(a).
2*a*(a + 388)**2/11
Let z be (8/12)/(3/(-9)) + 21. Suppose 4*p**3 - p**4 + 3*p**3 - 2*p**2 + 7*p**3 + 8*p - z*p**3 = 0. Calculate p.
-4, -2, 0, 1
Let g be (160/(-1680))/(36/(-14)). Let b(a) be the first derivative of -g*a**3 + 1/9*a**2 + 29 + 8/9*a. Suppose b(y) = 0. Calculate y.
-2, 4
Suppose 5*k + 288 + 36 = 2*w, 0 = k - w + 66. Let p = 67 + k. Factor -1 + 17*r**3 - 1 - 18*r**3 + p*r.
-(r - 1)**2*(r + 2)
Let f(v) be the second derivative of -19 + 8*v**3 - 22*v**2 - 2*v - 1/3*v**4. Factor f(t).
-4*(t - 11)*(t - 1)
Suppose 134 - 34 = 20*t. Solve 2*b + 547*b**5 - 12*b**3 - 18*b**2 + 18*b**4 - t*b - 532*b**5 = 0 for b.
-1, -1/5, 0, 1
Suppose c = -780 + 605. Let l be (-28)/(-54)*(-150)/c. Factor 4/9*r - 8/9 + 8/9*r**2 - l*r**3.
-4*(r - 2)*(r - 1)*(r + 1)/9
Let o(r) = -47*r**2 - r - 1. Let p(d) = 140*d**2 + 214*d - 1027. Let m(c) = 15*o(c) + 5*p(c). Determine s, given that m(s) = 0.
5, 206
Let l(x) = 4*x - 70. Let a(m) = 8*m - 140. Let c(o) = -3*a(o) + 5*l(o). Let f be c(17). Find s such that -40*s - 200 - s**f + 6*s**2 - 7*s**2 = 0.
-10
Suppose 4*z + 54 = -a, -5*a = -65*z + 67*z + 18. Factor 4761/7 - 138/7*x + 1/7*x**a.
(x - 69)**2/7
Let v = -337421/4 - -84356. Let m = -3/5 - -11/10. Determine p, given that v*p + m + 1/4*p**2 = 0.
-2, -1
Suppose -v = 5*h - 12099, h = -2*h + 4*v + 7264. Factor 190*i**2 + 880*i - h + 1100*i - 595*i**2.
-5*(9*i - 22)**2
Let 52/7*z**2 - 38/7*z**3 + 8/7 - 1/7*z**5 + 12/7*z**4 - 33/7*z = 0. What is z?
1, 8
Suppose -232*h + 227*h + 10 = -3*s, -4*s = 5*h - 10. Factor 3/4*u - 3/4*u**h + 9/2.
-3*(u - 3)*(u + 2)/4
Let i(k) be the first derivative of 2/3*k**3 - 49 + 0*k - k**2. Factor i(f).
2*f*(f - 1)
Let q(z) be the first derivative of -8/11*z**2 - 112 - 24/11*z - 2/33*z**3. Factor q(j).
-2*(j + 2)*(j + 6)/11
Let w(x) be the second derivative of x**6/120 + x**5/15 + 71*x**2/2 - 38*x. Let b(d) be the first derivative of w(d). Factor b(h).
h**2*(h + 4)
Let l be (-3)/(-5) - 14/(-10). Let w(q) = -2*q**3 + q**2 - 2*q + 1. Let p(k) = k**3 - 3*k**2 + 5*k - 1. Let t(z) = l*w(z) + 2*p(z). Factor t(j).
-2*j*(j - 1)*(j + 3)
Let p = -224 + 251. Let 3*g**4 - p*g**2 - 66*g**2 + 97 - 48 + 90*g**3 - 49 = 0. What is g?
-31, 0, 1
Let j(b) be the first derivative of -79 - 75/16*b**4 + 0*b - 5/8*b**2 - 5/6*b**6 - 35/12*b**3 - 13/4*b**5. Factor j(y).
-5*y*(y + 1)**3*(4*y + 1)/4
Factor 1/4*r**3 + 0 + 13/4*r**2 + 0*r.
r**2*(r + 13)/4
Let c = 527312 + -527309. Factor -44/7*r**c - 16/7*r**2 + 0*r - 10/7*r**4 + 0.
-2*r**2*(r + 4)*(5*r + 2)/7
Let w = 190 + -185. Suppose -g - 23 = -w*k, -5*g - 5 + 40 = 5*k. Solve 2/3*o**g - 16/3*o + 32/3 = 0.
4
Let a(h) be the third derivative of h**5/120 - 415*h**4/48 + 69*h**3/2 - 21*h**2 - 20*h. Find q such that a(q) = 0.
1, 414
Let 3/2*s**5 + 9*s - 21/2*s**3 - 3/2*s**2 + 0 + 3/2*s**4 = 0. What is s?
-3, -1, 0, 1, 2
Let q(a) be the third derivative of -241*a**2 + 0*a + 1/20*a**5 + 7/8*a**4 + 3*a**3 + 0. Factor q(o).
3*(o + 1)*(o + 6)
Let b be 1/(390/55 - 7). Solve b*j - 5*j + 4*j + 48 - 2*j**2 = 0.
-3, 8
Let x = 19 + -75/4. Let i = 393517 + -393517. Factor i - x*n**2 - 1/4*n.
-n*(n + 1)/4
Let s = 10781 + -32342/3. Factor 4/3 + 5/3*n + s*n**2.
(n + 1)*(n + 4)/3
Let m = -161652/5 + 32340. Determine b so that -m*b**2 + 24/5*b**3 + 32/5*b + 0 - 4/5*b**4 = 0.
0, 2
Let g = 9 - 5. Let x be 0/((1815/660 - (-4 - 3*-2))*-4). Suppose 0 - 1/3*v**g + x*v**2 - v**3 + 4/3*v = 0. Calculate v.
-2, 0, 1
Let f(n) be the second derivative of -n**7/105 - 8*n**6/25 + 17*n**5/25 + 118*n**4/15 + 93*n**3/5 + 20*n**2 - 24*n + 166. Let f(r) = 0. Calculate r.
-25, -1, 4
What is w in -24*w + 17/4*w**3 + 0 - 47*w**2 - 1/2*w**5 + 17/4*w**4 = 0?
-3, -1/2, 0, 4, 8
Let w(o) = -10*o**2 + 13*o - 7. Let g(i) = -5*i**2 + 6*i - 4. Suppose -11*j + 7*j = 68. Let l = -10 - j. Let s(z) = l*g(z) - 4*w(z). Factor s(c).
5*c*(c - 2)
Let o(w) = -2*w**3 - 84*w**2 + 454*w + 528. Let n(q) = -3*q**3 - 88*q**2 + 453*q + 528. Let u(j) = 4*n(j) - 5*o(j). Factor u(r).
-2*(r - 24)*(r - 11)*(r + 1)
Let l(i) = 2*i - 11. Let n be l(7). Suppose -n - 9 = -3*d. Factor 7*m**5 - 8*m**3 - 5 + 10*m**2 - 2*m**5 + 5*m - 26*m**d + 21*m**4 - 2*m**3.
5*(m - 1)**3*(m + 1)**2
Let q be (-19162)/(-60) - (-192)/240. Let f = q + -320. Solve 1/3*g - f - 1/6*g**2 = 0.
1
Let o(m) = -m**3 - 6*m**2 - m - 3. Let q be o(-6). Suppose 0 = -w + q. Factor 0*y**2 + y - w*y - y - 15*y**2.
-3*y*(5*y + 1)
Factor -180 - 57/2*p**2 + 3/2*p**3 + 141*p.
3*(p - 12)*(p - 5)*(p - 2)/2
Let i(w) = 5*w + 2*w - 14*w + 2*w**2 - 3*w**2 - 10. Let l be i(-3). Solve -3*o**l - 3*o**3 + 2*o**2 - 2 + 0 + 3*o**2 + 3*o = 0.
-1, 2/3, 1
Let c be (-6 - -4)/2506*(1370 - 8). Let r = 10/179 - c. What is j in 4/7*j**4 + 0*j**3 - 12/7*j**2 + 0 + r*j = 0?
-2, 0, 1
Let g be 17052/189 - (-120)/(-12). Find k such that -76/9*k + g + 2/9*k**2 = 0.
19
Let t be 45/7 - (144/(-152) + 1 + 1469/247). Suppose -123/7 - 120/7*v + t*v**2 = 0. What is v?
-1, 41
Let g = 177 + -77. Solve -g*w**2 - 4*w + 4*w + 4*w + 0*w = 0.
0, 1/25
Let k(v) be the third derivative of v**6/120 + 2*v**5/15 + 89*v**2. Let s(z) = 6*z**3 + 41*z**2. Let t(n) = 11*k(n) - 2*s(n). What is r in t(r) = 0?
0, 6
Factor -463*w + 733*w - 525*w - 5*w**2 - 490.
-5*(w + 2)*(w + 49)
Let t(f) be the third derivative of -f**6/240 + 2*f**5/3 + f**4/48 - 20*f**3/3 + 1386*f**2. Suppose t(z) = 0. What is z?
-1, 1, 80
Let r be 2/4 + 369/6. Find k, given that -30*k**2 - k**4 - k**3 - 30*k**2 + r*k**2 = 0.
-2, 0, 1
Let o(d) be the third derivative of -4/15*d**4 + 0*d - 65*d**2 - 8/3*d**3 + 0 + 1/75*d**5. Determine i so that o(i) = 0.
-2, 10
Let t be ((-1000)/6000)/(2/48*-2). Factor 10/13*q + 2/13*q**t - 12/13.
2*(q - 1)*(q + 6)/13
Let l(p) = 63*p - 70. Let f be l(5). Let q = -1219/5 + f. Factor 21/5*a - q*a**2 - 18/5.
-3*(a - 2)*(2*a - 3)/5
Let o(p) be the first derivative of -1/8*p**2 - 138 - 1/24*p**3 - 1/8*p. Find f such that o(f) = 0.
-1
Determine p, given that 5/4 + 7*p**2 + 39/8*p + 3/4*p**4 - 1/8*p**5 + 17/4*p**3 = 0.
-1, 10
Let r(o) be the third derivative of 61/20*o**5 - 250*o**2 + 21/40*o**6 + 0 - 45/4*o**4 + 0*o + 4*o**3. Factor r(n).
3*(n - 1)*(n + 4)*(21*n - 2)
Let s(y) be the third derivative of y**6/1620 - y**5/90 + 5*y**4/108 + 52*y**3/3 - y**2 - 19*y. Let h(d) be the first derivative of s(d). Factor h(c).
2*(c - 5)*(c - 1)/9
Let q(w) be the first derivative of -w**6/40 + 3*w**4/16 + w**3/4 - 36*w - 95. Let p(d) be the first derivative of q(d). Suppose p(g) = 0. Calculate g.
-1, 0, 2
What is f in 0 + 2/5*f**4 + 14/5*f**3 + 0*f + 0*f**2 = 0?
-7, 0
Let m be (10/25 - 0)/(0 + 3/45). Let s(v) be the second derivative of -1/20*v**5 + 0 + 15*v + 1/12*v**4 + 4/3*v**3 - m*v**2. Let s(z) = 0. Calculate z.
-3, 2
Let s(u) be the second derivative of 2*u**5 - 5995*u**4/3 - 23995*u**3/12 - 750*u**2 + 3*u - 3881. Factor s(k).
5*(k - 600)*(4*k + 1)**2/2
Suppose 4*i = 2*w - 76, -26*i + 78 = 3*w - 23*i. Let z be 9/(-27) - w/(-45). Solve z*m + 0 + 1/6*m**2 = 0 for m.
-2, 0
Let z(y) be the third derivative of -y**6/40 - 4*y**5/5 - 69*y**4/8 - 27*y**3 + 658*y**2. Suppose z(b) = 0. Calculate b.
-9, -6, -1
Let -4*f**3 + 8*f + 1/2*f**5 + 8 + 1/2*f**4 - 4*f**2 = 0. Calculate f.
-2, -1, 2
Let l(w) be the second derivative of w**6/15 + 21*w**5/5 - 48*w**4 + 32*w**3/3 + 1536*w**2 - 2267*w. Factor l(n).
2*(n - 4)**2*(n + 2)*(n + 48)
Let k(b) = 7*b + 0*b - 4*b**2 - 3*b + 20*b - 2. Let r(o) = -5*o**2 + 25*o - 3. Let c(w) = -6*k(w) + 4*r(w). Factor c(a).
4*a*(a - 11)
Let d be (-19)/(190/(-116))*9/(-819)*-35. Suppose -2/13*h**2 - d*h + 0 = 0. What is h?
-29, 0
Let y = 153 - 151. Let p be (-48)/((6/(-4))/(-5*4/(-180))). Factor 4/9*c**y + 8/9*c - p.
4*(c - 2)*(c + 4)/9
Let f be (6/4)/((-106)/(-212)). Let c(n) be the second derivative of 6*n - 1/120*n**5 + 0*n**2 + 1/9*n**4 - 4/9*n**f + 0. Let c(i) = 0. What is i?
0, 4
Suppose 4*y = -y + 5*n - 10, -3*y - 5*n = -34. Let d(x) be the first derivative of 9*x**3 - 10 + 0 - 13*x**y - 4*x**2 - x**4. Factor d(h).
-4*h*(h + 1)*(h + 2)
What is l in 8192/5 - 138/5*l**3 - 10752/5*l + 2/5*l**4 + 2696/5*l**2 = 0?
1, 4, 32
Suppose -8 = -b + 4*y, 2*b - 26*y - 6 = -28*y. Suppose 4*s + 6*s - 30 = 0. Factor 33/7*c**2 + 15/7*c + 3/7*c**b + 0 + 3*c**s.
3*c*(c + 1)**2*(c + 5)/7
Let k be 16/70*((-3525)/188 + 4*5). Factor -6/7*o - 4/7 + k*o**4 + 6/7*o**3 + 2/7*o**2.
2*(o - 1)*(o +