1)*(i + 1)/5
Let u be ((-6)/(-140))/(900/630). Let r(p) be the third derivative of -7/150*p**5 - u*p**6 + 1/30*p**4 + 0 + 0*p**3 + 0*p + p**2. Factor r(o).
-2*o*(o + 1)*(9*o - 2)/5
Determine p, given that 2/9*p**4 + 10/9*p**2 + 0 + 4/3*p**3 + 0*p = 0.
-5, -1, 0
Suppose -7*s = 21*s + 2*s. Factor 3/5*v + s*v**2 - 9/5*v**3 + 0 + 6/5*v**4.
3*v*(v - 1)**2*(2*v + 1)/5
Let d(h) = h**3 - 7*h**2 + 6*h + 2. Let l be d(6). Suppose y - 2 - l = 0. Find x, given that 34*x**y - 14*x + 98*x + 2 + 16 + 140*x**2 + 104*x**3 + 4*x**5 = 0.
-3, -1, -1/2
Let d(n) be the second derivative of -n**7/7560 + n**6/2160 - n**4 + 9*n. Let z(y) be the third derivative of d(y). Factor z(c).
-c*(c - 1)/3
Factor -633 + 2*h**2 + 100*h + 1075 + 808.
2*(h + 25)**2
Let n = 221 - 197. Let z(b) be the first derivative of 12*b**2 - 9 - 6*b**4 + n*b - 4*b**3 - 21/10*b**5 - 1/4*b**6. Factor z(r).
-3*(r - 1)*(r + 2)**4/2
Find b, given that 2/13*b**5 + 50/13*b - 22/13*b**4 - 4*b**3 - 4/13*b**2 + 2 = 0.
-1, 1, 13
Suppose 59 + 57 = 29*x. Let i(j) be the second derivative of -1/42*j**x + 0*j**2 + j - 1/21*j**3 + 0. Determine s, given that i(s) = 0.
-1, 0
Let g(w) = -w**3 - w**2 - 2*w + 4. Let d be g(0). Let l be -3 + (3 - (-4 + d)). Find p such that 3/2*p**4 - 3/2*p**2 + 0*p + 0*p**3 + l = 0.
-1, 0, 1
Let r(h) be the second derivative of -h**5/30 + 5*h**4/9 - 4*h**3/3 - 24*h**2 + h + 16. Factor r(w).
-2*(w - 6)**2*(w + 2)/3
Let m(y) be the second derivative of 0 + 0*y**2 + 9/80*y**5 + 4*y + 1/4*y**3 - 5/16*y**4. Find o such that m(o) = 0.
0, 2/3, 1
Let b(l) be the second derivative of l**5/40 + l**4/6 + l**3/4 + 27*l - 1. Factor b(w).
w*(w + 1)*(w + 3)/2
Let t be (-2 + 0 + -1)/(-9 + 8). Suppose 5439*x - 1536*x**2 + 2753*x - 6*x**3 - 4*x**4 - 16384 + 134*x**t = 0. Calculate x.
8
Let t(h) be the second derivative of -29/65*h**5 + 0 - 1/39*h**6 - 36/13*h**4 - 7*h + 128/13*h**2 - 224/39*h**3. Determine f so that t(f) = 0.
-4, 2/5
Let s be 20/(-88)*(-104)/130. Factor 24/11 - s*c**2 + 2/11*c.
-2*(c - 4)*(c + 3)/11
Let i(k) = 16*k**4 + 13*k**3 - 69*k**2 + 35*k. Let d(l) = 8*l**4 + 6*l**3 - 34*l**2 + 18*l. Let j(a) = 5*d(a) - 2*i(a). Factor j(c).
4*c*(c - 1)**2*(2*c + 5)
Suppose -3*p - 5*w - 2 = -5*p, 4*w = -2*p + 2. Let b = 3 - p. Find f, given that 0*f**4 + 2*f**4 - f**4 - b*f**3 + f**4 = 0.
0, 1
Let h(w) be the third derivative of -w**5/12 + 5*w**4/8 + 15*w**3 - 49*w**2 + w. Factor h(u).
-5*(u - 6)*(u + 3)
Suppose 3*s = -2*p + 1, 4*s + 3*p = -0*p. Suppose -w = -3*w + s*w. Find q, given that 0*q**3 - 1/5*q**4 + w*q + 0*q**2 + 0 = 0.
0
Let p(i) = -12*i**4 + 72*i**3 - 57*i**2 - 81*i + 51. Let b(m) = -3*m**4 + 18*m**3 - 14*m**2 - 20*m + 13. Let x(y) = 9*b(y) - 2*p(y). Solve x(c) = 0 for c.
-1, 1, 5
Let z = -199/6 - -253/2. Factor z*j**4 + 0 - 196/3*j**5 - 16/3*j + 4*j**3 - 80/3*j**2.
-4*j*(j - 1)**2*(7*j + 2)**2/3
Determine s so that 4*s + 2/7*s**4 + 0 + 52/7*s**2 - 1/7*s**5 + 27/7*s**3 = 0.
-2, -1, 0, 7
Let g(j) = 3*j**3 + j**2 - 4*j + 4. Let d be g(4). Let d + 3*p + 4*p**2 - 15*p - 44*p = 0. Calculate p.
7
Let w(y) be the second derivative of 1/16*y**4 + 0 - 1/16*y**3 - 3/8*y**2 + 3/160*y**5 + 23*y. Let w(q) = 0. What is q?
-2, -1, 1
Let p(h) be the third derivative of 0*h**7 + 0*h + 0*h**5 + 9*h**2 + 0 + 1/8*h**4 + 1/112*h**8 - 1/20*h**6 + 0*h**3. Factor p(v).
3*v*(v - 1)**2*(v + 1)**2
Suppose -286 + 1201 = 3*l. Let s be ((-24)/(-14))/(l/(-35) + 9). Factor -2*t**2 + t**5 + 0 - 9/2*t**4 + s*t**3 + 0*t.
t**2*(t - 2)**2*(2*t - 1)/2
Let s(w) be the second derivative of 17*w**5/20 - 19*w**4/12 + w**3/3 - 431*w. Factor s(z).
z*(z - 1)*(17*z - 2)
Let r(v) be the first derivative of -5*v**3/3 + 340*v**2 - 23120*v + 542. Factor r(h).
-5*(h - 68)**2
Let k(b) be the first derivative of 5 + 2/11*b + 2/11*b**2 + 2/33*b**3. Factor k(f).
2*(f + 1)**2/11
Let f = 30856/38545 - 4/7709. Factor 0*r**2 - 4/5*r**3 + 0 + 0*r + f*r**4.
4*r**3*(r - 1)/5
Suppose 16265 = 63*x + 16076. Let g be 4 + (-2 - (-2 - -2)). Factor -9/5*r**g - 9/5*r - 3/5*r**x - 3/5.
-3*(r + 1)**3/5
Suppose -330 = -3*v - 107*v. Solve -1/2 + 2*s**3 + 2*s - v*s**2 - 1/2*s**4 = 0 for s.
1
Let r = -619/2 - -383. Let -r*b**2 - 7*b**3 - 2401/4 - 1/4*b**4 - 343*b = 0. Calculate b.
-7
Let k(f) = 12*f**3 - 16*f**2 + 4*f + 2. Let t(r) = -25*r**3 + 31*r**2 - 7*r - 4. Let q(y) = -5*k(y) - 2*t(y). Suppose q(s) = 0. What is s?
-1/5, 1
Let r(c) = -c**2 - 40*c - 71. Let y be r(-38). Factor 1/3*i**y + i**2 + 0 + 1/3*i**3 - i**4 - 2/3*i.
i*(i - 2)*(i - 1)**2*(i + 1)/3
Let t(g) be the third derivative of -g**9/6048 + g**7/560 + g**6/360 - g**3/2 + 2*g**2. Let w(m) be the first derivative of t(m). Factor w(b).
-b**2*(b - 2)*(b + 1)**2/2
Factor 1/3*n**2 - 26/3 + 25/3*n.
(n - 1)*(n + 26)/3
Let b(w) be the second derivative of -w**9/52920 + w**8/23520 - 4*w**4/3 + 2*w. Let g(k) be the third derivative of b(k). Find o such that g(o) = 0.
0, 1
Let z(c) be the first derivative of 5*c - 5/6*c**4 + 0*c**2 + 3/4*c**5 + 1 + 0*c**3. Let a(y) be the first derivative of z(y). Solve a(j) = 0 for j.
0, 2/3
Let h = -1265/9 - -8945/63. Factor 8/7 - h*z + 2/7*z**2.
2*(z - 4)*(z - 1)/7
Let s(a) be the first derivative of -5*a**4/4 - 10*a**3 - 45*a**2/2 - 20*a + 427. What is r in s(r) = 0?
-4, -1
Let k(j) be the second derivative of j**7/1120 - j**5/160 - 8*j**3/3 - 13*j. Let x(u) be the second derivative of k(u). Factor x(v).
3*v*(v - 1)*(v + 1)/4
Let k(g) = 2*g + 21. Let o be k(0). Factor -4 - 1 - 9*h**2 - o*h - 1.
-3*(h + 2)*(3*h + 1)
Let w(a) = -87*a**3 - 93*a**2 - 14*a - 4. Let y(r) = 174*r**3 + 186*r**2 + 30*r + 9. Let t(d) = 9*w(d) + 4*y(d). Factor t(g).
-3*g*(g + 1)*(29*g + 2)
Let j(a) be the first derivative of -a**7/5040 + a**5/240 + a**4/72 - 17*a**3/3 + 5. Let i(x) be the third derivative of j(x). Factor i(k).
-(k - 2)*(k + 1)**2/6
Let m be (-1917)/(-355) - (1 + 4). Let -4/5 - 6/5*n + 0*n**2 + m*n**3 = 0. What is n?
-1, 2
Let m = 1483 + -1480. Determine p, given that 8/9 + 98/9*p**m + 14/3*p**2 - 16/3*p = 0.
-1, 2/7
Let q be 15/(-6)*(-2)/10*2. Let b be (-6 + 0)/(4/(-2)). Factor 11*a - q + 7 + b*a**2 - 2*a.
3*(a + 1)*(a + 2)
Let c(j) be the third derivative of 0 + 0*j**4 - 1/3*j**6 + 0*j**3 + 1/15*j**5 + j**2 - 3/7*j**8 + 22/35*j**7 + 0*j. Factor c(p).
-4*p**2*(3*p - 1)**2*(4*p - 1)
Suppose -3*h - 16 = -4*h. Suppose -h*b = -21*b. Factor 0*m**2 + 2/7*m**3 + b - 2/7*m.
2*m*(m - 1)*(m + 1)/7
Let o(b) be the third derivative of b**6/30 + 73*b**5/15 + 228*b**4 + 864*b**3 + 147*b**2. Factor o(a).
4*(a + 1)*(a + 36)**2
Suppose 3 = 2*l + x, -2*l + x = 2*l + 3. Let s(g) be the third derivative of 0 + l*g - g**2 + 0*g**3 + 1/330*g**5 - 1/132*g**4. What is p in s(p) = 0?
0, 1
Let k = -24 + 21. Let z = 5 + k. Factor i**3 - i**4 - 2*i**3 + i**z + 0*i**3 + i.
-i*(i - 1)*(i + 1)**2
Let q(l) be the third derivative of -l**7/13860 + l**6/990 - l**5/220 + 7*l**4/8 - 15*l**2. Let f(o) be the second derivative of q(o). Let f(y) = 0. What is y?
1, 3
Let r = 7 + -4. Let u = -797 + 800. Factor -9 + 8*h + r - h**u - 2*h**3 + h.
-3*(h - 1)**2*(h + 2)
Let z = 3023/9060 - 1/3020. Find t, given that z*t**4 + 0*t**2 - 2/3*t**3 + 0 + 0*t = 0.
0, 2
Let w(t) be the first derivative of t**6/27 + 2*t**5/9 + 997. Determine o so that w(o) = 0.
-5, 0
Let g be 0/(((-3)/(-3))/(2 + -3)). Let c(b) be the first derivative of b**2 + 1/3*b**6 + 5 + g*b - 8/3*b**3 - 8/5*b**5 + 3*b**4. Let c(k) = 0. What is k?
0, 1
Let o(r) be the first derivative of -r**4/24 - 7*r**3/18 - r**2 - 87. Factor o(f).
-f*(f + 3)*(f + 4)/6
Factor 0 - 6*m**4 + 0*m + 2/3*m**2 + 16/3*m**3.
-2*m**2*(m - 1)*(9*m + 1)/3
Let o be (1 - 18/(-12))*2. Suppose 0 = 5*v - o*k - 25, -1 = v - 8*k + 13*k. Factor -9/5*r**3 - 3/5*r**5 + 0 + 9/5*r**v + 3/5*r**2 + 0*r.
-3*r**2*(r - 1)**3/5
Factor -14/3 - 4/3*r - 2/21*r**2.
-2*(r + 7)**2/21
Determine o so that 1/6*o**3 + 25/6*o**2 - 169/6 + 143/6*o = 0.
-13, 1
Let u = 15 + 17. Find q such that 0*q - u*q**2 + 30*q**2 + 2*q = 0.
0, 1
Factor 44/5 - 4/5*y**3 + 36/5*y**2 + 84/5*y.
-4*(y - 11)*(y + 1)**2/5
Suppose v - 22 = -6*u + 3*u, -u + 82 = 3*v. Suppose 10 = -v*k + 33*k. Suppose -2/15*i**k - 2/15 + 4/15*i = 0. What is i?
1
Let k(s) be the third derivative of -s**7/42 + 3*s**6/8 + 7*s**5/4 + 55*s**4/24 + 3*s**2 + 3*s. Suppose k(d) = 0. What is d?
-1, 0, 11
Let a be (18/(-4)*1/(-3))/((-1)/(-2)). Suppose 0 - 3/5*h**2 