(i) = 0.
-1, 0, 1
Factor 0 + 3/5*x**3 + 0*x - 6/5*x**2.
3*x**2*(x - 2)/5
Suppose 2*g - 6 = h, 5*g + 0 = h + 15. Let r(c) be the second derivative of c + 0 + 1/48*c**4 + 1/24*c**g + 0*c**2. Determine k so that r(k) = 0.
-1, 0
Suppose n - 6 = -n. Determine t so that -12 - 15*t**2 + 24*t + 17*t**2 - 10*t**2 - 7*t**2 + n*t**3 = 0.
1, 2
Suppose -6 = -a - 6. Let r(y) be the second derivative of 1/6*y**4 + 3*y - 1/15*y**6 + a*y**2 + 1/42*y**7 + 0*y**5 + 0 - 1/6*y**3. Factor r(m).
m*(m - 1)**3*(m + 1)
Let i(w) be the second derivative of -w**9/1512 + w**8/168 - 2*w**7/105 + w**6/45 + w**3/6 - 4*w. Let p(a) be the second derivative of i(a). Solve p(v) = 0.
0, 1, 2
Let j be (1/2)/((-3)/72). Let g = -6 - j. Determine d, given that 10*d**3 + 2*d**5 - g*d**4 - 5*d**2 + d**2 - 2*d**4 = 0.
0, 1, 2
Let y(n) be the second derivative of n**6/360 - 7*n**5/360 + n**4/36 - 5*n**3/6 - n. Let d(c) be the second derivative of y(c). Factor d(u).
(u - 2)*(3*u - 1)/3
Suppose -j = -0*x + 2*x - 2, 0 = -2*j + x + 4. Suppose -j*h = -6*h + 8. Suppose -1/5*f**5 + 0 + 0*f - 3/5*f**4 - 3/5*f**3 - 1/5*f**h = 0. What is f?
-1, 0
Factor 3*a**2 - 3/2*a**3 + 3/2*a - 3.
-3*(a - 2)*(a - 1)*(a + 1)/2
Suppose -3*v - 2*v = 10. Let t be (-6 + 4/2)/v. Find b, given that 4*b**4 - 2 - 2*b + 4*b - 10*b**3 - b**2 + 7*b**t = 0.
-1/2, 1
Let n(d) be the first derivative of 0*d**3 - 1/20*d**5 + 1/8*d**4 - 1/4*d**2 + 1/4*d - 3. Factor n(a).
-(a - 1)**3*(a + 1)/4
Factor 0*y**4 + 0 + 1/4*y**3 - 1/4*y**5 + 0*y**2 + 0*y.
-y**3*(y - 1)*(y + 1)/4
Suppose b + 10*b = 33. Factor -3/4*k**2 - 1/4*k**b + 0*k + 1.
-(k - 1)*(k + 2)**2/4
Let g = -511 + 515. Let x = 0 + 0. Determine t, given that x + 5/2*t**2 + 1/2*t + 2*t**4 + g*t**3 = 0.
-1, -1/2, 0
Suppose -5 = 5*d - 0. Let m be (0 - d)/(5/15). Let -2*w**5 + 2*w**3 - w**4 + 3*w**5 - w**4 - w**m = 0. Calculate w.
0, 1
Factor 6*l**3 - 4*l**2 - 2 + 45*l - 40*l - 5*l**3.
(l - 2)*(l - 1)**2
Let x(o) = -3*o**2 - 8*o + 12. Let n(j) = j**2 + 1. Let h(d) = 4*n(d) + x(d). Determine v, given that h(v) = 0.
4
Let m(y) be the first derivative of -y**3 - 7*y**2/6 + 2*y/3 - 11. Factor m(i).
-(i + 1)*(9*i - 2)/3
Let s(j) = 5*j**3 + 2*j**2 + 5*j + 4. Let n(u) = 0*u**3 - 3 - 4*u - 4*u**3 - 6*u**2 + 5*u**2. Let g(x) = 4*n(x) + 3*s(x). Factor g(d).
-d*(d - 1)**2
Let k(x) be the third derivative of -2*x**2 + 0*x + 5/24*x**4 + 1/120*x**6 + 0 + 1/3*x**3 + 1/15*x**5. Suppose k(o) = 0. What is o?
-2, -1
Let r(j) be the first derivative of -j**4/14 - 8*j**3/21 - 5*j**2/7 - 4*j/7 - 4. Suppose r(a) = 0. Calculate a.
-2, -1
Let f(w) be the second derivative of -w**7/231 + w**6/55 - 3*w**5/110 + w**4/66 + 35*w. Find r such that f(r) = 0.
0, 1
Let x(k) be the second derivative of -k**6/6 - 3*k**5/2 - 5*k**4 - 20*k**3/3 + 18*k. Factor x(z).
-5*z*(z + 2)**3
Let r(u) = 32*u**2 - 67*u + 36. Let d(x) = -x**2 + x. Let h(j) = 21*d(j) + 3*r(j). Factor h(y).
3*(5*y - 6)**2
Let s be (16/12)/(2*2). Let c(l) be the first derivative of 1/2*l + 1/4*l**2 - s*l**3 - 1/4*l**4 + 1/12*l**6 - 1 + 1/10*l**5. Determine j so that c(j) = 0.
-1, 1
Let q(g) be the third derivative of -g**7/420 - g**6/60 - g**5/24 - g**4/24 + 5*g**2. Factor q(f).
-f*(f + 1)**2*(f + 2)/2
Let m be 1 + 285/(-429) - (-2)/(-11). Determine c, given that 0*c + 2/13*c**2 + m*c**4 - 4/13*c**3 + 0 = 0.
0, 1
Suppose 12*c = 8*c. Solve -1/4*z**2 - 1/4*z + c = 0.
-1, 0
Let v(u) be the third derivative of u**6/80 - u**4/16 - 9*u**2. Determine n, given that v(n) = 0.
-1, 0, 1
Let v = -1/11 + 26/165. Let p(r) be the second derivative of 1/5*r**2 + v*r**3 - 1/30*r**4 - 1/50*r**5 + 0 - 4*r. Factor p(x).
-2*(x - 1)*(x + 1)**2/5
Let f be 0 - ((0 - (-116)/(-36)) + 3). Factor -2/9*y**2 + f + 0*y.
-2*(y - 1)*(y + 1)/9
Suppose -2*r = 3*r - 20. Let n be 16/(-8)*5/(-2). Factor -3*q**5 + 8*q**3 + 4*q**2 + n*q**4 + r*q**5 + 0*q**2.
q**2*(q + 1)*(q + 2)**2
Let q(x) be the second derivative of -x**4/4 - 2*x**3 - 6*x**2 - 2*x. Factor q(y).
-3*(y + 2)**2
Let r be ((-1330)/24)/(-7) + (-3)/12. What is n in 0 + r*n**4 + 1/3*n - 4*n**5 - n**2 - 3*n**3 = 0?
-1/3, 0, 1/4, 1
Let a = 42552 + -6978475/164. Let v = a + -3/41. Factor 1/4*x**2 + 1/4*x + 0 - v*x**4 - 1/4*x**3.
-x*(x - 1)*(x + 1)**2/4
Let j(k) be the third derivative of k**8/6720 + k**7/840 - k**6/80 - k**5/30 + 5*k**2. Let r(t) be the third derivative of j(t). Solve r(i) = 0 for i.
-3, 1
Let y(w) = -w**2 - 9*w. Let h be y(-9). Solve 2/3*u**3 + h*u**2 + 0*u + 0 - 7/3*u**4 = 0 for u.
0, 2/7
Let x(y) be the third derivative of y**6/120 + y**5/20 + 6*y**2. Find o, given that x(o) = 0.
-3, 0
Let g(k) = k**3 + k - 2. Let o be g(-2). Let j be (30/(-9))/(8/o). Find x such that -9*x**4 + 9*x + 6*x**2 - 8*x**3 - 5*x**3 - 4*x**5 + x**j + 3 + 7*x**3 = 0.
-1, 1
Let g(n) be the first derivative of -4*n**5/5 - 2*n**4 + 4*n**3/3 + 4*n**2 - 18. Factor g(a).
-4*a*(a - 1)*(a + 1)*(a + 2)
Suppose 72 = -45*y + 63*y. Factor 0 + 2/9*w**2 + 1/9*w**y + 0*w - 1/3*w**3.
w**2*(w - 2)*(w - 1)/9
Let l(h) be the first derivative of 2 + 0*h**3 + 1/5*h**2 - 1/30*h**4 - h. Let q(x) be the first derivative of l(x). Solve q(v) = 0 for v.
-1, 1
Solve -1/4*g**3 + 1/4 + 1/4*g - 1/4*g**2 = 0 for g.
-1, 1
Let g(i) be the second derivative of 0*i**3 + 3*i + 0 - 1/36*i**4 + 1/6*i**2. What is o in g(o) = 0?
-1, 1
Let j(k) = k - 5. Let l be j(6). Let x be 12/4*1/l. Determine d so that -1/2*d**2 + 0*d + 1/2*d**x + 0 = 0.
0, 1
Let i be 1 - (-11)/(-24) - (-13)/104. Factor 0*w**3 - 2/3*w**4 + 0 + i*w**2 + 0*w.
-2*w**2*(w - 1)*(w + 1)/3
Let w be (2/5)/(6/60). Let i = w + -2. Let -4*z + 0*z**2 - 3*z**i + 4*z = 0. Calculate z.
0
Factor -1 + 2*k**3 - 3*k**3 - 2*k**2 - k**2 + 0*k - 3*k.
-(k + 1)**3
Let u(r) be the third derivative of -r**7/56 + 7*r**6/160 - r**5/40 + 6*r**2. What is b in u(b) = 0?
0, 2/5, 1
Let j be ((-6)/7)/((-1)/7). Let n = -2 + j. Solve 0*l + 0 - 7/5*l**3 - 3/5*l**5 - 2/5*l**2 - 8/5*l**n = 0 for l.
-1, -2/3, 0
Let g(s) = -9*s**2 - s. Let x(f) = -f**2. Let z(w) = 3*g(w) - 24*x(w). Determine a so that z(a) = 0.
-1, 0
Let u(a) be the first derivative of -2*a**3/3 - 2*a**2 - 2*a + 5. Let u(v) = 0. Calculate v.
-1
Let z = -2/117 - -43/234. Let y(u) be the third derivative of 0*u + 3*u**2 - 1/12*u**4 - 1/60*u**5 + 0 + z*u**3 + 1/60*u**6. Factor y(m).
(m - 1)*(m + 1)*(2*m - 1)
Let c(m) = m**2 + 7*m + 2. Let z be c(-7). Let 2/3*x + 0 - 1/3*x**z = 0. What is x?
0, 2
Suppose 4*q - 18 + 10 = 0. Factor -4/9 + 10/9*n**3 - q*n**2 + 14/9*n - 2/9*n**4.
-2*(n - 2)*(n - 1)**3/9
Let m = 14/5 + -8/3. Let l(o) be the second derivative of -1/75*o**6 + m*o**3 + 0*o**4 + 1/5*o**2 + 3*o + 0 - 1/25*o**5. Factor l(f).
-2*(f - 1)*(f + 1)**3/5
Let o(y) be the second derivative of 0 + 1/24*y**4 + 0*y**3 + 3*y - 1/4*y**2. Solve o(a) = 0 for a.
-1, 1
Let x(j) be the first derivative of 3/20*j**4 + 3/25*j**5 + 3 - 3/10*j**2 - 1/5*j**3 + 0*j. Factor x(i).
3*i*(i - 1)*(i + 1)**2/5
Suppose -4*k = -0*t - t - 12, t + 10 = 3*k. Let w(q) = -q**2 + 4*q + 1. Let u(z) = -3*z**2 + 9*z + 2. Let j(s) = k*u(s) - 5*w(s). Factor j(p).
-(p + 1)**2
Let u(o) = -9*o + 2*o + o**2 + 8*o**2. Let l(d) = -45*d**2 + 36*d. Let g(s) = 4*l(s) + 21*u(s). Factor g(y).
3*y*(3*y - 1)
Let 14*l**3 + 0*l**2 + 8 + 7*l**3 + 4*l + 4*l**4 - 28*l**2 + 8*l**5 - 49*l**3 = 0. Calculate l.
-1, 1/2, 2
Let p(y) be the third derivative of -y**6/540 - y**5/270 - y**2. Find f such that p(f) = 0.
-1, 0
Factor -2/9*n**4 + 4/9*n + 0 + 8/9*n**3 - 10/9*n**2.
-2*n*(n - 2)*(n - 1)**2/9
Let n(v) be the third derivative of 0*v**4 + 1/300*v**6 - v**2 + 0*v + 4/525*v**7 + 0*v**3 - 1/280*v**8 + 0 - 1/75*v**5. Factor n(o).
-2*o**2*(o - 1)**2*(3*o + 2)/5
Suppose x + 0 = 6. Let k be x/15 - 2/5. Factor 4/3*o - 4/3*o**3 + k*o**2 - 2/3*o**4 + 2/3.
-2*(o - 1)*(o + 1)**3/3
Suppose w + 0*w - 4 = 0. Let a be w - 0 - (0 + 1). Let -4*u**5 + 2*u**2 + 4*u**a - 10*u**2 + 0*u**3 + 6*u**4 + 2 = 0. Calculate u.
-1, -1/2, 1
Suppose 5*q - r - 11 = 0, -2*r - 8 = -q - 2*q. Determine t so that -2/5 + 2/5*t + 2/5*t**q - 2/5*t**3 = 0.
-1, 1
Let 3/5*w**2 + 9/5*w - 6/5 - 9/5*w**3 + 3/5*w**4 = 0. Calculate w.
-1, 1, 2
Let i = -3 + 5. Solve -2*a + i*a**2 - 2/3*a**3 + 2/3 = 0 for a.
1
Let j(p) = -4*p + 1. Let v be -4 + (2 - (-3 + 2)). Let z be j(v). Factor 14/3*a**3 - 2/3*a**2 - 16/3*a**4 + 0 - 32/3*a**z + 0*a.
-2*a**2*(a + 1)*(4*a - 1)**2/3
Let r(i) be the second