etermine f, given that -3/5*f**3 + 0*f**4 + 0*f + 0*f**o + 0 + 3/5*f**5 = 0.
-1, 0, 1
Let m be (-1*(-6)/(-24))/(2/(-2)). Factor 1/4*s + 0 - m*s**2.
-s*(s - 1)/4
Factor 72 + 2*r**2 - 72.
2*r**2
Let c(v) be the second derivative of v**6/40 + v**5/20 - v**4/8 - v**3/2 - 2*v**2 - 4*v. Let f(j) be the first derivative of c(j). Find k, given that f(k) = 0.
-1, 1
Let v(c) = -c**3 + 2*c**2 + 2*c - 4. Let h be v(2). Suppose -4*x = -12, -4*r = x - h*x - 3. Find k such that 1/2*k**4 + r - 7/6*k**2 + 1/3*k**3 + 1/3*k = 0.
-2, 0, 1/3, 1
Suppose -4*v - 3*l + 24 = 0, -3*v + 2*v = -4*l + 13. Find a such that -a**v + 4*a + a**3 - 4*a**3 + 1 + 2*a**4 - 3 = 0.
-1, 1
Let v(w) be the second derivative of -w**8/47040 + w**7/2520 - w**6/336 + 3*w**5/280 - w**4/12 - 3*w. Let i(c) be the third derivative of v(c). Factor i(g).
-(g - 3)**2*(g - 1)/7
What is j in 0 - 2*j**3 - 12/7*j**2 + 0*j - 2/7*j**4 = 0?
-6, -1, 0
Let n(i) be the third derivative of i**6/420 + i**5/70 + i**4/28 + i**3/21 - 8*i**2. Factor n(h).
2*(h + 1)**3/7
Suppose -2*y - 14 = -2*a - 4*y, 2*a = 4*y - 10. Let t(m) be the second derivative of 0*m**a + 0*m**2 + 0 + 2*m + 1/30*m**4. Factor t(o).
2*o**2/5
Let y(p) be the second derivative of p**3 + 0 + 1/6*p**4 - p + 2*p**2. Solve y(z) = 0.
-2, -1
Let r = 673/38 + 15/19. Let c = 19 - r. Factor -1/2*j**2 + 0 + 1/6*j - 1/6*j**4 + c*j**3.
-j*(j - 1)**3/6
Let n(f) = -f**4 - 4*f**3 + 4*f**2 - 6*f - 1. Let z(w) = -4*w**4 - 12*w**3 + 11*w**2 - 19*w - 4. Let t(g) = 14*n(g) - 4*z(g). Factor t(y).
2*(y - 1)**4
Let c = 4 + -1. Let t(v) be the first derivative of -c*v**2 + 2/3*v**3 - 1 + 4*v. Determine j so that t(j) = 0.
1, 2
Let p be (0 + 1)*(6 - 5). Let d = 8 + -5. Factor -7*o + 15*o**4 + p - d + 6*o**2 - o**4 + 25*o**3.
(o + 1)**2*(2*o - 1)*(7*o + 2)
Let t(i) = i**2 - 10*i + 9. Let g(w) be the third derivative of -w**5/20 + 13*w**4/8 - 6*w**3 - 4*w**2. Let u(c) = 2*g(c) + 9*t(c). Factor u(n).
3*(n - 3)*(n - 1)
What is i in -19*i**2 + 1/2*i**5 + 14*i - 4*i**4 + 25/2*i**3 - 4 = 0?
1, 2
Let t(k) = -1 + 1 + 2 - k**3. Let u be t(0). Factor 0 + 3/2*h**3 + 1/2*h - 3/2*h**u - 1/2*h**4.
-h*(h - 1)**3/2
Let h(s) = s**4 - s**3 - 18*s**2 + 35*s - 7. Let b(y) = -3*y**4 + 3*y**3 + 45*y**2 - 87*y + 18. Let t(l) = 5*b(l) + 12*h(l). Determine u, given that t(u) = 0.
-2, 1
Suppose 3*v + 2*x - 2 = -9, 0 = v - 2*x - 11. Let q be (-35)/(-15) - v/3. Factor -3*c - c**2 + 6*c - q*c**2.
-3*c*(c - 1)
Suppose 3*q = 5*o - 32, 4*o + 0*q = -q + 12. Solve 0*v**3 - 1/4 + 0*v + 1/2*v**2 - 1/4*v**o = 0 for v.
-1, 1
Find q, given that 3*q**3 - 4*q**3 + 20*q + 8 + 16*q**2 + 5*q**3 = 0.
-2, -1
Determine o, given that 21/4*o**4 + 0*o + 3*o**2 + 0 - 33/4*o**3 = 0.
0, 4/7, 1
Suppose 5*v + 60 = 70. Let g = 8 + -3. Find o such that 0*o**4 + 0*o**v + 0*o - 1/4*o**3 + 1/4*o**g + 0 = 0.
-1, 0, 1
Let y(x) be the first derivative of -1/3*x**3 + 1/4*x**2 + 1/8*x**4 + 0*x - 2. What is q in y(q) = 0?
0, 1
Let q(c) be the first derivative of -8/7*c**4 - 3 - 16/7*c**3 - 9/7*c**2 - 2/7*c. Factor q(f).
-2*(f + 1)*(4*f + 1)**2/7
Factor -14*m + 0*m**2 + m**2 - 16*m + 289 - 4*m.
(m - 17)**2
Let h(j) be the second derivative of 13/3*j**3 - 10/3*j**4 + 0 - 6*j - 2*j**2 + 9/10*j**5. Factor h(k).
2*(k - 1)**2*(9*k - 2)
Let r(y) be the first derivative of 4*y**2 + 8/5*y + 2/5*y**5 + 2 + 11/5*y**4 + 22/5*y**3. Suppose r(z) = 0. What is z?
-2, -1, -2/5
Let x be 1/(-2) + (-34)/(-4). Let m be (-2)/10 + -6 + x. Factor 2/5*s**3 - m*s**4 + 1/5 + 4/5*s**5 - 6/5*s + 8/5*s**2.
(s - 1)**3*(s + 1)*(4*s - 1)/5
Let v(j) be the second derivative of -j**5/20 + j**4/12 + j**3/6 - j**2/2 - 2*j. Suppose v(z) = 0. What is z?
-1, 1
Suppose -3*k + 36 - 30 = 0. Let i(d) be the first derivative of -3 + d**k - 1/3*d**3 - d. Suppose i(f) = 0. Calculate f.
1
Let u(m) = 4*m**4 - m**3 - 13*m**2 - 17*m - 9. Let p(k) = -k**4 - k**3 + k + 1. Let z(d) = 5*p(d) + u(d). Solve z(h) = 0.
-2, -1
Let s(b) be the first derivative of b**6/3 - 3*b**4/2 + 4*b**3/3 - 1. Factor s(d).
2*d**2*(d - 1)**2*(d + 2)
Let p(c) be the third derivative of c**5/60 - c**4/6 + 2*c**3/3 - 10*c**2. Factor p(y).
(y - 2)**2
Let l(s) be the third derivative of -1/24*s**3 + 0 + 0*s - 1/480*s**6 - 1/32*s**4 - 1/80*s**5 + 2*s**2. Factor l(r).
-(r + 1)**3/4
Find c such that 2/3*c**2 + 338/3 + 52/3*c = 0.
-13
Let x(b) be the first derivative of -b**6/1440 + 4*b**3/3 - 1. Let j(o) be the third derivative of x(o). Suppose j(v) = 0. What is v?
0
Suppose 2*h - 2 = 6. Let m(k) = 4*k + 19. Let i be m(-4). Suppose -19*p**5 + 5*p**4 - 15*p**4 + 10*p**2 + 13*p**5 + 2*p**i + h*p = 0. What is p?
-1, -2/3, 0, 1
Let g(j) be the second derivative of -j**8/16800 + j**6/1800 + j**4/4 + 2*j. Let b(q) be the third derivative of g(q). Factor b(t).
-2*t*(t - 1)*(t + 1)/5
Suppose -937 = -6*z - 907. Factor -5/3*c - 1/3*c**z - 5/3*c**4 - 10/3*c**2 - 1/3 - 10/3*c**3.
-(c + 1)**5/3
Find r such that 0*r + 3/5*r**3 + 0 - 3/5*r**2 = 0.
0, 1
Let h(o) be the third derivative of o**7/30 + o**6/12 - o**5/140 - 5*o**4/42 + 2*o**3/21 - 6*o**2. Find k, given that h(k) = 0.
-1, 2/7
Let x(s) = -s**4 - 2*s**3 - 3*s**2 - 3. Let o(v) = 2*v**4 + 2*v**3 + 4*v**2 + 4. Let m = -1 - 3. Let p(t) = m*x(t) - 3*o(t). Determine b, given that p(b) = 0.
0, 1
Let x(y) be the second derivative of -2*y**7/525 + y**6/150 + y**5/25 - y**4/6 + 4*y**3/15 + y**2 + 8*y. Let m(r) be the first derivative of x(r). Factor m(i).
-4*(i - 1)**3*(i + 2)/5
Let t(y) be the second derivative of y**5/10 + y**4/6 - 2*y**3/3 - 4*y. Factor t(p).
2*p*(p - 1)*(p + 2)
Factor -55*y**3 - 13*y - 14*y - 48*y**3 + 9*y**2 + 27 + 102*y**3.
-(y - 3)**3
Let h(c) be the first derivative of c**6/8 + 3*c**5/5 + 3*c**4/4 - 12. Suppose h(a) = 0. Calculate a.
-2, 0
Let t(k) be the third derivative of k**8/2016 + k**7/315 + k**6/120 + k**5/90 + k**4/144 + 4*k**2. Factor t(n).
n*(n + 1)**4/6
Determine q so that 0*q**4 + 0 + 0*q**2 + 2/3*q - 4/3*q**3 + 2/3*q**5 = 0.
-1, 0, 1
Suppose 3*k = -4 - 5. Let a = -2 - k. Let f(l) = l**4 + l**3 + l**2. Let q(y) = 7*y**4 + 8*y**3 + 7*y**2. Let r(t) = a*q(t) - 6*f(t). Factor r(x).
x**2*(x + 1)**2
Let g(o) be the first derivative of -4*o**5/15 - o**4 - 8*o**3/9 + 5. Factor g(f).
-4*f**2*(f + 1)*(f + 2)/3
Let v(k) = k - 2. Let y be v(2). Let t = -28 - -57/2. Factor s**2 + 1/2*s**3 + t*s + y.
s*(s + 1)**2/2
Let l(i) be the second derivative of i**4/3 + i**3/6 + i**2/2 - 3*i. Let c be l(-1). Factor 2*z + 4*z**2 - z**3 - c*z**2 + z**2.
-z*(z - 2)*(z + 1)
Let n(d) be the third derivative of -d**5/24 + 25*d**4/24 - 125*d**3/12 + 6*d**2. Factor n(g).
-5*(g - 5)**2/2
Factor 0 - 2*v**3 + 5/2*v**2 + 1/2*v**4 - v.
v*(v - 2)*(v - 1)**2/2
Let m(h) be the third derivative of h**8/252 + h**7/90 + h**6/180 - h**5/180 + h**2. Factor m(c).
c**2*(c + 1)**2*(4*c - 1)/3
Factor 142 - 142 - 2*l**3 - 6*l**2.
-2*l**2*(l + 3)
Let r be 8 - (-2 - (-2 - 2)). Let a = r + -4. Factor 0*y**a + y**5 - 6*y**4 + 2*y**3 + 4*y**3 - 2*y**2 + y**5.
2*y**2*(y - 1)**3
Let w be ((-6)/(-12) - -1)/18. Let r(q) be the second derivative of w*q**4 - 1/6*q**3 + 0 + 0*q**2 + 5*q. Determine j so that r(j) = 0.
0, 1
Let z(o) = o**3 + o**2 - 2*o. Let l(y) = y - 4*y**3 + y**3 + 2*y**3. Let w(r) = -3*l(r) - 2*z(r). Suppose w(h) = 0. What is h?
0, 1
Suppose 56*y**2 - 12 - 191*y**2 - 75*y**3 + 51*y - 123*y = 0. What is y?
-1, -2/5
Let z(g) be the first derivative of g**3/6 - g**2/6 - g/6 - 9. Factor z(x).
(x - 1)*(3*x + 1)/6
Suppose -s + 2 = -3. Let b = 7 - s. Determine n, given that 2/3*n**2 + 4/3 - b*n = 0.
1, 2
Let p(b) = b**2. Let a(y) = -20*y**2 - 6*y - 4. Let c(v) = 2*a(v) + 36*p(v). Find s such that c(s) = 0.
-2, -1
Let z = -1 + 4. Suppose 17 = -n - 5*s, -7*n + z*n = 3*s. Factor 8*y - n*y**2 + 2*y**2 - 4*y**2 + y**3 - 4.
(y - 2)**2*(y - 1)
Let c = -61 - -65. Factor 1/5*j**3 - 1/5*j**2 - 1/5*j + 0 + 1/5*j**c.
j*(j - 1)*(j + 1)**2/5
Factor 9/5*o + 1/5*o**2 + 14/5.
(o + 2)*(o + 7)/5
Let a(k) = k**2 + 12*k - 14. Let u be a(-12). Let t = -11 - u. Factor -2/5*y**5 + 4/5*y**4 - 2/5*y**t + 0*y**2 + 0*y + 0.
-2*y**3*(y - 1)**2/5
Let x(f) = -3*f**4 - f**3 + f**2 + f + 2. Let r(c) = -c**3 + 19*c - c**4 + 0*c**3 + 1 - 18*c. Let h(b) = -6*r(b) + 3*x(b). What is l in h(l) = 0?
-1, 0, 1
What is n in 0 - 8/3*n**2 - 4/3*n + n**5 + 1/3*n**3 + 8/3*n**4 = 0?
-2, -1, -2/3, 0, 1
Let o(d) be the third derivative of 