)). Let k(i) be the first derivative of 0*i - 1/5*i**2 + 1 - q*i**3. Factor k(y).
-2*y*(y + 1)/5
Let j(r) = 12*r**5 + 18*r**3 + 15*r - 15. Let m(v) = -v**5 - v**3 - v + 1. Let a(l) = -j(l) - 15*m(l). Factor a(h).
3*h**3*(h - 1)*(h + 1)
Let j(v) be the third derivative of -v**8/560 + 4*v**7/315 - v**6/60 - v**5/15 + 5*v**4/24 - 3*v**2. Let b(f) be the second derivative of j(f). Factor b(i).
-4*(i - 2)*(i - 1)*(3*i + 1)
Let b(z) be the second derivative of z**4/84 - z**3/6 + 3*z**2/7 + 30*z. Factor b(v).
(v - 6)*(v - 1)/7
Factor 7*d**4 - d**3 + 2*d**3 - 8*d**4.
-d**3*(d - 1)
Let h(q) = 110*q**3 + 175*q**2 + 110*q. Let g(f) = -5*f**3 - 8*f**2 - 5*f. Let z(o) = -45*g(o) - 2*h(o). Determine a, given that z(a) = 0.
-1, 0
Suppose -9 = x - 3*f, -6*x + x + 3*f = 9. Solve x*y + 0 - 2/3*y**4 + 0*y**3 + 2/3*y**2 = 0.
-1, 0, 1
Let d(y) be the second derivative of -y**6/120 - 3*y**5/80 - y**4/24 - 22*y. Factor d(p).
-p**2*(p + 1)*(p + 2)/4
Let l = 8 - 8. Let p(v) be the second derivative of -1/7*v**2 + 1/42*v**4 - 2*v + 0*v**3 + l. Factor p(k).
2*(k - 1)*(k + 1)/7
Determine y so that 11*y - y**2 + y + 2*y**2 + 36 = 0.
-6
Let w(t) be the second derivative of -t**8/336 + t**7/84 - t**6/80 - t**5/120 + t**4/48 - t**2/2 - 3*t. Let n(b) be the first derivative of w(b). Factor n(d).
-d*(d - 1)**3*(2*d + 1)/2
Let h(b) be the first derivative of -2/9*b**3 - 1/6*b**2 - 2 + 0*b**4 + 2/15*b**5 + 0*b + 1/18*b**6. Determine q so that h(q) = 0.
-1, 0, 1
Factor -1/4*x**5 + 0*x**4 - 1/4*x + 0*x**2 + 1/2*x**3 + 0.
-x*(x - 1)**2*(x + 1)**2/4
Let k be 6/4*(-10)/30*0. Factor 2/5*c**2 + k + 0*c.
2*c**2/5
What is h in 6/5*h**4 + 2/5*h**2 + 0 + 0*h - 2/5*h**5 - 6/5*h**3 = 0?
0, 1
Let r(j) = -j**3 + 4*j**2 + 2*j - 6. Let g be r(4). Let 0 - 2/7*z**g - 2/7*z**4 + 0*z - 4/7*z**3 = 0. What is z?
-1, 0
Let t(l) = -3*l**2 + 120*l + 1095. Let x(p) = 2*p**2 - 119*p - 1093. Let o(i) = 5*t(i) + 6*x(i). Factor o(a).
-3*(a + 19)**2
Suppose 16*m - 43 = 309. Determine s, given that -m*s - 147/2*s**4 - 173/2*s**2 - 140*s**3 - 2 = 0.
-1, -1/3, -2/7
Let w(o) be the third derivative of 0*o + 1/30*o**6 - 1/10*o**5 + 0*o**3 + 1/35*o**7 + 0 + o**2 - 1/6*o**4. What is r in w(r) = 0?
-1, -2/3, 0, 1
What is m in -1/5 - 1/5*m**2 - 2/5*m = 0?
-1
Let m be 2/(-5) + (-46)/(-90). Let p(c) be the first derivative of 0*c + m*c**3 - 2 - 1/6*c**2. Find b, given that p(b) = 0.
0, 1
Find k, given that 4*k**4 + 2*k**2 - 2*k**2 - 8*k**4 - 8*k**3 + 4*k**5 = 0.
-1, 0, 2
Let s be (25/75)/(10/8). Let g(c) be the third derivative of 1/9*c**3 + 0*c + 4/45*c**6 + s*c**5 - 4*c**2 + 1/4*c**4 + 0. Suppose g(q) = 0. Calculate q.
-1, -1/4
Find i such that -5*i - 6 + 2*i**2 + i**2 + 0*i**2 + 8*i = 0.
-2, 1
Let k(u) be the second derivative of 0*u**2 + 0 - 2*u + 1/9*u**3 - 1/36*u**4. Suppose k(d) = 0. What is d?
0, 2
Suppose 0*g = 4*g - 16. Let k be (-37)/(-7) + g/(-14). Factor -2*b**5 - 3*b**4 - 2*b**k + 0*b**4 + b**3.
-b**3*(b + 1)*(4*b - 1)
Let a be 9/15*(-6130)/(-15). Let o = a - 244. Factor -2/5*t**3 + 6/5*t**2 - o*t + 2/5.
-2*(t - 1)**3/5
Suppose 2*j = 3*j. Let t(m) be the second derivative of 1/5*m**2 + 1/30*m**3 + j - 1/60*m**4 + m. Suppose t(b) = 0. What is b?
-1, 2
Let f be (-49)/(-45) - (-1)/(-5). Factor 8/9*x - f - 2/9*x**2.
-2*(x - 2)**2/9
Let z(g) be the third derivative of g**7/1575 - g**5/225 + g**3/45 - 30*g**2. Find o, given that z(o) = 0.
-1, 1
Suppose -4*n + 0*q + 16 = -q, -n = -2*q - 11. Solve -3*o**2 - 3*o**n + 2*o**2 + 7*o**2 = 0.
0, 2
Factor -1/4*k**3 - 1/4*k**4 + 0 + 0*k**2 + 0*k.
-k**3*(k + 1)/4
Find j such that 40 + 9 - 4 - 9*j**2 + 4*j**2 = 0.
-3, 3
Suppose -28 = -2*l - 5*l. Let v(z) be the first derivative of -2/15*z**3 - 1/10*z**l + 1/15*z**6 - 3 + 2/25*z**5 + 0*z**2 + 0*z. Factor v(j).
2*j**2*(j - 1)*(j + 1)**2/5
Let f(j) be the first derivative of j**4/18 - 2*j**3/9 - 4*j - 11. Let n(s) be the first derivative of f(s). Let n(g) = 0. What is g?
0, 2
Solve -4 + 5/2*c**3 + c**4 - 3*c**2 - 10*c = 0.
-2, -1/2, 2
Factor 25/4*x**5 + 6*x**3 - x**2 + 0*x + 0 - 45/4*x**4.
x**2*(x - 1)*(5*x - 2)**2/4
Suppose -2/5*c**2 + 2/5*c**3 + 1/5*c**5 - 3/5*c + 3/5*c**4 - 1/5 = 0. Calculate c.
-1, 1
Factor -3/7*w**4 + 6/7*w**3 + 0*w - 3/7*w**2 + 0.
-3*w**2*(w - 1)**2/7
Let v(t) be the third derivative of -3*t**2 + 1/360*t**6 + 0 + 0*t**4 + 1/180*t**5 + 0*t**3 + 0*t. What is r in v(r) = 0?
-1, 0
Let l = 16 + -11. Let c(v) be the second derivative of v + 3/70*v**l + 4/21*v**4 + 2/7*v**2 + 0 + 1/3*v**3. Factor c(s).
2*(s + 1)**2*(3*s + 2)/7
Let y(t) = 7*t - 2*t - 2*t - 7 + 4*t**2 + t. Let u(p) = -p**2 - p + 2. Let l(o) = -21*u(o) - 6*y(o). Factor l(x).
-3*x*(x + 1)
Let o(c) be the third derivative of -c**9/4536 + c**7/1260 + c**3/3 - 6*c**2. Let b(w) be the first derivative of o(w). Suppose b(p) = 0. Calculate p.
-1, 0, 1
Let j(n) be the second derivative of 0 + 5*n - 1/6*n**3 - 1/12*n**4 + 0*n**2. Let j(l) = 0. Calculate l.
-1, 0
Let i(w) be the third derivative of -49*w**6/40 - 7*w**5/10 - w**4/8 - w**2 - 4*w. Suppose i(y) = 0. What is y?
-1/7, 0
Let x be (1/(-12))/(12/(-9) + 1). What is k in x*k + 0 - 1/4*k**2 = 0?
0, 1
Let x be ((-4)/8)/((6 - 5)/(-6)). Find q, given that -q**4 - 2 - 11*q - 25/4*q**x - 27/2*q**2 = 0.
-2, -1/4
Let s(k) be the second derivative of k**8/168 - k**7/105 - k**6/60 + k**5/30 - 2*k**2 + 3*k. Let x(w) be the first derivative of s(w). Solve x(o) = 0.
-1, 0, 1
Suppose 0 = -5*b - d + 13 + 31, -4*d + 8 = -b. Suppose 5*j = 2*u + 14, -5*u = -u - j - b. Factor -1/3*r**u + 0*r**2 + 0*r + 0 + 4/3*r**4 - r**5.
-r**3*(r - 1)*(3*r - 1)/3
Suppose -6*l + 2*l - 5*a = 1, -a = l. Let c be ((-3)/(-15))/l - 0. Factor 1/5 + 2/5*n**3 - c*n**2 - 2/5*n.
(n - 1)*(n + 1)*(2*n - 1)/5
Let c be (-7)/2*28/(-49). Factor 1 - 3*y**2 + 2 - 5*y + 5*y**2 - c*y.
(y - 3)*(2*y - 1)
Suppose j - 81 = -2*j. Let h = j + -53/2. Factor h + 1/2*g**2 + g.
(g + 1)**2/2
Let q be (-1)/(2/12*-2). Let 2*j**4 - 10*j**q - j**2 + 11*j**2 - 4*j + 2*j**3 = 0. Calculate j.
0, 1, 2
Let w = 1456/9 - 160. Suppose 4/9*r + 0 + w*r**3 - 14/9*r**2 - 2/3*r**4 = 0. What is r?
0, 2/3, 1
Let t(f) be the third derivative of f**7/70 + f**6/40 - 3*f**5/20 - 5*f**4/8 - f**3 + 4*f**2. Find v, given that t(v) = 0.
-1, 2
Let q(z) = -6*z - z**2 + 3 + 0 - 4 + 0. Let p be q(-5). What is b in -5*b**4 - 6*b**2 + 2*b + 2*b**4 + 6*b**3 + b**p = 0?
0, 1
Let j(v) be the first derivative of -2*v**5/55 - v**4/22 + 2*v**3/33 + v**2/11 + 15. Factor j(o).
-2*o*(o - 1)*(o + 1)**2/11
Let r = -721 + 9379/13. Factor 8/13*g - 2/13*g**2 - r.
-2*(g - 3)*(g - 1)/13
Let c be (-5 - -4)/((-2)/4). Solve n + 2*n**3 + 0*n**3 - 3*n**2 - n**c + n = 0.
0, 1
Let k = -72 + 72. Factor 8/5*u**3 + 0*u + 2/5*u**4 + k + 8/5*u**2.
2*u**2*(u + 2)**2/5
Suppose -2*b = b. Let l = 0 - b. Suppose -3 - n + 3*n**2 + 1 - 2*n**2 + l = 0. Calculate n.
-1, 2
Suppose 4/9*q**2 - 2/9*q + 2/9*q**5 + 0*q**3 + 0 - 4/9*q**4 = 0. What is q?
-1, 0, 1
Let p(u) be the second derivative of u**4/12 - 2*u**3/3 + 3*u**2 - 4*u. Let f be p(4). Solve 1/4*n**4 - 2*n**3 + f*n**2 - 8*n + 4 = 0 for n.
2
Let r(w) = w**2 - 5*w + 2. Suppose -2*i - 19 = -5*q, 5*q - 15 + 5 = 5*i. Let y be r(q). What is c in -3*c**3 - c**4 + 4*c**3 - c**y - 2*c**3 + c + 2*c**2 = 0?
-1, 0, 1
Let g(a) be the third derivative of 0*a**4 - 1/60*a**5 - 5*a**2 - 1/120*a**6 + 1/210*a**7 + 0 + 0*a**3 + 1/336*a**8 + 0*a. Factor g(k).
k**2*(k - 1)*(k + 1)**2
Factor 23*y**3 - 25*y**3 - 32*y**4 + 18*y**3 - 31*y**5 + 11*y**5.
-4*y**3*(y + 2)*(5*y - 2)
Factor 0 - 1/6*o**2 - 1/3*o.
-o*(o + 2)/6
Factor 0*m**2 - 1/8*m**3 + 1/8*m + 0.
-m*(m - 1)*(m + 1)/8
Let b(z) be the first derivative of z**4/2 + 4*z**3/3 + z**2 + 24. Determine a so that b(a) = 0.
-1, 0
Let r(s) be the first derivative of s**6/2 + 3*s**5/5 - 3*s**4/2 - 2*s**3 + 3*s**2/2 + 3*s - 2. Factor r(q).
3*(q - 1)**2*(q + 1)**3
Let y(u) be the first derivative of -u**4/4 + 5*u**3/3 - 7*u**2/2 + 3*u + 7. Let y(x) = 0. Calculate x.
1, 3
Factor -6*b - b**3 - 11*b + 12*b - 4*b**2 - 2.
-(b + 1)**2*(b + 2)
Let t(i) be the third derivative of i**8/1176 + i**7/735 - i**6/210 - i**5/105 + i**4/84 + i**3/21 - 3*i**2. Factor t(o).
2*(o - 1)**2*(o + 1)**3/7
Let y(v) = -v**3 - 3*v**2 - v**2 - v - v**2. Let l be y(-5). Find n such that n**3 + 0*n - 2 - 3*n**4 + l*n**2 + 2*n**3 + n - 4*n**3 = 0.
-1, 2/3, 1
Factor -4 - 5*o**2 + 12*o**2 