243*j. Determine p, given that l(p) = 0.
-5, 39
Let z(l) be the first derivative of 0*l - 1/30*l**4 + 1/15*l**2 + 2/45*l**3 - 210 - 2/75*l**5. Factor z(d).
-2*d*(d - 1)*(d + 1)**2/15
Let u(b) be the first derivative of -b**4/44 + 4*b**3 + 271*b**2/22 - 402*b/11 + 1773. Factor u(s).
-(s - 134)*(s - 1)*(s + 3)/11
Suppose 0 + 128/7*f**3 - 2/7*f**2 - 128/7*f + 2/7*f**4 = 0. What is f?
-64, -1, 0, 1
Let h(z) be the second derivative of 0 + 14*z - 6*z**2 + 1/30*z**5 + 7/3*z**3 - 4/9*z**4. Factor h(j).
2*(j - 3)**2*(j - 2)/3
Factor 1202/3*a**3 + 25*a**4 + 128/3*a + 0 + 4832/3*a**2.
a*(a + 8)**2*(75*a + 2)/3
Let h(n) = 13*n**2 + 6*n + 7. Let c = -70 - -90. Let w(l) = -4 + c*l - 7*l**2 - 14*l - 9*l. Let i(z) = 4*h(z) + 7*w(z). Factor i(k).
3*k*(k + 1)
Factor 7256*r**2 + 3825 + 4*r**4 + 15456*r + 1056*r**3 + 7864 - 2437.
4*(r + 1)*(r + 3)**2*(r + 257)
Suppose 27*g = -6155 - 17524. Let b = g + 1757/2. Factor 1/4*y - b - 1/12*y**3 + 1/3*y**2.
-(y - 3)**2*(y + 2)/12
Let f(r) = 2*r**3 + 61*r**2 + 94*r + 203. Let o be f(-29). Let c(t) be the third derivative of 0*t + o*t**4 - 1/140*t**5 + 0 + 0*t**3 + 13*t**2. Solve c(v) = 0.
0
Let w(j) = j**3 + 8*j**2 - 10*j - 5. Let n be w(-9). Suppose -u + 64 = 2*u + 2*z, -n*z + 56 = 2*u. Factor 3*b**2 + 5*b**4 - 3*b - 20 + 43*b - 10*b**3 - u*b**2.
5*(b - 2)*(b - 1)**2*(b + 2)
Let x(t) be the first derivative of -5*t**6/6 + 101*t**5/4 - 4205*t**4/16 + 3695*t**3/3 - 2510*t**2 + 1040*t - 3909. Find j, given that x(j) = 0.
1/4, 4, 13
Let i(u) be the third derivative of -2*u**7/63 - u**6/15 - u**5/45 - 2091*u**2 - 2*u + 3. Factor i(k).
-4*k**2*(k + 1)*(5*k + 1)/3
Let r(b) = -20*b**3 - 995*b**2 - 4745*b. Let s(d) = 3*d**3 + 141*d**2 + 678*d. Let o(z) = 2*r(z) + 15*s(z). Find v, given that o(v) = 0.
-17, -8, 0
Determine h, given that -2/15*h**5 + 0*h - 492032/5*h**3 + 244047872/15*h**2 + 992/5*h**4 + 0 = 0.
0, 496
Let w(s) be the first derivative of -s**3/18 + 125*s**2/12 + 86*s + 3630. Factor w(p).
-(p - 129)*(p + 4)/6
Let o = -324/1409 - -4875/2818. Find s such that 11/6*s + o*s**2 - 1/6*s**4 + 2/3 + 1/6*s**3 = 0.
-1, 4
Let h = -6 - -8. Suppose l - 5*p = -23, -h*p = -1 - 9. Solve 9*i + 8*i**l - 12*i**2 + i**2 + 0*i**2 = 0.
0, 3
Let y(h) be the second derivative of -h**6/120 - 9*h**5/10 - 2*h**3/3 - h**2/2 + 53*h. Let i(f) be the second derivative of y(f). Find g, given that i(g) = 0.
-36, 0
Let v(m) be the second derivative of m**4/3 - 212*m**3 + 634*m**2 + 228*m. Factor v(h).
4*(h - 317)*(h - 1)
Suppose -32*m - 30 = -34*m. Suppose 12*c = 7*c + m. Factor 6*w**2 + w**c + 9*w - 7*w**2 - 9*w.
w**2*(w - 1)
Suppose -6*s - 9*s = -3045. Factor 3*c**2 - 198*c - 15*c**4 - 4*c**3 + 12*c**2 - c**3 + s*c.
-5*c*(c - 1)*(c + 1)*(3*c + 1)
Solve 2*s**2 - 786*s + 164*s + 23 - 23 = 0.
0, 311
Suppose -6122*h + 6287*h = 330. Factor 40/11 - 48/11*u - 2/11*u**3 + 18/11*u**h.
-2*(u - 5)*(u - 2)**2/11
What is m in 828*m**2 - 116236*m + 1818573*m + 259052664 + 55939*m + 3150*m**2 + 3*m**3 = 0?
-442
Factor -174*w**4 - 1731/5*w**3 + 0*w - 3/5*w**5 - 864/5*w**2 + 0.
-3*w**2*(w + 1)**2*(w + 288)/5
Let p = -116 + 200. Let a be 2*(p/8)/3. Factor 2*d**3 - a*d - 5*d - 16*d**2 + 4*d**3 + 72 - 2*d**3.
4*(d - 3)**2*(d + 2)
Let o = -7018/15 - -1408/3. Let j be (-18)/8*1456/(-273) + -10. Determine y, given that -2/3*y + 0 - o*y**j - 14/15*y**3 - 2/15*y**4 = 0.
-5, -1, 0
Suppose 2*x + 16 = 4*g, 2*x - 7 + 39 = -2*x. Suppose 2*t + 3/2*t**2 + g - 1/2*t**3 = 0. What is t?
-1, 0, 4
Factor -h**2 - 1366 - 299*h - 1367 - 1371 + 4104.
-h*(h + 299)
Suppose -h = -g + 79, 12 = g + h - 65. Factor 40*v - g*v**2 - 82 - 11*v - 191*v + 2*v**3.
2*(v - 41)*(v + 1)**2
Let t be 4*20/(-4) - -23. Determine l so that -3/2*l**2 - l - 1/2*l**t + 0 = 0.
-2, -1, 0
Let y(l) = -24*l**2 + 33*l**3 + 75*l - 16*l**3 + 0 - 6 - 11*l**3. Let t(v) = 5*v**3 - 26*v**2 + 75*v - 4. Let b(n) = -3*t(n) + 2*y(n). Solve b(j) = 0.
0, 5
Let a(d) = -36*d**4 + 284*d**3 - 708*d**2 + 185*d. Let m(k) = -39*k**4 + 285*k**3 - 708*k**2 + 186*k. Let c(w) = -6*a(w) + 5*m(w). Solve c(j) = 0 for j.
0, 2/7, 3, 10
Let b = -34127 - -34129. Let l(r) be the first derivative of 34 + 2/63*r**3 - 4/21*r - 1/21*r**b. Factor l(s).
2*(s - 2)*(s + 1)/21
Let x(h) be the second derivative of 3*h**5/20 - 271*h**4/4 - 136*h**3 - 6*h - 38. Find u, given that x(u) = 0.
-1, 0, 272
Let h(x) be the third derivative of 1/20*x**4 - 2/75*x**6 - 3 + 0*x**3 + 11*x**2 + 17/300*x**5 - 1/150*x**7 + 0*x. Factor h(m).
-m*(m - 1)*(m + 3)*(7*m + 2)/5
Let n = -122 + 79. Let r = n + 46. Find t such that 0*t + 8*t + 5*t**r - 8*t = 0.
0
Let u(m) be the second derivative of -2/105*m**6 - 8/7*m**2 - 13/21*m**4 + 8/7*m**3 + 6/35*m**5 - 62 - m. What is z in u(z) = 0?
1, 2
Let p(c) be the first derivative of 20*c**5 + 0*c**2 + 35/4*c**4 - 12 - 10*c**3 + 0*c. Factor p(t).
5*t**2*(4*t + 3)*(5*t - 2)
Let b = -417747 - -417751. Factor -14/3*u**b + 0 + 0*u + 74/3*u**3 - 20/3*u**2.
-2*u**2*(u - 5)*(7*u - 2)/3
Let u = -1461/2 + 4385/6. Let k(y) be the first derivative of 11 - 5/24*y**4 + 1/10*y**5 + 5/12*y**2 + u*y - 5/18*y**3. Determine p so that k(p) = 0.
-1, -1/3, 1, 2
Let r(h) be the second derivative of h**4/3 - 92*h**3/3 + 1058*h**2 - 976*h. Factor r(c).
4*(c - 23)**2
Let s(b) be the first derivative of -2*b**5/35 - 5*b**4 - 768*b**3/7 + 2592*b**2/7 + 2419. Factor s(d).
-2*d*(d - 2)*(d + 36)**2/7
Let s(f) = -3*f**4 + 27*f**3 - 143*f**2 - 195*f + 706. Let t(x) = -15*x**4 + 129*x**3 - 714*x**2 - 981*x + 3531. Let r(n) = 21*s(n) - 4*t(n). Factor r(l).
-3*(l - 13)*(l - 3)**2*(l + 2)
Let w(o) be the first derivative of -9 + 5/8*o**4 - 3/40*o**5 - 3/4*o**3 - 27/4*o**2 - 5*o. Let l(q) be the first derivative of w(q). Factor l(g).
-3*(g - 3)**2*(g + 1)/2
Let k be -70 + 59 - (-35)/3. Suppose 7*s = 3*s. Factor 0 + s*z + k*z**3 + 8/3*z**2.
2*z**2*(z + 4)/3
Let g(i) be the first derivative of 5*i**6/6 - 26*i**5 + 965*i**4/4 - 520*i**3 + 360*i**2 - 622. Factor g(q).
5*q*(q - 12)**2*(q - 1)**2
Suppose 0*l = 3*l - 6. Let d be (-5 - 130/13)/(-4 + 1). Determine p so that d*p**2 + 9*p**3 - 3*p**5 + 6*p**4 - 6*p**2 + p**l = 0.
-1, 0, 3
Let i(l) be the third derivative of l**6/120 - 33*l**5/40 + 4*l**4 - 25*l**3/3 - 21*l**2. Let x(t) be the first derivative of i(t). Factor x(p).
3*(p - 32)*(p - 1)
Let y be 14*13/(1001/33). Suppose f = -y*q + q - 1, 3*q + f + 1 = 0. Factor 0*j + 3/4*j**3 + q + 3/4*j**2.
3*j**2*(j + 1)/4
Factor 48/5*b - 3/5*b**2 - 9.
-3*(b - 15)*(b - 1)/5
Let l(c) = 2*c**3 - 11*c - 7 + 13326*c**2 - 13316*c**2 + 16. Let b be l(-6). Suppose -4/3*r**b + 8/3*r**2 - 4/3*r**4 - 4/3 + 2/3*r**5 + 2/3*r = 0. What is r?
-1, 1, 2
Let 0 - 654/5*z + 2/5*z**2 = 0. What is z?
0, 327
Suppose 2*f - 5*b = 74, -302*f - 19*b = -300*f + 262. Factor 0*j - 2*j**3 + 2*j**f - 3/2*j**4 + 0.
-j**2*(j + 2)*(3*j - 2)/2
Suppose 598*b = 3794*b + 203 - 203. Factor b*r + 3/5*r**3 + 0 + 78/5*r**2.
3*r**2*(r + 26)/5
Let -3819*f**2 - 8251733668 + 1/2*f**3 + 9723174*f = 0. What is f?
2546
Let s(c) be the first derivative of c**6/90 + c**5 + 75*c**4/2 + 95*c**3/3 - 48. Let d(j) be the third derivative of s(j). Suppose d(k) = 0. What is k?
-15
Let z(u) be the first derivative of -14/9*u**3 + 14/3*u + 33 - 1/3*u**2 + 1/6*u**4. Find b, given that z(b) = 0.
-1, 1, 7
Let h(n) be the second derivative of -200/3*n**3 + 54*n**4 - 83/5*n**5 + 28/15*n**6 - 16*n**2 - 10 - 8*n. Factor h(c).
4*(c - 2)**3*(14*c + 1)
Suppose -362*h - 606 = -564*h. Factor 1/8*r**h + 7/4 - 7/4*r**2 - 1/8*r.
(r - 14)*(r - 1)*(r + 1)/8
Let v(q) be the third derivative of -q**8/1344 - q**7/280 + 37*q**6/480 - 29*q**5/240 - 3*q**4/8 + 4*q**3/3 - 147*q**2. Determine j so that v(j) = 0.
-8, -1, 1, 4
Let -19*t + 15*t**2 + 3*t**3 + 12/5 - 7/5*t**4 = 0. What is t?
-3, 1/7, 1, 4
Let m(s) be the first derivative of 0*s - 1/3*s**6 + 2*s**4 - 6/5*s**5 - 33 + 0*s**3 + 0*s**2. Solve m(f) = 0.
-4, 0, 1
Suppose -124/9*w**2 - 320/9*w - 2/9*w**3 + 6400 = 0. What is w?
-40, 18
Let z = 372 + 235. Let b = z - 604. Factor -2/7*g**b + 4/7*g**2 - 16/7 + 8/7*g.
-2*(g - 2)**2*(g + 2)/7
Let b be 317/21 + (-2115)/4935. What is j in 16/3*j**2 - 56/3*j**3 + b*j**4 + 0 + 0*j - 10/3*j**5 = 0?
0, 2/5, 2
Solve 684*w**3 + 60*w**4 + 634*w - 4*w**5 - 1532*w**2 + 391*w - 233*w = 0 for w.
-9, 0, 1, 22
Let k(x) be the third derivative of -x**5/120 + 1187*x**4/24 - 1408969*x**