Factor v(i).
-3*i**2*(i + 1)*(i + 2)/4
Suppose 4*z = 3*x - x, z = 2*x. Find r, given that -3/4*r + 1/8*r**2 + x = 0.
0, 6
Factor -24*o + 1/4*o**3 - 7/2*o**2 + 360.
(o - 12)**2*(o + 10)/4
Let -19/8 - 9/4*t + 1/8*t**2 = 0. What is t?
-1, 19
Let f(t) be the first derivative of t**6/8 + 27*t**5/8 + 45*t**4/8 - 65*t**3/8 - 63*t**2/8 - 547. Solve f(a) = 0.
-21, -2, -1/2, 0, 1
Let k = 41 - 9. Let c = k + -24. Factor 5*b**3 - 8*b**3 + c*b**3.
5*b**3
Let c(l) be the first derivative of 1/14*l**4 - 1/7*l**2 + 4/7*l - 2/7*l**3 - 3 + 2/35*l**5. Suppose c(q) = 0. Calculate q.
-2, -1, 1
Factor -5*s**3 - 10*s + 25/2*s**2 + 5/2.
-5*(s - 1)**2*(2*s - 1)/2
Suppose 5*r = 2*v + 14*r - 5*r, 0 = -4*v - 2*r. Factor -3*p**3 + 0*p**2 - 3/2*p**4 + v + 0*p.
-3*p**3*(p + 2)/2
Suppose 4*j + 3*k = 6, -3*j = 17*k - 19*k - 13. Let d(x) be the first derivative of -16/9*x + 4/3*x**2 - 8 + 1/18*x**4 - 4/9*x**j. What is a in d(a) = 0?
2
Let z(f) = 2*f - 4. Let o be z(6). Suppose -3*k + o = -k. Factor k*n**2 + 10*n**3 + 7*n**4 - 2*n**4 + n**2.
5*n**2*(n + 1)**2
Let v = -32 - -161/5. Let r = 10186/50855 - 3/10171. Factor 0*h + 0 + v*h**3 + 0*h**2 + r*h**4.
h**3*(h + 1)/5
Let s(b) = b**2 + 4*b - 4. Let l = 21 - 18. Let f(i) = 4 - 11 + l*i + 4. Let k(p) = 4*f(p) - 3*s(p). Factor k(x).
-3*x**2
Let k(f) be the first derivative of -f**4/18 - 2*f**3/9 - 31*f + 7. Let z(o) be the first derivative of k(o). Let z(l) = 0. Calculate l.
-2, 0
Let l(c) be the third derivative of c**10/30240 - c**9/12096 + 4*c**5/15 - 2*c**2. Let q(p) be the third derivative of l(p). Suppose q(s) = 0. Calculate s.
0, 1
Determine u, given that 168*u - 87/4*u**2 - 147 + 3/4*u**3 = 0.
1, 14
Let s(x) be the third derivative of -x**7/1155 + 2*x**5/165 - 7*x**2 - 4. Let s(d) = 0. What is d?
-2, 0, 2
Let u(o) be the first derivative of 2*o**3/21 + o**2/7 - 12*o + 329. Determine p so that u(p) = 0.
-7, 6
Let n(k) be the second derivative of -14*k**6/5 + 19*k**5/10 - k**4/3 + 2*k + 10. Let n(x) = 0. What is x?
0, 1/6, 2/7
Find w such that -129*w**3 + 52*w**4 - 24*w**4 - 55*w**4 + 30*w**2 = 0.
-5, 0, 2/9
Let b(v) be the third derivative of v**6/120 + v**5/15 - 5*v**4/24 - 50*v**2. Factor b(q).
q*(q - 1)*(q + 5)
Suppose -20 = -3*q + 4*t + t, -4*t + 21 = 5*q. Find o, given that 4*o**q - 2*o**2 - 5*o**5 - o**3 + 4*o**3 = 0.
-2, 0, 1
Let b(j) be the first derivative of -6*j**5/25 + 3*j**4/4 - j**3/5 - 3*j**2/5 - 472. Suppose b(v) = 0. Calculate v.
-1/2, 0, 1, 2
Suppose 5*b - 5 = -5*q, -b + 1 = -q - 0*b. Suppose q*y + y = 2. Factor -2*o**5 + 4*o**5 - 2*o**3 - 2*o**2 + y*o**4 - o + o.
2*o**2*(o - 1)*(o + 1)**2
Factor 232/7*y + 228/7 + 4/7*y**2.
4*(y + 1)*(y + 57)/7
Let n(m) be the third derivative of m**8/1680 - m**7/168 + m**6/45 - m**5/30 - 3*m**3 + 13*m**2. Let t(r) be the first derivative of n(r). Factor t(o).
o*(o - 2)**2*(o - 1)
Let y(c) be the first derivative of 405*c**4 - 588*c**3 + 368*c**2/5 - 16*c/5 + 95. Solve y(a) = 0.
2/45, 1
Suppose 0*d**4 - 1947*d**2 + d**3 + 1955*d**2 + d**4 - 9 - 11*d**3 + 10*d = 0. What is d?
-1, 1, 9
Let c(x) be the third derivative of -x**8/7 + 16*x**7/35 + x**6/40 - x