rst derivative of x**5/30 + x**4/12 + x**3/18 + 6. Suppose u(y) = 0. Calculate y.
-1, 0
Let b(p) = p**3 - p. Let z(h) = -2*h**3 - 3*h**2 + 5*h - 4. Let m(r) = 3*b(r) + z(r). Let l be m(3). Factor 0 + 1/4*f**l - 1/4*f.
f*(f - 1)/4
Let x(h) be the third derivative of -h**6/420 + h**5/70 - h**4/42 - 3*h**2. Let x(n) = 0. Calculate n.
0, 1, 2
Factor 0 + 0*j - 6/5*j**2 + 2/5*j**3.
2*j**2*(j - 3)/5
Let h(o) = -o**3 - 3*o**2 + 3. Let v be h(-3). Suppose v*m = -3*k - 15, 4*k - 5 = 6*k + m. Let -2*p**3 + 4*p + k*p**2 + 0*p + 2*p**2 = 0. What is p?
-1, 0, 2
Let w(b) = 8*b**2 - b. Let l be w(1). Let t = l + -4. Suppose 9 + 4*a**t - 2*a**2 - 9 - 2*a**4 = 0. What is a?
0, 1
Let d(f) be the first derivative of -4*f**6/9 - 14*f**5/15 + f**4 + 14*f**3/9 - 2*f**2/3 - 8. Find k, given that d(k) = 0.
-2, -1, 0, 1/4, 1
Suppose 3/8*i**4 + 0*i**2 - 3/8*i**5 + 9/4*i**3 + 0*i + 0 = 0. What is i?
-2, 0, 3
Let q be (-97)/2328 - (-1)/6. Factor 0*m - q*m**2 + 0 + 1/8*m**4 + 1/8*m**3 - 1/8*m**5.
-m**2*(m - 1)**2*(m + 1)/8
Let r(w) be the second derivative of w**6/420 + w**5/105 - w**2/2 + 2*w. Let x(c) be the first derivative of r(c). Factor x(i).
2*i**2*(i + 2)/7
Let d = -19 - -23. Let f(j) = j**3 - 3*j**2 - 5*j + 4. Let m be f(d). Factor 0*l + m - 2/3*l**3 + 0*l**2.
-2*l**3/3
Let u be 2/(-36)*-6 + 2/6. Factor -u - 7/3*o - 1/3*o**4 - 3*o**2 - 5/3*o**3.
-(o + 1)**3*(o + 2)/3
Suppose 0 = 3*w - 3 - 6. Let z = 8 + -5. Suppose 5*x - z*x - 5*x**2 + w*x**2 = 0. Calculate x.
0, 1
Factor 0*y**3 + 8/5*y**4 + 0*y**2 + 2/5*y**5 + 0 + 0*y.
2*y**4*(y + 4)/5
Let t(x) be the third derivative of 1/3*x**3 + 0*x + 0 + 1/120*x**5 + 2*x**2 + 1/12*x**4. Let t(u) = 0. Calculate u.
-2
Let x(y) = -10*y**4 - 29*y**3 - 150*y**2 - 491*y - 625. Let p(c) = -c**4 - c**3 + c. Let m(o) = 18*p(o) - 2*x(o). Factor m(r).
2*(r + 5)**4
Let b(t) be the third derivative of -t**6/240 - t**5/80 - t**3/2 + 5*t**2. Let g(v) be the first derivative of b(v). Determine m so that g(m) = 0.
-1, 0
Let i = -3 + 5. Determine u so that -i*u + 0*u**2 + 4*u**2 + 2*u**2 - 2*u**2 - 2*u**3 = 0.
0, 1
Let z be ((-3)/(-9))/(1 + (-15)/18). Factor 0 + 4/11*l - 14/11*l**z.
-2*l*(7*l - 2)/11
Suppose -4*f = -3*w + 19, w - f = -w + 6. Suppose w + 1/2*b**2 + 3/2*b = 0. What is b?
-2, -1
Suppose 4*y + 6 = -14. Let d = y - -10. Factor -4/3*x**3 + 0 - 2/9*x + 8/9*x**2 + 8/9*x**4 - 2/9*x**d.
-2*x*(x - 1)**4/9
Let s(x) be the third derivative of x**5/30 - 4*x**3/3 - 17*x**2. Solve s(q) = 0 for q.
-2, 2
Let m(w) be the first derivative of -w**6/60 + w**5/10 - w**4/4 + w**3/3 + 2*w**2 + 1. Let u(p) be the second derivative of m(p). Factor u(g).
-2*(g - 1)**3
Let u(v) = -17*v - 15*v + 13*v**2 + 20 + 17. Let o(g) = -32*g**2 + 80*g - 92. Let p(d) = -5*o(d) - 12*u(d). Find c such that p(c) = 0.
2
Let a(y) be the second derivative of 1/10*y**6 - 5*y + 0 + 3/4*y**4 - 9/20*y**5 - 1/2*y**3 + 0*y**2. Suppose a(o) = 0. What is o?
0, 1
Let d be ((-82)/(-205))/((-4)/(-30)). Factor 68/5*l**d + 44/5*l - 4*l**4 - 8/5 - 84/5*l**2.
-4*(l - 1)**3*(5*l - 2)/5
Let c = 28 - 26. Let l = -23/3 + 8. Factor l*j**c + 1/3 + 2/3*j.
(j + 1)**2/3
Factor 16/3*k**2 - 8/3*k**4 - 4/3*k**5 + 4*k**3 + 0 - 16/3*k.
-4*k*(k - 1)**2*(k + 2)**2/3
Let n(k) be the second derivative of 8*k**6/3 + 18*k**5 + 125*k**4/12 - 45*k**3/2 + 10*k**2 + 45*k. Solve n(w) = 0 for w.
-4, -1, 1/4
Let l(u) = -37*u**4 + 77*u**3 - 43*u**2 + 8*u - 5. Let h(d) = -22*d**2 + 38*d**3 - 7 + 5*d - d + 5 - 18*d**4. Let p(r) = 5*h(r) - 2*l(r). Factor p(g).
-4*g*(g - 1)**2*(4*g - 1)
Let z(x) be the second derivative of x**6/30 - x**5/10 - x**4/12 + x**3/3 + 3*x. Factor z(u).
u*(u - 2)*(u - 1)*(u + 1)
Let v(h) be the first derivative of 7*h**6/3 - 38*h**5/5 + 15*h**4/2 - 2*h**3/3 - 2*h**2 + 28. Factor v(y).
2*y*(y - 1)**3*(7*y + 2)
Suppose -k + 1168 - 1165 = 0. Factor -2/3*m + 2/3*m**k - 1/6 + 1/6*m**2.
(m - 1)*(m + 1)*(4*m + 1)/6
Let s(j) = j**2 + j - 5. Let c(q) = 3*q**2 + 0*q**3 - 19 + 2*q**2 + 4*q - q**3. Suppose -30 = -2*r - 3*r. Let n(w) = r*c(w) - 22*s(w). Factor n(g).
-2*(g - 1)**2*(3*g + 2)
Let y(c) = 5*c**2 - 7*c - 5. Let w(j) = 3*j**2 - 4*j - 3. Let m(g) = -7*w(g) + 4*y(g). Factor m(q).
-(q - 1)*(q + 1)
Suppose -11*g + 6*g = -3*l - 22, -3*g + 10 = -l. Factor 3/2*p**g + 24 - 12*p.
3*(p - 4)**2/2
Let y(m) be the third derivative of 0 + 3*m**2 + 0*m - 1/36*m**4 + 0*m**3 + 1/180*m**5. What is g in y(g) = 0?
0, 2
Suppose 0*l + 45 = 3*l. Find g such that 4/3 - 8*g - l*g**4 + 25/3*g**5 + 41/3*g**2 - 1/3*g**3 = 0.
-1, 2/5, 1
Let w be -2 + (11 - -3)/2. Let -2*t**3 - t**3 - 3*t**w + 0*t**5 + 6*t**3 - 3*t**2 + 3*t**4 = 0. What is t?
-1, 0, 1
Let i(l) be the third derivative of 1/210*l**6 + 0*l**4 + 0*l**3 + l**2 + 0*l + 0 - 1/245*l**7 + 0*l**5 - 5/1176*l**8. Factor i(y).
-2*y**3*(y + 1)*(5*y - 2)/7
Let y = -57 - -16. Let n = -122/3 - y. Factor 1/3*m**5 + 0*m + 0 + n*m**2 - 1/3*m**3 - 1/3*m**4.
m**2*(m - 1)**2*(m + 1)/3
Let u(n) be the first derivative of n**3/9 + n**2/3 + n/3 + 32. Find y, given that u(y) = 0.
-1
Let p(v) be the third derivative of -v**8/560 - v**7/350 + v**6/200 + v**5/100 + 14*v**2. Determine q so that p(q) = 0.
-1, 0, 1
Let h be (-6)/8 - (-54)/8. Suppose h*y + 7 - 31 = 0. Solve -2/9*j**y + 2/9*j**2 + 0*j**3 + 0*j + 0 = 0 for j.
-1, 0, 1
Let h = 604 - 4204/7. Let x be 46/35 + (-2)/(-5). Factor h*a - 16/7 - x*a**2 + 2/7*a**3.
2*(a - 2)**3/7
Suppose -41 = -5*b + 54. Suppose 0 = 2*l - 3 - b. Factor 5*c - l*c**2 - 10*c**4 - 9*c**2 - 5*c**4 - c + 31*c**3.
-c*(c - 1)*(3*c - 2)*(5*c - 2)
Let v(i) be the third derivative of -1/30*i**6 - 1/84*i**4 + 3*i**2 + 0 + 2/21*i**3 + 0*i - 17/210*i**5. Determine q so that v(q) = 0.
-1, -1/2, 2/7
Let w = 2151/7 - 307. Suppose -w + 6/7*j + 8/7*j**2 = 0. What is j?
-1, 1/4
Determine y so that -17/6*y**2 - 1/12*y + 17/12*y**3 - 4/3*y**5 + 8/3*y**4 + 1/6 = 0.
-1, -1/4, 1/4, 1, 2
Let d(u) = u**3 - 14*u**2 + 12*u + 16. Let j be d(13). Suppose -p + 6*p + j*p + 4*p**2 - 12 = 0. Calculate p.
-3, 1
Let q be (-12)/(-20) - (85/(-225))/(-1). Factor -2/9 - q*i**4 - 8/9*i - 4/3*i**2 - 8/9*i**3.
-2*(i + 1)**4/9
Let y(c) be the second derivative of c**5/90 + 2*c**4/27 + 5*c**3/27 + 2*c**2/9 + 5*c. Factor y(u).
2*(u + 1)**2*(u + 2)/9
Let -3*c**3 + 4*c - 3*c + 5*c - 3*c**2 + 0*c = 0. What is c?
-2, 0, 1
Let f be 1/(-2) - 21/(-6). Let c(t) = -2*t**2 + 12*t + 8. Let s(y) = -y**2 + 4*y + 3. Let q(u) = f*c(u) - 8*s(u). Factor q(x).
2*x*(x + 2)
Let v be (-3)/(-3)*(3 + 0). Let b be (2 - 2) + (v - 1). Factor 12/5*c + 8/5*c**3 - 18/5*c**b - 2/5.
2*(c - 1)**2*(4*c - 1)/5
Let y = -83 + 89. Let a(s) be the first derivative of 1 + 0*s + 3/5*s**4 + 1/10*s**y - 2/5*s**3 - 2/5*s**5 + 1/10*s**2. What is t in a(t) = 0?
0, 1/3, 1
Suppose -20 + 2 = -3*m. Let l(n) = n - 4. Let s be l(m). Factor 0 - 2*h**2 + h + 1 - 3*h**s + 3*h**3.
(h - 1)**2*(3*h + 1)
Let g = -73 - -147/2. Solve g*w**2 + 1/4*w + 0 = 0.
-1/2, 0
Let d(u) be the third derivative of -u**9/1512 + u**8/420 - u**7/420 + u**3/6 + 6*u**2. Let c(m) be the first derivative of d(m). Factor c(q).
-2*q**3*(q - 1)**2
Let o(w) be the second derivative of -w**4/24 + 7*w**3/12 - 3*w**2/2 - 12*w. Factor o(i).
-(i - 6)*(i - 1)/2
Let k be (-6)/(-6*3/12). Factor 0*l**3 + 0 + 0*l**2 + 0*l + 2/7*l**k.
2*l**4/7
Factor 6/5*v - 6/5*v**3 - 3/5*v**4 + 3/5 + 0*v**2.
-3*(v - 1)*(v + 1)**3/5
Let r(u) be the second derivative of 2*u**7/21 + 4*u**6/15 + u**5/5 + 9*u. Factor r(b).
4*b**3*(b + 1)**2
Factor 4/7*l**3 + 16/7 - 4/7*l**2 - 16/7*l.
4*(l - 2)*(l - 1)*(l + 2)/7
Let w = -57 + 173/3. Let -10/3*y**2 - 8/3*y - w - 4/3*y**3 = 0. Calculate y.
-1, -1/2
Suppose -1/4 - 1/2*x - 1/4*x**2 = 0. Calculate x.
-1
Suppose -5*q + c = -19, 3*q + 4*c + 0*c = -7. Let h(b) be the second derivative of -2/3*b**q + b - 1/6*b**4 - b**2 + 0. Factor h(x).
-2*(x + 1)**2
Let a(b) be the first derivative of -b**5/4 + b**4/4 + b**3/3 - 5*b - 4. Let d(u) be the first derivative of a(u). Find t such that d(t) = 0.
-2/5, 0, 1
Let x(f) be the first derivative of f**4/12 - f**3 + 9*f**2/2 - 4*f + 4. Let v(t) be the first derivative of x(t). Factor v(p).
(p - 3)**2
Factor -38/3*t**2 - 7/3 - 1/3*t**5 + 9*t - t**4 + 22/3*t**3.
-(t - 1)**4*(t + 7)/3
Let l(j) be the first derivative of j**6/21 + 2*j**5/7 + 4*j**4/7 + 8*j**3/21 - 22. Factor l(b).
2*b**2*(b + 1)*(b + 2)**2/7
Let w(d) = -2*d**4 - 2*d**4 