 given that g(m) = 0.
-1, 0, 1
Let i be (-18)/(-27) + 30/(-45). Let p(m) be the first derivative of 2/3*m**3 - 24 + m**4 + 2/5*m**5 + i*m + 0*m**2. Factor p(x).
2*x**2*(x + 1)**2
Let j be -2 - ((-612)/15)/17. Let f(d) be the second derivative of 0 - j*d**2 - 2/15*d**3 - d - 1/60*d**4. Factor f(m).
-(m + 2)**2/5
Let o(h) be the first derivative of 2*h**3/33 + 63*h**2/11 + 277. Suppose o(i) = 0. Calculate i.
-63, 0
Let f(u) = -2*u**3 + 5*u**2 - 5*u - 3. Suppose 8*i + 286 = -3*i. Let w(o) = -9*o**3 + 21*o**2 - 20*o - 11. Let g(k) = i*f(k) + 6*w(k). Factor g(x).
-2*(x - 2)*(x + 1)*(x + 3)
Factor -2784/7 - 3/7*a**2 + 2787/7*a.
-3*(a - 928)*(a - 1)/7
Let l = 259 - 247. Factor -l*u**3 - 55*u**2 + 7*u**2 + 144*u + 64 - 8*u**3.
-4*(u - 2)*(u + 4)*(5*u + 2)
Let k(z) be the second derivative of -z**5/4 + 20*z**4/3 - 245*z**3/6 - 165*z**2 - 18*z - 27. Find v, given that k(v) = 0.
-1, 6, 11
Let d = -1143 - -1066. Let a be d/(-9) + (-525)/75. Solve -2/9*t**3 + 0 - 4/3*t**2 + a*t = 0.
-7, 0, 1
Let l be (3 - -132) + (1 + 2 - 8). Let g be 6/5 - (-104)/l. Factor 2/7*c**g + 1/7*c**5 + 8/7*c**3 + 4/7 - 6/7*c**4 - 9/7*c.
(c - 4)*(c - 1)**3*(c + 1)/7
Let b(z) be the first derivative of -z**3 - 105*z**2 - 408*z - 1082. Let b(l) = 0. Calculate l.
-68, -2
Let x = -739 - -760. Factor x*f + 46 - 10 + 30*f**2 - 27*f**2.
3*(f + 3)*(f + 4)
Let q(a) be the third derivative of -1/24*a**4 - 2/21*a**3 - 1/210*a**5 + 1/840*a**6 - 60*a**2 + 0*a + 0. Factor q(h).
(h - 4)*(h + 1)**2/7
Let s = -74 + 89. Suppose -31 + 1 = -s*f. Factor -1/5*p**f + 4/5*p + 1.
-(p - 5)*(p + 1)/5
Let f(l) be the third derivative of -l**7/140 - 7*l**6/40 - 6*l**5/5 - 268*l**2 + 3*l. Determine p so that f(p) = 0.
-8, -6, 0
Let c(p) = -17*p**2 + 81*p - 50. Let a(q) = 8*q**2 - 40*q + 26. Let v be (-2 - (3 - 2))*-1. Let u(h) = v*c(h) + 7*a(h). Factor u(m).
(m - 1)*(5*m - 32)
Factor -844*h + 124*h**3 - 183 + 115 + 40 + 748*h**2.
4*(h - 1)*(h + 7)*(31*h + 1)
Let y(w) be the third derivative of w**8/420 + w**7/210 + 34*w**3/3 + 101*w**2. Let z(q) be the first derivative of y(q). Factor z(h).
4*h**3*(h + 1)
Let k = 180 + -172. Factor -k*d**3 + 2 - 2 + 3*d**3 - 10*d**2.
-5*d**2*(d + 2)
Let n(k) be the third derivative of -31*k**6/40 - 49*k**5/10 - 77*k**4/8 - 5*k**3 - 3304*k**2. Factor n(u).
-3*(u + 1)*(u + 2)*(31*u + 5)
Suppose 109 = -2*h + 121. Suppose 0 = h*c - 364 + 340. Factor 5/4*r**2 + 5/4*r**3 + 0 + 0*r - 5/4*r**c - 5/4*r**5.
-5*r**2*(r - 1)*(r + 1)**2/4
Let o = 278403/5 + -55679. Determine j so that -2/5*j**5 + 28/5*j**2 + 0 - 6*j**3 + 13/5*j**4 - o*j = 0.
0, 1/2, 2
Factor 0*t**5 - 24*t**4 + 34*t**3 + t**5 - 3*t**5 - 36*t + 6*t**5 - 2*t**3 + 24*t**2.
4*t*(t - 3)**2*(t - 1)*(t + 1)
Let c(y) = 5*y**2 - 452*y - 1389. Let o(j) = 5*j**2 - 454*j - 1393. Let w(t) = 7*c(t) - 6*o(t). Factor w(h).
5*(h - 91)*(h + 3)
Let z be 25/(2*(4 + (-103)/26)). Let y = -325 + z. Determine p, given that 0*p**2 + 0*p + 4/17*p**5 - 2/17*p**4 + y - 2/17*p**3 = 0.
-1/2, 0, 1
Let a = -8 + 13. Factor 3*b - 24 - 6*b**2 + 32 - 2*b**4 + a*b - 8*b**3.
-2*(b - 1)*(b + 1)*(b + 2)**2
Suppose -42 = -4*j - 6. Suppose n = -j*n. Factor 24 + n*c + 2*c + 2*c**3 - 18*c - 2*c**2.
2*(c - 2)**2*(c + 3)
Suppose c = 5*h - 14, -5*c + 8 = -18*h + 19*h. Factor -2*d**4 + 13*d**4 - 16*d**2 + 8*d**3 + 4*d**h - d**4.
2*d**2*(d + 2)*(5*d - 4)
Let r be -1*(6 + -14 + 5). Solve -13580*i + 13580*i - 4*i**3 + 3*i**4 + i**r = 0.
0, 1
Let q(p) be the third derivative of p**5/20 + 44*p**4 + 15488*p**3 - 47*p**2 + 20. Factor q(m).
3*(m + 176)**2
Let k(q) be the third derivative of q**8/112 - 11*q**7/70 + 23*q**6/40 + 11*q**5/20 - 3*q**4 - 14*q**2 + 23*q. Suppose k(b) = 0. Calculate b.
-1, 0, 1, 3, 8
Let q(r) be the second derivative of 5/4*r**4 + 1/4*r**5 - 5/6*r**3 - 15/2*r**2 + 7*r - 5. Factor q(d).
5*(d - 1)*(d + 1)*(d + 3)
Factor -1/4*w**2 - 377/4*w - 465.
-(w + 5)*(w + 372)/4
Factor 118*j**3 + 455*j**2 - 189*j**3 + 1127844 + 568170*j + 73*j**3 + 1673*j**2.
2*(j + 2)*(j + 531)**2
Let f(t) be the second derivative of t**6/1440 - t**5/24 - 7*t**4/32 + t**3/3 + 2*t**2 - 14*t. Let g(l) be the second derivative of f(l). What is s in g(s) = 0?
-1, 21
Let b(m) be the second derivative of 0 - 1/60*m**6 + 79*m + 0*m**2 + 1/20*m**5 + 1/3*m**3 + 7/24*m**4. Determine c, given that b(c) = 0.
-1, 0, 4
Suppose 41*s = 80*s + 49*s - 528. Let o(a) be the first derivative of -3/4*a**4 + 1/6*a**s - 1/5*a**5 + a**2 - 6 + 1/3*a**3 + 0*a. Let o(x) = 0. What is x?
-1, 0, 1, 2
Suppose 2*j + 2*j + t = 171, t = 4*j - 165. Solve 18*b**2 - 2077*b**4 + 2080*b**4 - 21*b**3 - j*b**2 = 0.
-1, 0, 8
Let s(w) be the third derivative of -w**6/150 - 439*w**5/300 + 277*w**4/60 - 37*w**3/10 + w**2 + 629*w - 4. Factor s(q).
-(q - 1)*(q + 111)*(4*q - 1)/5
Suppose 3*j - 343 = 29*j - 395. Let t(r) be the first derivative of -5/2*r**j - 30*r + 50 + 5/3*r**3. What is n in t(n) = 0?
-2, 3
Let j = -130947 + 130949. Let f be (-2)/4*(1 + -4). Determine b so that -1/2*b**j - 3/2*b**4 + 1/2*b**5 + 0*b + f*b**3 + 0 = 0.
0, 1
Let q(b) be the first derivative of b**4/26 + 418*b**3/39 - 1720*b**2/13 + 6944*b/13 + 7131. Factor q(z).
2*(z - 4)**2*(z + 217)/13
Suppose 49*w - 76*w = -54. Let j(v) be the first derivative of -13 + 1/4*v**4 + 1/5*v**5 + 0*v - 1/2*v**w - 1/3*v**3. Let j(z) = 0. What is z?
-1, 0, 1
Let g be -24 - ((-4148)/51)/((-210)/(-63)). Factor g*u**3 - 6*u**2 + 0 + 0*u.
2*u**2*(u - 15)/5
Let u(n) = -19*n**2 - 5*n + 4. Let j be u(1). Let w(z) = z + 25. Let b be w(j). Solve -15*o - 53*o**2 + b*o + 58*o**2 - 15 = 0.
-1, 3
Let x(i) = i**2 - 89*i + 72. Let r(n) = n**2 + n - 6. Suppose 517*w - 1 = 516*w. Let y(t) = w*x(t) - 4*r(t). Solve y(u) = 0.
-32, 1
Let a(u) be the third derivative of -u**10/453600 + u**8/60480 + u**5/30 - 5*u**4/4 + 64*u**2. Let h(w) be the third derivative of a(w). Factor h(i).
-i**2*(i - 1)*(i + 1)/3
Suppose 0 = -5*p + 10*p - 3*b + 2707, 3*p - 4*b + 1633 = 0. Let k = p - -542. Determine m so that 68/7*m**2 + 16/7 - 16/7*m**k - 80/7*m = 0.
1/4, 2
Suppose 2*x - k - 9 = 0, 5*x - 15 = -4*k + 1. Solve 144*j**2 + 192*j + 1 + 6*j**5 + 21*j**5 - 156*j**3 - 49 - 32*j**x - j**4 = 0.
-2, -1, 2/9, 2
Let s = 219 + -196. Factor 5*g**3 - s*g**4 - 12*g**2 + 3*g**3 - 8*g + 35*g**4.
4*g*(g - 1)*(g + 1)*(3*g + 2)
Suppose 28*a**2 - 424*a**3 + 8 + 2 + 423*a**3 - 10 = 0. Calculate a.
0, 28
Let s(v) = -14*v**3 - 66*v**2 - 4*v + 3. Let r(f) = -14*f**3 - 64*f**2 - 8*f + 2. Let c(k) = 6*r(k) - 4*s(k). Factor c(o).
-4*o*(o + 4)*(7*o + 2)
Let d = -113 + 118. Suppose -1535*x**2 + 3096*x**2 - 1541*x**2 - d*x**3 - 15*x = 0. What is x?
0, 1, 3
Let p(m) = m**3 + 15*m**2 - 10*m. Let f(s) be the first derivative of s**4/2 + 5*s**3 - 5*s**2 + 291. Let z(k) = 6*f(k) - 7*p(k). Find w, given that z(w) = 0.
0, 1, 2
Suppose -571 = -3*i - 187. Suppose -16*h**5 - 22*h**2 - 8*h + 65*h**3 + i*h**4 - 11*h**3 - 76*h**4 = 0. What is h?
-1, -1/4, 0, 1/2, 4
Let x(n) be the second derivative of n**5/4 + 5*n**4/2 - 125*n**3/6 + 45*n**2 - 313*n + 3. Factor x(t).
5*(t - 2)*(t - 1)*(t + 9)
Suppose 140 = -6*a + 140. Suppose 0 = 4*v + 4, a = -3*d + 5*v + 5. Determine t, given that 0 + d*t**2 + 1/6*t**3 + 0*t = 0.
0
Suppose -21 = -3*i + 2*b, -21 - 15 = -5*i + 3*b. Suppose -i*o + 5*o = -20. Factor 0*c**2 + c**o + c**3 + 3*c**4 + 4 - 7*c**2 - 2*c**3.
(c - 1)**2*(c + 1)*(c + 2)**2
Let y(j) be the second derivative of -3*j**8/560 - j**7/280 + j**6/60 + j**3/2 + 13*j**2/2 + j - 25. Let r(x) be the second derivative of y(x). Factor r(d).
-3*d**2*(d + 1)*(3*d - 2)
Let w(s) be the third derivative of -1/12*s**5 + 1/2688*s**8 + 0 + 0*s + 11/320*s**6 + 1/12*s**4 - 56*s**2 - 1/168*s**7 + 0*s**3. What is u in w(u) = 0?
0, 1, 4
Let o(g) = 2*g**2 - 2827*g - 19882. Let d be o(-7). Factor -d*r + 1/5*r**2 - 26/5.
(r - 26)*(r + 1)/5
Let b(a) = 5*a**3 + 49*a**2 - 52*a - 602. Let c(n) = 5*n**3 + 56*n**2 - 43*n - 603. Let v(d) = 3*b(d) - 2*c(d). Factor v(p).
5*(p - 4)*(p + 5)*(p + 6)
Suppose 5*d - 20 = s, s - 5*s = -20. Suppose 5*g - 4*v = 23, -3*g + d*g - 5*v = 16. Factor -7*j + 5*j - 130*j**2 - 4*j + 151*j**2 - 15*j**g.
-3*j*(j - 1)*(5*j - 2)
Solve -2/3*l**3 + 232/3*l**2 - 468 + 82*l = 0 for l.
-3, 2, 117
Let i be 6/1 + 874/(-161). Let b(d) be the first derivative of -11 + 2/21*d**3 + i*d**2 + 0*d. Solve b(y) = 0 for y.
-4, 0
What is d in 8495*d + 5*d**4 + 13