r -2/7*a**5 - 2/7*a**2 + 2/7*a**3 + 0 + 2/7*a**q + 0*a.
-2*a**2*(a - 1)**2*(a + 1)/7
Let g(o) be the first derivative of 3*o**5/5 - 9*o**4 - 12*o**3 + 240*o**2 - 576*o - 881. Factor g(v).
3*(v - 12)*(v - 2)**2*(v + 4)
Let m(v) be the second derivative of 95*v - 1/22*v**4 + 0 - 3/11*v**3 - 5/11*v**2 + 1/110*v**5. Determine a so that m(a) = 0.
-1, 5
Let p = -4193 - -4193. Let v(g) be the second derivative of 4*g**2 + p + 7*g - 11/3*g**4 + 6*g**3. Find j, given that v(j) = 0.
-2/11, 1
Factor 3*k**2 - 2067 + 490 - 1965*k + 208 - 599.
3*(k - 656)*(k + 1)
Suppose 41*w = -3*y - 35, 294*y + 2 = 297*y + 4*w. Determine c so that 0*c + 0 + 44/15*c**y - 2/15*c**3 = 0.
0, 22
Let q = 51/149 + -891/5215. Let f(a) be the first derivative of 0*a + 23 + 1/21*a**6 - q*a**5 + 1/7*a**4 + 0*a**2 + 0*a**3. Factor f(g).
2*g**3*(g - 2)*(g - 1)/7
Suppose 2*c = -0*f + 5*f - 245, 4*c + 147 = 3*f. Let i be -1 + 70/f*1. Factor -15/7*q**3 + 27/7*q - 9/7*q**2 + 0 - i*q**4.
-3*q*(q - 1)*(q + 3)**2/7
Let i(r) = -17*r**2 + 7194*r + 7175. Let q(n) = 56*n**2 - 21585*n - 21524. Let j(a) = 13*i(a) + 4*q(a). Factor j(b).
3*(b + 1)*(b + 2393)
What is z in -1/4*z**4 + 29/4*z**3 + 3/4*z**2 + 29/2 - 89/4*z = 0?
-2, 1, 29
Let d = -383322 + 383325. Factor -1/3*m**d + 2/3*m**4 + m - 4/3*m**2 + 0.
m*(m - 1)**2*(2*m + 3)/3
Let v(w) be the second derivative of w**6/120 - 13*w**5/160 - 29*w**4/32 - 8*w**3/3 - 11*w**2/4 - 3644*w. Let v(c) = 0. What is c?
-2, -1/2, 11
Suppose -20*c + 25*c = 5*o - 40, -5*o - 3*c = -16. Let p(r) be the first derivative of 0*r + 0*r**2 + 8 - 1/7*r**4 - 2/35*r**o - 2/21*r**3. Factor p(s).
-2*s**2*(s + 1)**2/7
Let g(o) = 12*o**3 + 54*o**2 + 58*o + 4. Let p(k) = -31*k**3 - 107*k**2 - 116*k - 10. Let y(v) = 5*g(v) + 2*p(v). Factor y(q).
-2*q*(q - 29)*(q + 1)
Let s = -110 + 117. Suppose 6*u = s*u - 3. What is i in -4*i + 5*i**u - 5*i**3 + i**3 = 0?
-2, 0, 2
Suppose -27*r = -30*r + 30. Let x be (28/r)/((-84)/(-120)). Factor 32/7 - 2/7*o**5 - 64/7*o**3 - 96/7*o + 16*o**2 + 18/7*o**x.
-2*(o - 2)**4*(o - 1)/7
Let a be 336/(-252) + (-8)/(-18)*3. Let z(r) be the third derivative of 43*r**2 + a*r - 1/30*r**6 + 4/3*r**3 + 1/6*r**4 - 2/15*r**5 + 0. Factor z(m).
-4*(m - 1)*(m + 1)*(m + 2)
Factor -160*s**2 + 1739*s**3 + 1751*s**3 + 2*s**4 - 5241*s**3 + 1675*s**3.
2*s**2*(s - 40)*(s + 2)
Let o(u) be the second derivative of -u**4/78 - 2*u**3/3 + 315*u**2/13 - 3*u + 166. Factor o(j).
-2*(j - 9)*(j + 35)/13
Solve -24*j**3 + 740*j + 372*j**2 + 120 + 35*j**3 + 44*j**3 + 78*j**2 = 0.
-6, -2, -2/11
Suppose -8 = -10*a + 2. Let x be (10/(-20))/(a/(-24)). Factor -7*d - 66 - 5*d + x*d**2 - 4*d**3 + 70.
-4*(d - 1)**3
Let f(y) be the third derivative of 0*y**3 - 17/450*y**5 + 0 + 1/90*y**4 + 1/210*y**8 + 4*y**2 - 43/1575*y**7 + 23/450*y**6 + 23*y. Find b such that f(b) = 0.
0, 1/4, 1/3, 1, 2
Let o(z) = -25*z**3 - 25*z**2 + 256*z - 338. Let b(a) = 14 - 20*a - 15*a + 6*a**3 + 4 - 29*a + 66 + 6*a**2. Let x(g) = -9*b(g) - 2*o(g). Factor x(m).
-4*(m - 2)**2*(m + 5)
Find b, given that -45/2 - 3/8*b**2 - 12*b = 0.
-30, -2
Suppose 157*w = -153*w + 788 + 1072. Let r(l) be the first derivative of 4/33*l**3 - 2/55*l**5 - 1/11*l**4 + 1/11*l**2 + 7 + 1/33*l**w - 2/11*l. Solve r(k) = 0.
-1, 1
Let r(w) be the third derivative of w**7/735 + 34*w**6/105 - 137*w**5/210 + 3*w**2 + 723. Factor r(d).
2*d**2*(d - 1)*(d + 137)/7
Suppose 5*d = 4*s + 12, 0*s - 3*d + 2 = -5*s. Let r(a) be the second derivative of -2/3*a**3 - 1/20*a**5 - 1/3*a**4 + 0 + 0*a**s + 14*a. What is p in r(p) = 0?
-2, 0
Suppose 5*o = 3*z + 5, -5*z - 994 = -2*o - 1011. Find h, given that -1/6*h + 1/6*h**2 - 1/6*h**o + 0 + 1/6*h**3 = 0.
-1, 0, 1
Let g = 8471 - 50825/6. Let n(s) be the second derivative of 0 - 1/5*s**5 - 4*s**2 + g*s**4 - 14*s + 8/3*s**3. Factor n(b).
-2*(b - 2)*(b + 2)*(2*b - 1)
Let p(b) be the first derivative of 2*b**5/25 + 58*b**4/5 + 2392*b**3/5 + 12992*b**2/5 + 25088*b/5 + 1443. Factor p(v).
2*(v + 2)**2*(v + 56)**2/5
Suppose 0 = -r - 48 + 27. Let b be ((-4)/(-14) - 246/r)/2. Factor -20*y + b*y**2 + 30*y + 25*y - y**2.
5*y*(y + 7)
Factor 692/5*v + 4494/5*v**2 - 26/5*v**3 + 0.
-2*v*(v - 173)*(13*v + 2)/5
Let u be -12*-1*(-4)/(-4). Let t = -9 + u. Factor -11*k + 32*k**2 + 2*k**t + k - 17*k**2 - 7*k**3.
-5*k*(k - 2)*(k - 1)
Let u = -2315 - -2315. Let c(s) be the third derivative of u + 0*s + 1/210*s**5 - 3*s**2 + 1/21*s**4 + 1/7*s**3. Factor c(i).
2*(i + 1)*(i + 3)/7
Let k(h) = -5*h**2 + 295*h. Let l(z) = z**2 + 18*z. Let t(g) = -5*k(g) - 20*l(g). Find b, given that t(b) = 0.
0, 367
Let n = -5687 + 5690. Let u(a) be the first derivative of 0*a + 1 + 8/65*a**5 + 8/39*a**n + 3/13*a**4 + 1/39*a**6 + 1/13*a**2. Factor u(i).
2*i*(i + 1)**4/13
Let b(t) be the second derivative of -7*t**6/540 + 11*t**5/135 - 69*t**2/2 + 105*t. Let d(u) be the first derivative of b(u). Find g such that d(g) = 0.
0, 22/7
Let c = 38 + -5. Suppose -q + 37 = c. Let 0*i + 0*i**2 - 2*i + i**2 - q*i = 0. What is i?
0, 6
Suppose -136*d - 9*d = 0. Let y(k) be the second derivative of d + 1/6*k**3 + 3*k + 0*k**2 - 1/72*k**4. Factor y(b).
-b*(b - 6)/6
Let i(w) be the first derivative of 3*w**5/5 + 77*w**4/4 - 191*w**3/3 + 139*w**2/2 - 28*w + 675. Factor i(o).
(o - 1)**2*(o + 28)*(3*o - 1)
Let g(l) be the third derivative of -l**8/1512 + 611*l**7/945 - 18727*l**6/108 + 18605*l**5/54 - 152*l**2 - 2*l + 3. Factor g(u).
-2*u**2*(u - 305)**2*(u - 1)/9
Let i be (114/(-111) + 1)/(9 - 7). Let q = 575/1258 - i. Determine m, given that 22/17*m**3 + 38/17*m**2 + 8/17*m + 0 - q*m**4 = 0.
-1, -1/4, 0, 4
Let u(g) be the third derivative of g**7/280 + 81*g**6/160 - 249*g**5/80 + 251*g**4/32 - 21*g**3/2 - g**2 + 861. Solve u(a) = 0 for a.
-84, 1
Let a(w) = -7*w**2 + 268*w - 573. Let g be a(36). Suppose -9 - 4*m**2 + 1/2*m**g + 21/2*m = 0. What is m?
2, 3
Let y = 930 - 916. Determine i so that -88 - y*i**2 - 63*i + 155*i + 10*i**2 = 0.
1, 22
Let 16*m + 5/8*m**2 - 13/2 = 0. What is m?
-26, 2/5
Factor -1434*t + 353 + 901 + 1786*t - 2*t**2 + 414 + 894.
-2*(t - 183)*(t + 7)
Factor -62*o**2 - 39*o**2 - 60*o - 3*o**3 - 41*o**2 + 288 + 106*o**2.
-3*(o - 2)*(o + 6)*(o + 8)
Let n(p) be the second derivative of p**5/60 - 17*p**4/18 - 625*p**3/18 + 329*p**2/3 + 4416*p - 2. Factor n(s).
(s - 47)*(s - 1)*(s + 14)/3
What is g in 531/7*g**3 - 531/7*g + 3/7*g**4 - 3/7*g**2 + 0 = 0?
-177, -1, 0, 1
Let n = -5383 + 5412. Let p(j) be the third derivative of 0*j - n*j**2 - 1/120*j**4 + 1/300*j**5 - 1/30*j**3 + 1/600*j**6 + 0. Let p(a) = 0. Calculate a.
-1, 1
Let l(d) be the first derivative of -d**4/20 + 22*d**3/15 + 289*d**2/10 - 62*d + 4792. Factor l(x).
-(x - 31)*(x - 1)*(x + 10)/5
Suppose 0*q = -3*q + 6, 6 = 5*t - 2*q. Suppose 5*s + 61 = -3*g, 0 = -g - 4732*s + 4728*s - 53. Factor -2/9*v + 2/9*v**t + 2/9*v**g - 2/9.
2*(v - 1)*(v + 1)**2/9
Suppose 0 = 4*u - 3*i - 27, 3*i = u + 4*i - 5. Let p be ((-84)/315)/(u/(-27)). Solve -p - 3/5*z**3 - 3/5*z + 18/5*z**2 - 6/5*z**4 = 0 for z.
-2, -1/2, 1
Let b(c) be the second derivative of 2*c**6/15 - 4*c**5 + 42*c**4 - 216*c**3 + 594*c**2 + 443*c. Factor b(h).
4*(h - 11)*(h - 3)**3
Let d be 1428/126*(-1)/(-17). Factor 1/6*n - 1/2*n**2 + 0 - d*n**3.
-n*(n + 1)*(4*n - 1)/6
Let c(j) be the third derivative of j**7/105 + 16*j**6/15 + 34*j**5 - 64*j**4/3 - 4096*j**3/3 + 174*j**2. Factor c(p).
2*(p - 2)*(p + 2)*(p + 32)**2
Let i(s) = 7*s**2 - 169*s - 3136. Let r(j) = -8*j**2 + 164*j + 3136. Let z(m) = 12*i(m) + 11*r(m). Determine b, given that z(b) = 0.
-28
Let g = -5356 - -5358. Let m(n) be the first derivative of 1/30*n**3 - 1/10*n**g + 24 - 4/5*n. Suppose m(i) = 0. What is i?
-2, 4
Let r(f) be the third derivative of f**7/350 - 63*f**6/50 + 645*f**5/4 - 3125*f**4/4 + 4*f**2 + 9*f. Factor r(h).
3*h*(h - 125)**2*(h - 2)/5
Let s = -5 - -5. Suppose -9*a + 105*a = -1834 + 2026. Factor 4/3*f**5 + 2/3*f**3 - a*f**4 + s*f + 0 + 0*f**2.
2*f**3*(f - 1)*(2*f - 1)/3
Suppose -2*s = 4*d + 20, -126*d + 167*d = 4*s + 138. Factor 0 + 2/3*n**5 + 0*n - 8*n**d + 50/3*n**3 - 28/3*n**4.
2*n**2*(n - 12)*(n - 1)**2/3
Suppose 8*d = 29 + 107. Let 1 + 1062*q**3 - 16*q**4 + d*q + 1055*q**3 + 15*q**2 - 2134*q**3 = 0. What is q?
-1, -1/16, 1
Let t be (-42)/35*(-120)/(-9). Let v be ((-8)/t)/(4/16). Suppose 10*b + 8*b**v - 18*b**2 + 15*b**2 = 0. What is b?
-2, 0
Let k(p) be the first deriv