 third derivative of n(t). Suppose i(b) = 0. What is b?
-2, -1
Factor 2/5*i**2 - 14/5*i + 12/5.
2*(i - 6)*(i - 1)/5
Let n be 3/10 + (-2)/(-10). Let w(r) be the first derivative of -1/10*r**5 + 0*r**2 + 1 - n*r + 1/3*r**3 + 0*r**4. Factor w(x).
-(x - 1)**2*(x + 1)**2/2
Let w(x) be the first derivative of -2*x**3/9 + 2*x/3 - 10. Suppose w(d) = 0. What is d?
-1, 1
Let r(i) = -i**3 + 2*i - 1. Let a be r(-2). Let b(o) be the first derivative of 1/9*o**a + 0*o**2 + 1/12*o**4 + 0*o - 2. What is q in b(q) = 0?
-1, 0
Let t be -8 - -1 - (-1 + 0). Let u = t - -11. Factor g**5 - 1 - g**4 + 6*g**3 - 2*g - 2*g**u - 4*g**3 + 2*g**2 + g.
-(g - 1)**2*(g + 1)**3
Factor 1/3*o + 0 - 1/6*o**4 + 1/6*o**2 - 1/3*o**3.
-o*(o - 1)*(o + 1)*(o + 2)/6
Let k(f) = -f + 1. Let y be k(0). Let s be 0 + 2 + 0/y. Factor -13*w - s*w**2 + 13*w.
-2*w**2
Let s = -429 - -432. Suppose 1/3 + 5/3*u**4 + 10/3*u**s + 1/3*u**5 + 5/3*u + 10/3*u**2 = 0. What is u?
-1
Let h be 9/189 - ((-2)/(-7))/(-1). Suppose -h*g**4 + 2/3*g - 2/3*g**3 + 0*g**2 + 1/3 = 0. What is g?
-1, 1
Let y(a) = -a**2 + 7. Let x be y(0). Let g = -5 + x. Factor 2*q**g - 2*q**2 - 2*q - 1 - q**2.
-(q + 1)**2
Let i(l) be the third derivative of -41/120*l**6 + 2/3*l**4 + 25/336*l**8 + 0 + 1/42*l**7 + 0*l - 2/3*l**3 - 7*l**2 - 1/60*l**5. Let i(w) = 0. Calculate w.
-1, 2/5, 1
Let u(f) = -f**2 - 3*f - 11. Let m(h) = -h - 1. Let c(t) = 10*m(t) + 2*u(t). Factor c(v).
-2*(v + 4)**2
Find g such that 32*g - 39*g**2 + 18*g**3 + 4*g - 3*g**4 + 34 - 46 = 0.
1, 2
Let t be 3/((-9)/6 + 3). Solve -49*y**3 - 16*y + 8 - 6*y - 38*y + 126*y**t = 0 for y.
2/7, 2
Let b be 1/1 + (-4 - 3). Let o be -3 - -1*(-21)/b. Factor -1/2*v**2 + 0 + o*v.
-v*(v - 1)/2
Let v = -3269/2 + 1605. Let t = 30 + v. Factor 0 + 1/2*w + t*w**2.
w*(w + 1)/2
Let l(c) be the third derivative of -9*c**6/200 - 13*c**5/100 + 7*c**4/30 - 2*c**3/15 - 38*c**2. Find s, given that l(s) = 0.
-2, 2/9, 1/3
Let -3/2 + 2*b - 1/2*b**2 = 0. Calculate b.
1, 3
Suppose 2*r - 4 = -0. Let l(m) be the second derivative of 5/18*m**4 + 0 + 4/45*m**6 - 4/15*m**5 - 1/9*m**3 + m + 0*m**r. Factor l(c).
2*c*(c - 1)*(2*c - 1)**2/3
Let a(u) be the first derivative of 1/4*u**4 + 1/3*u**6 + 10 + 7/10*u**5 - 1/6*u**3 + 0*u + 0*u**2. Determine h, given that a(h) = 0.
-1, 0, 1/4
Let m be (3/(945/(-28)))/(1/(-10)). Factor -m - 2/9*q**2 - 8/9*q.
-2*(q + 2)**2/9
Suppose 5*c**2 - 15 - 15*c + c + 24*c = 0. What is c?
-3, 1
Let p(u) be the third derivative of u**8/1680 + u**7/1050 - u**6/600 - u**5/300 + 36*u**2. Find t such that p(t) = 0.
-1, 0, 1
Determine z so that 10*z**5 - 2*z**5 - 12*z**3 + 4*z + 4*z**4 + 3*z**2 - 2*z**2 - 5*z**2 = 0.
-1, 0, 1/2, 1
Let t(q) be the third derivative of q**7/525 + q**6/75 + q**5/30 + q**4/30 + 16*q**2. Factor t(h).
2*h*(h + 1)**2*(h + 2)/5
Let d(r) be the first derivative of -r**7/735 - r**6/420 + r**5/210 + r**4/84 + 5*r**2/2 + 1. Let v(s) be the second derivative of d(s). Factor v(t).
-2*t*(t - 1)*(t + 1)**2/7
Let w(o) be the first derivative of o**6/18 - 4*o**5/15 + o**4/3 + 24. Factor w(f).
f**3*(f - 2)**2/3
Let r(z) = 21*z**2 - 36*z - 9. Let j(d) = 21*d**2 - 36*d - 8. Let c(a) = 3*j(a) - 4*r(a). Find i such that c(i) = 0.
-2/7, 2
Let q be (6 - 1)*144/360. Determine x so that 2/5*x**3 - 4/5*x**q + 2/5*x + 0 = 0.
0, 1
Let o(x) be the third derivative of 0 - 4*x**2 + 0*x**4 + 0*x - 1/180*x**6 + 1/225*x**5 + 0*x**3. What is m in o(m) = 0?
0, 2/5
Let n(j) be the first derivative of -j**7/3360 - j**6/720 - j**5/480 + j**3/3 - 3. Let x(g) be the third derivative of n(g). Find r such that x(r) = 0.
-1, 0
Let q be (-4 + 7)*-2 + 6. Factor 0*l**3 - 4/7*l**2 + q*l + 2/7 + 2/7*l**4.
2*(l - 1)**2*(l + 1)**2/7
Let d(w) be the first derivative of 3*w**5/20 + 3*w**4/8 - 3*w**2/4 - 3*w/4 + 27. Factor d(v).
3*(v - 1)*(v + 1)**3/4
Factor 2/5*t**3 + 0*t + 0 + 2/5*t**2.
2*t**2*(t + 1)/5
Let k(s) = s**2 + s + 1. Let f(m) = 2*m**2 - 2*m + 8. Let y(j) = -f(j) + 12*k(j). Factor y(t).
2*(t + 1)*(5*t + 2)
Find d, given that 0 - 1/3*d - 4/3*d**2 = 0.
-1/4, 0
Suppose 2*d - 7 = 5*c + 17, 0 = -5*d - c + 6. Determine h, given that 27*h + 4*h**d - 3*h**3 + 4*h**3 + 27 + 5*h**2 = 0.
-3
Let w(c) be the first derivative of c**3/3 - 4*c - 12. Suppose w(a) = 0. Calculate a.
-2, 2
Let l(y) be the second derivative of 5*y**4/4 - 2*y**3 - 3*y**2/2 + 5*y. Factor l(c).
3*(c - 1)*(5*c + 1)
Let 1/4 + 3/4*v**2 + 1/4*v**3 + 3/4*v = 0. What is v?
-1
Suppose 10 = -9*v + 4*v. Let l be ((-3)/2)/(v/4). Factor c**3 + 4 + 2 - l*c - 4.
(c - 1)**2*(c + 2)
Let y be ((-91)/(-14) + 1)*(-2)/(-3). Factor -4/7*f**4 + 0 + 2/7*f**y + 0*f**3 + 0*f + 0*f**2.
2*f**4*(f - 2)/7
Let d = 4 - 32. Let l = -111/4 - d. Let l*f**4 + 0*f + 0*f**2 + 0*f**3 + 0 + 1/4*f**5 = 0. What is f?
-1, 0
Factor -15*j**2 + 20*j**3 + 2*j**4 - 5*j**4 - 29*j - 2*j**4 + 20 + 9*j.
-5*(j - 2)**2*(j - 1)*(j + 1)
Let v(z) be the third derivative of 0*z**4 + 0*z**3 - 1/60*z**5 + 0*z + 6*z**2 - 1/210*z**7 + 1/60*z**6 + 0. Solve v(t) = 0 for t.
0, 1
Let m(c) = c**3 - 2*c**2 - c + 2. Let w be m(2). Let d(y) be the first derivative of 1/8*y**4 + 2 + w*y + 1/6*y**3 + 0*y**2. Solve d(n) = 0.
-1, 0
Factor 2/3*v**2 + 10/3*v**4 + 0 + 8/3*v**3 + 0*v + 4/3*v**5.
2*v**2*(v + 1)**2*(2*v + 1)/3
Let s(n) be the third derivative of n**5/60 - n**4/4 + 3*n**3/2 - 12*n**2. Find a such that s(a) = 0.
3
Let w = 8124808/59841 - -30/6649. Let f = 136 - w. Factor 0 + 2/9*l**4 - f*l**2 + 0*l + 0*l**3.
2*l**2*(l - 1)*(l + 1)/9
Determine g so that -5/4*g**2 + 1/4*g**3 + 7/4*g - 3/4 = 0.
1, 3
Let t(k) be the third derivative of 11*k**5/105 - 3*k**4/14 - 4*k**3/21 + 18*k**2. Solve t(g) = 0 for g.
-2/11, 1
Let u be 0/(-3) + 16*1. Suppose 6 - u = -5*d. Factor -4/7 - 2/7*b**d + 6/7*b.
-2*(b - 2)*(b - 1)/7
Suppose 9*i - 4*i + 4*y + 2 = 0, 2*i + 11 = -5*y. Let -3/2 + 6*w**3 - 27/2*w**i + 9*w = 0. What is w?
1/4, 1
Let 58*t**3 - 3*t - 59*t**3 + 0*t + t**4 - 5*t**2 = 0. What is t?
-1, 0, 3
Find l such that 1/6*l**2 + 5/3 - 11/6*l = 0.
1, 10
Let w(p) be the third derivative of p**6/30 + p**5/15 + 13*p**2. Factor w(m).
4*m**2*(m + 1)
Let r(q) be the second derivative of -q**7/945 + q**6/180 - q**5/90 + q**4/108 + q**3/2 - 4*q. Let w(o) be the second derivative of r(o). Factor w(v).
-2*(v - 1)**2*(4*v - 1)/9
Let m be 2 - ((-7092)/(-5))/4. Let r = -351 - m. Factor -10*z**5 + 32/5*z**3 + 0 + 0*z - r*z**2 - 2*z**4.
-2*z**2*(z + 1)*(5*z - 2)**2/5
Factor 0 - 6/5*q + 6/5*q**3 + 3/5*q**2 - 3/5*q**4.
-3*q*(q - 2)*(q - 1)*(q + 1)/5
Let a(v) = v**3 + 3*v**2 - 2*v - 1. Let z be a(-3). Factor 3*b**4 - b**5 + 2*b**2 - b**2 + 2*b**z + 3*b**3.
b**2*(b + 1)**3
Let l(f) = -4*f**2 + 4. Let p(x) = x**2 - 1. Let o(i) = 2*i**2 + i. Let w be o(-1). Let j(v) = w*l(v) + 3*p(v). Let j(n) = 0. Calculate n.
-1, 1
Let g(n) be the first derivative of -n**6/27 - 4*n**5/45 + n**4/9 + 16*n**3/27 + 7*n**2/9 + 4*n/9 - 4. Factor g(t).
-2*(t - 2)*(t + 1)**4/9
Let z = 34/15 + -21/10. Let d(q) be the second derivative of 0*q**2 - 1/42*q**7 + 0*q**5 + 1/6*q**4 + z*q**3 - 2*q - 1/15*q**6 + 0. Factor d(w).
-w*(w - 1)*(w + 1)**3
Let x(y) = 3*y**5 + y**4 + 5*y**3 - y**2 + 4*y - 4. Let n(j) = j**5 + j**3 + j - 1. Let q be (-3)/9 + 13/3. Let p(u) = q*n(u) - x(u). Let p(m) = 0. What is m?
-1, 0, 1
Let h(b) be the first derivative of -b**6/90 + b**5/60 + b**4/12 - 5*b**3/18 + b**2/3 + b - 3. Let o(a) be the first derivative of h(a). Solve o(i) = 0.
-2, 1
Suppose y - 5*y + 8 = 0. Factor -3 - f**4 - 7*f**y + 2*f**3 + 2*f**2 - 2*f + 9*f**2.
-(f - 3)*(f - 1)*(f + 1)**2
Let c(s) = -s - 2. Let h be c(-4). Determine x so that 2*x**2 + 0*x**h - 3*x + 8 + 11*x = 0.
-2
Let r(g) be the third derivative of g**7/525 + g**6/60 + 4*g**5/75 + g**4/15 + 11*g**2. Factor r(s).
2*s*(s + 1)*(s + 2)**2/5
Let i = 4 - 4. Suppose 9 = 3*l - i*l. Factor 0*y**5 - y**4 + 0*y**4 + y**2 + y**5 - y**l.
y**2*(y - 1)**2*(y + 1)
Determine f so that 0 + f - 1/2*f**4 + 0*f**3 + 3/2*f**2 = 0.
-1, 0, 2
Let i be (-120)/(-48) - (-2)/(-12). Suppose 0 + 2/3*s**2 + 0*s + 16/3*s**4 + i*s**5 + 11/3*s**3 = 0. What is s?
-1, -2/7, 0
Let j be -1*2*(-4)/4. Let d(g) be the first derivative of 0*g - 1/9*g**3 + j + 1/12*g**4 + 0*g**2. Determine c, given that d(c) = 0.
0, 1
Let g(p) be the first derivative of -1/2*p**3 + 0*p + 3/8*p**4 - 3/4*p**2 + 5 + 3/10*p**5. Factor g(u).
3*u*(u - 1)*(u + 1)**2/2
Find