 - 2)*(i - 1)
Let x(t) be the third derivative of 1/4*t**4 - 2/5*t**5 + 7/60*t**6 + 0 + 0*t + 2/3*t**3 + 6*t**2. Determine j, given that x(j) = 0.
-2/7, 1
Let s(b) be the second derivative of b**6/60 + b**5/30 - b**4/6 - 3*b**2/2 - 2*b. Let a(q) be the first derivative of s(q). Suppose a(d) = 0. What is d?
-2, 0, 1
Let r(i) = 7*i**2 + 11*i + 6. Let a(y) = -y**2 - y - 1. Let c(g) = -6*a(g) - r(g). Factor c(b).
-b*(b + 5)
Let a = -235 - -238. Let 3/2*g**2 + 1/2*g**4 + 0 + 3/2*g**a + 1/2*g = 0. Calculate g.
-1, 0
Let c(z) be the third derivative of z**6/180 - z**5/45 + z**4/36 + 20*z**2. Factor c(t).
2*t*(t - 1)**2/3
Let a = 9 - 7. Solve w**4 - w**a + w**5 + 2*w**2 - w**3 - 2*w**4 = 0 for w.
-1, 0, 1
Let a be (-2)/((-4)/14) + 3. Let m be 1*-2 + 32/a. Factor 4/5 - 2*b**2 - m*b.
-2*(b + 1)*(5*b - 2)/5
Suppose 6 = 3*a - 0. Solve 8*b + 3 + a - 5 + 2*b**4 - 6*b**3 = 0.
-1, 0, 2
Determine p, given that -2/3*p**5 - 22*p + 16/3*p**2 - 4/3*p**4 + 12 + 20/3*p**3 = 0.
-3, 1, 2
Let s = 281/3 - 93. Factor -s*x**2 - 2/3*x + 4/3*x**3 + 0.
2*x*(x - 1)*(2*x + 1)/3
Factor 0 + 0*o + 36/5*o**4 - 27/5*o**3 + 6/5*o**2 - 3*o**5.
-3*o**2*(o - 1)**2*(5*o - 2)/5
Let s(b) be the first derivative of -b**6/3 + 6*b**5/5 - 3*b**4/2 + 2*b**3/3 - 1. Find x such that s(x) = 0.
0, 1
Let v = -2/2217 + 6661/11085. Let v*x**5 - 3/5*x**2 + 0 + 7/5*x**4 + 3/5*x**3 - 2/5*x = 0. What is x?
-1, 0, 2/3
Let b be (-4)/((-12)/(-3))*0/(-3). Solve 1/4*v**2 + b + 1/2*v = 0.
-2, 0
Let b = -2/191 - -197/573. Factor 1/3*i**2 + 0*i + b*i**3 + 0.
i**2*(i + 1)/3
Let p(w) = 39*w**3 - 66*w**2 - 51*w. Let z(n) = 3*n**3 - 4*n + 0*n**3 + n**2 + 0*n - 6*n**2. Let h(b) = 2*p(b) - 27*z(b). Determine m, given that h(m) = 0.
-1, 0, 2
Let d(l) be the first derivative of 0*l**2 - 36/5*l**5 - 1 - 2*l**3 + 0*l - 33/4*l**4. Suppose d(k) = 0. Calculate k.
-2/3, -1/4, 0
Let g(r) = r**2 + r. Let b(x) = 2*x**2 - 6*x. Let c(m) = -b(m) - 2*g(m). Factor c(a).
-4*a*(a - 1)
Let o(v) be the first derivative of 5 - 3/4*v**4 + 0*v + 0*v**2 + v**3. Factor o(l).
-3*l**2*(l - 1)
Let l(t) be the second derivative of 1/70*t**7 - 3/50*t**5 + 0 + 0*t**6 + 8*t + 0*t**4 + 0*t**2 + 1/10*t**3. Determine p, given that l(p) = 0.
-1, 0, 1
Let t(b) be the first derivative of b**4 + 4*b**3/3 - 16*b**2 - 48*b - 15. Factor t(n).
4*(n - 3)*(n + 2)**2
Let i(r) be the second derivative of r**5/240 + r**4/96 - r**2 - 3*r. Let q(j) be the first derivative of i(j). Find c such that q(c) = 0.
-1, 0
Factor -2/13*s + 0*s**2 + 0 + 2/13*s**3.
2*s*(s - 1)*(s + 1)/13
Suppose -5*q + 4*p - 126 = -16, 3*p - 115 = 5*q. Let x = q + 26. Factor 1/5*m**3 + 1/5*m**4 + 0*m**2 + x + 0*m.
m**3*(m + 1)/5
Let d(m) be the first derivative of 4*m**3/3 - 1. What is q in d(q) = 0?
0
Let l be ((-20)/(-8))/(1/2). Let s(p) = -p + 7. Let c be s(l). Factor 2/7*a**3 + 2/7*a + 0 - 4/7*a**c.
2*a*(a - 1)**2/7
Let z(c) be the third derivative of 4*c**2 + 0*c**3 + 0*c**4 - 1/336*c**8 + 0 + 1/120*c**6 + 1/840*c**7 + 0*c - 1/240*c**5. What is k in z(k) = 0?
-1, 0, 1/4, 1
Solve -18/7*r + 0 - 18/7*r**2 + 2/7*r**3 + 2/7*r**4 = 0 for r.
-3, -1, 0, 3
Let u be (1 - 48/(-30)) + (-4)/(-10). Factor 0*o**2 - 1/3*o + 0 + 1/3*o**u.
o*(o - 1)*(o + 1)/3
Let g = -5 - -7. Suppose k = 4*k - g*w - 16, -5 = w. Suppose 4*b**3 - b - k*b**2 + b**3 - 6*b**3 = 0. What is b?
-1, 0
Let p(j) = 11*j**3 - 11*j**2 - 7*j + 5. Let x(b) = -b + 8 - 12*b + 3*b - 23*b**2 + 17*b**3 + 6*b**2. Let q(a) = 8*p(a) - 5*x(a). Find f such that q(f) = 0.
-1, 0, 2
Let w(o) be the second derivative of -27*o**6/10 - 27*o**5/5 - 3*o**4/2 + 2*o**3 + 3*o**2/2 + 11*o. Let w(z) = 0. What is z?
-1, -1/3, 1/3
Let x(d) be the third derivative of 0 + 1/3*d**4 - 1/30*d**5 + 6*d**2 + 0*d - 4/3*d**3. Factor x(c).
-2*(c - 2)**2
Let c = 5 + -2. Factor -2*r**3 - r**4 - r**3 + 5*r**c - r**2.
-r**2*(r - 1)**2
Let s(p) be the second derivative of -3*p + 0*p**2 + 2/15*p**3 + 0 + 1/30*p**4. Factor s(l).
2*l*(l + 2)/5
Let p be (5/(-2*10))/((-4)/12). Factor -1/4*t**2 - p - t.
-(t + 1)*(t + 3)/4
Let n be (-1)/(1 + 1)*0. Let f(q) be the second derivative of -1/10*q**5 + 0*q**4 + n*q**2 + q + 0 + 1/3*q**3. Determine j so that f(j) = 0.
-1, 0, 1
Let d(g) be the third derivative of 1/150*g**5 + 2/15*g**3 + 3*g**2 + 0*g + 1/20*g**4 + 0. Factor d(s).
2*(s + 1)*(s + 2)/5
Let t(r) be the second derivative of -r**6/50 + 3*r**5/50 - r**4/20 + 8*r. Factor t(q).
-3*q**2*(q - 1)**2/5
Suppose 0*q = -5*q + 10. Let m be q*4/((-24)/(-9)). Factor 3*h**2 + h**4 - 2*h**2 + h**5 - 2*h**2 - h**m.
h**2*(h - 1)*(h + 1)**2
Let o(u) = u + 15. Let f be o(-11). Factor 10 - 10 - 5*i**2 + 2*i - f*i.
-i*(5*i + 2)
Suppose 0 = -z + 10 - 6. Let -2*g**2 - 2*g**3 + 2*g + 0*g**4 - g**z - 5*g**2 + 8*g**2 = 0. Calculate g.
-2, -1, 0, 1
Let s(u) be the first derivative of u**6/30 - 6*u**5/25 + 2*u**4/5 + 2*u**3/5 - 9*u**2/10 + 37. Factor s(y).
y*(y - 3)**2*(y - 1)*(y + 1)/5
Factor 2*j**3 + 15 + 26 + 31 + 26*j**2 - 4*j**3 - 96*j.
-2*(j - 6)**2*(j - 1)
Let m(s) = -35*s**4 - 100*s**3 + 100*s**2 + 55. Let i(b) = 4*b**4 + 11*b**3 - 11*b**2 - 6. Let g(z) = 55*i(z) + 6*m(z). Factor g(j).
5*j**2*(j + 1)*(2*j - 1)
Let v(q) be the third derivative of q**5/80 - 3*q**4/32 - q**3/2 - 5*q**2. Factor v(b).
3*(b - 4)*(b + 1)/4
Let m(w) be the second derivative of 0 + 6*w + 1/42*w**4 + 0*w**2 - 1/21*w**3. Suppose m(k) = 0. What is k?
0, 1
Let y(p) be the third derivative of p**8/90720 - p**7/22680 - p**5/30 + 4*p**2. Let b(w) be the third derivative of y(w). Let b(v) = 0. Calculate v.
0, 1
Let b(l) be the first derivative of l**5/25 - l**3/5 + l**2/5 + 3. Suppose b(s) = 0. Calculate s.
-2, 0, 1
Suppose 2*u + 2*l + 20 - 26 = 0, 0 = -4*u - 3*l + 11. Factor -4/9 - 2/9*s + 2/9*s**u.
2*(s - 2)*(s + 1)/9
Let d = -32222/5 - -6476. Let z = 174/5 - d. Factor 0 + 4/5*a**2 - z*a**4 + 2/5*a**3 + 2*a**5 + 0*a.
2*a**2*(a - 1)**2*(5*a + 2)/5
Let j(v) = 3*v**3 - 8*v**2 - 22*v + 38. Let r(g) = -20*g**3 + 55*g**2 + 155*g - 265. Let k(a) = 15*j(a) + 2*r(a). Suppose k(c) = 0. What is c?
-2, 2
Let o = 371/30 + -61/5. Let x(j) be the first derivative of 0*j**3 + 0*j + o*j**2 - 1/12*j**4 + 4. What is f in x(f) = 0?
-1, 0, 1
Let f = 41 + -35. Let l(g) be the second derivative of 0 + 1/2*g**2 + 11/8*g**4 + g - 29/40*g**5 + 3/20*g**f - 5/4*g**3. Solve l(t) = 0.
2/9, 1
Let p(f) = -2*f**2 + 30*f - 72. Let l be p(3). Find m such that m - 1/3*m**3 + l*m**2 - 2/3 = 0.
-2, 1
Let p = 640/3 + -213. Factor 0 + 1/3*h**3 + p*h + 2/3*h**2.
h*(h + 1)**2/3
Let u(g) be the third derivative of -g**7/2520 - g**6/240 - g**5/60 - 5*g**4/24 + 3*g**2. Let m(i) be the second derivative of u(i). Factor m(s).
-(s + 1)*(s + 2)
Let v(p) be the second derivative of 2*p**2 + 1/12*p**4 + 2*p + 0 + 2/3*p**3. Determine o, given that v(o) = 0.
-2
Find b, given that 8*b - 3*b**2 + 16*b + b - 7*b = 0.
0, 6
Let n(l) be the second derivative of -l**5/70 - l**4/42 + 8*l. Let n(t) = 0. Calculate t.
-1, 0
Let s(k) be the third derivative of -16*k**7/1365 - 2*k**6/65 + k**5/26 - k**4/78 + 34*k**2. Let s(i) = 0. Calculate i.
-2, 0, 1/4
Let i(f) be the third derivative of -f**7/210 - 15*f**2. Factor i(p).
-p**4
Let l = -6 - -8. Suppose 0 = -4*p - 16, l*p + 13 = 3*w + p. Factor -5/2*i**4 - 1 - 21/2*i**2 - 11/2*i - 17/2*i**w.
-(i + 1)**3*(5*i + 2)/2
Suppose 0 = q - 5 - 5. Let a(d) = -29*d + 6 - 17*d**2 - q - 7 - 7*d**3. Let j(m) = -4*m**3 - 9*m**2 - 15*m - 5. Let g(n) = 3*a(n) - 5*j(n). Factor g(z).
-(z + 2)**3
Let d(h) be the third derivative of 11*h**7/140 + h**6/4 + 7*h**5/40 - h**4/8 + 23*h**2. Suppose d(c) = 0. Calculate c.
-1, 0, 2/11
Let k(f) be the first derivative of 4*f**5/5 - f**4/2 - 13*f**3/4 - 17*f**2/8 - f/2 - 4. Determine h so that k(h) = 0.
-1, -1/4, 2
Suppose -2*r + g = -0 + 5, 5*g - 25 = 2*r. Suppose r*z = -2*z. Determine m, given that z*m**2 + m**3 - 1/2*m**4 + 1/2 - m = 0.
-1, 1
Let k(x) = -x**3 - 4*x**2 + 5*x + 1. Let s be k(-5). Suppose -4*t + 5*t = s. Factor -6*h**2 + h**3 - t + 6*h - 1 + h**3.
2*(h - 1)**3
Let v = -11/9 + 73/45. Let g(r) be the second derivative of 0 - 1/10*r**5 + 1/15*r**4 - v*r**2 + 3*r + 1/3*r**3. Factor g(h).
-2*(h - 1)*(h + 1)*(5*h - 2)/5
Let m(z) = z**3 - z**2 - z + 1. Let b be m(5). Determine o, given that -b*o**3 - 18*o**4 - 80*o**2 - 37*o**4 - 7*o**5 + 11*o**4 - 16*o = 0.
-2, -2/7, 0
Suppose k - 4*z - 6 = 0, -5*z - 2 = 4*k - 5. 