2*g - 6 = -2. Factor 2/7*n**3 - 2/7*n**g + 0 - 2/7*n + 2/7*n**4.
2*n*(n - 1)*(n + 1)**2/7
Let z(d) be the third derivative of 0 + 0*d + 1/1176*d**8 - 1/140*d**6 + 1/42*d**5 - 1/42*d**4 - d**2 - 1/735*d**7 + 0*d**3. Factor z(f).
2*f*(f - 1)**3*(f + 2)/7
Let a(r) = 4*r**3 - 12*r**2 + 8*r. Let f(j) = -4*j**3 + 13*j**2 - 9*j. Let g(t) = 5*a(t) + 4*f(t). Let g(u) = 0. What is u?
0, 1
Factor 2*m**3 + m**2 + 0*m**3 - 21*m**4 + 40*m**4 - 18*m**4.
m**2*(m + 1)**2
Factor -6/13*i**2 - 6/13 - 20/13*i.
-2*(i + 3)*(3*i + 1)/13
Suppose -3 = 3*o + 15. Let h be ((-1)/2)/(3/o). Let -9*r + 3*r**2 - r**4 + 2*r**2 + 1 + 9*r**3 + h - 6*r**4 = 0. What is r?
-1, 2/7, 1
Factor -2*f + f + 12 + 9*f - 4*f**2.
-4*(f - 3)*(f + 1)
Determine r, given that 4*r - 14*r + 6*r**3 + 7*r - r**2 - 2*r**2 = 0.
-1/2, 0, 1
Let n be ((-4)/(-18))/((-3)/(-6)). Let a(c) be the first derivative of -1/4*c**4 + n*c**3 + 1 + 0*c - 1/6*c**2. Factor a(r).
-r*(r - 1)*(3*r - 1)/3
Suppose 2*j**3 - 301 - j**5 + 301 - j = 0. What is j?
-1, 0, 1
Suppose -3*l + 22 = 4*v, -l + 5*v - 10 = 4*l. Factor 2/7*n - 2/7*n**3 + 2/7*n**4 - 2/7*n**l + 0.
2*n*(n - 1)**2*(n + 1)/7
Suppose -3*k = -w - 20, 0 = -3*k + 13*w - 11*w + 25. Factor -s**2 + 1/2*s**k + 1/2*s + 1/2*s**4 + 1/2 - s**3.
(s - 1)**2*(s + 1)**3/2
Let m(w) be the third derivative of 2*w**7/105 - w**5/15 + w**2. Factor m(h).
4*h**2*(h - 1)*(h + 1)
Let m(y) be the first derivative of y**6/2 - 12*y**5/5 - 9*y**4 + 32*y**3 + 96*y**2 + 37. Solve m(t) = 0 for t.
-2, 0, 4
Let i(x) be the first derivative of x**3/4 + 3*x**2/4 + 2. Solve i(h) = 0.
-2, 0
Let v(f) be the third derivative of -f**2 + 0*f + 0 + 0*f**3 + 1/150*f**5 + 1/300*f**6 - 1/840*f**8 + 0*f**4 - 1/525*f**7. Suppose v(u) = 0. What is u?
-1, 0, 1
Let j(o) = 22*o**2 - 10*o. Suppose q - 40 = 5*h - 16, 0 = -4*h - q - 21. Let k(z) = -7*z**2 + 3*z. Let f(x) = h*j(x) - 16*k(x). Suppose f(i) = 0. What is i?
-1, 0
Let t(s) be the second derivative of -s**4/12 + 7*s**3/6 + 4*s**2 + s. Let q(z) = 6*z - z**2 - z + z + 0*z + 7. Let h(v) = -6*q(v) + 5*t(v). Factor h(b).
(b - 2)*(b + 1)
Determine t so that -8/3*t - 8/3*t**3 + 4*t**2 + 2/3 + 2/3*t**4 = 0.
1
Suppose 5 = 3*b - 1. Let u(s) be the second derivative of -3*s + 0*s**3 + 0*s**b + 0 - 1/24*s**4 + 1/40*s**5. Factor u(g).
g**2*(g - 1)/2
Let k(v) be the second derivative of -v**7/112 + 3*v**6/40 - 39*v**5/160 + 3*v**4/8 - v**3/4 - 7*v. Suppose k(o) = 0. What is o?
0, 1, 2
Let x(b) = -b**3 - 7*b**2 - 4*b + 7. Let m be x(-6). Let k = 7 + m. Suppose 2 - 2*o - o + 2*o**k - o = 0. Calculate o.
1
Let j(t) = 6*t**2 - 14*t + 8. Let c be 6/(-9) - (-51)/9. Let a(d) = -7*d**2 + 15*d - 8. Let w(f) = c*j(f) + 6*a(f). Factor w(h).
-4*(h - 1)*(3*h - 2)
Let f = 1 - -4. Suppose -2*w + 3 = -f*r, -3*w + 18 = -2*r + 2*w. Let r + 1/4*o**2 - o = 0. Calculate o.
2
Let i = 48 + -238/5. Let n(r) be the first derivative of i*r + 1 - 1/5*r**2 + 1/10*r**4 - 2/15*r**3. Factor n(l).
2*(l - 1)**2*(l + 1)/5
Let y(a) be the third derivative of a**8/30240 + a**5/60 + a**2. Let j(n) be the third derivative of y(n). Find f, given that j(f) = 0.
0
Let j(u) be the first derivative of -2*u**5/15 + u**4/6 + 2*u**3/9 - u**2/3 - 7. Factor j(h).
-2*h*(h - 1)**2*(h + 1)/3
Let b be (-4)/(-12) + 13/(-3). Let u = 6 + b. What is x in -4*x**3 - u*x**4 + 4*x + 2 + 4*x**2 - 4*x**2 = 0?
-1, 1
Let b(n) be the third derivative of n**7/350 + n**6/100 - n**5/25 - n**4/5 - 51*n**2. Factor b(k).
3*k*(k - 2)*(k + 2)**2/5
Let p(t) = -6*t**2 + 3*t - 2. Let o(n) be the second derivative of 7*n**4/12 - n**3/2 + n**2 + n. Let h(r) = -5*o(r) - 6*p(r). Factor h(u).
(u - 2)*(u - 1)
Suppose y - 7 = -4, -5*r + 5*y - 5 = 0. Let 0 + 2/3*p**3 - p**4 + p**r - 2/3*p = 0. What is p?
-1, 0, 2/3, 1
Let m(x) be the first derivative of 3*x - 3/2*x**4 + 3*x**2 - 3/5*x**5 + 3 + 0*x**3. Factor m(u).
-3*(u - 1)*(u + 1)**3
Let g(t) be the first derivative of -1/20*t**5 + 1/24*t**6 + 0*t**2 + 1 + 0*t + 1/12*t**3 - 1/16*t**4. Factor g(f).
f**2*(f - 1)**2*(f + 1)/4
Let v = 12 - 14. Let q be ((-2)/(-5))/(v/(-6)). Let -6/5*m + 4/5*m**2 + 2/5 + 2/5*m**5 + 4/5*m**3 - q*m**4 = 0. What is m?
-1, 1
Let s(t) = -2*t - 13. Let k be s(-8). Find z, given that 11*z - 5*z + 3*z**k - 2*z + 12*z**2 + 6 + 11*z = 0.
-2, -1
Let p(l) be the third derivative of l**5/390 + l**4/78 + l**3/39 - 26*l**2. Let p(z) = 0. Calculate z.
-1
Let p = -67/39 - -31/13. Determine h so that -2/3*h**3 - 2*h + 2*h**2 + p = 0.
1
Suppose -t + 0*t - 107 = -5*d, 5*t + 95 = 5*d. Let j = -43/2 + d. Factor 1/4 + j*y + 1/4*y**2.
(y + 1)**2/4
Determine p so that 0 - 1/3*p + 1/3*p**3 + 1/3*p**2 - 1/3*p**4 = 0.
-1, 0, 1
Suppose -4*d = -3 - 5. Factor -d*c**4 + 34/5*c**3 - 4/5 - 42/5*c**2 + 22/5*c.
-2*(c - 1)**3*(5*c - 2)/5
Suppose -11 + 2 = -3*i. Let h be 0/((0 - i) + 1). Factor 4/11*c - 2/11*c**2 + h.
-2*c*(c - 2)/11
Let s(o) be the first derivative of 1/8*o**4 - 1/24*o**6 - 1/20*o**5 - 1/8*o**2 - 1 + 1/6*o**3 - 1/4*o. Factor s(l).
-(l - 1)**2*(l + 1)**3/4
Determine s so that -1 + 1/2*s**2 + 1/2*s = 0.
-2, 1
Factor -23 + 25*z + 11 + 15*z**2 - z.
3*(z + 2)*(5*z - 2)
Let 1/2*k**2 + 0*k - 1/4*k**4 + 1/4*k**3 + 0 = 0. Calculate k.
-1, 0, 2
Let a(t) be the first derivative of t**6/240 + t**5/120 + 11*t**2/2 + 6. Let o(w) be the second derivative of a(w). Factor o(r).
r**2*(r + 1)/2
Let j(o) be the third derivative of -o**4/12 - 5*o**3/6 + 2*o**2. Let f be j(-4). Factor -2*u**f + 0 - 5 - 2*u**2 + u**4 + 6 + u**5 + u.
(u - 1)**2*(u + 1)**3
Factor 2*f**3 + 13*f**4 + 10*f**3 - 8*f**2 - 7*f**4 + 14*f**4.
4*f**2*(f + 1)*(5*f - 2)
Suppose 0*u - 6 = -2*u. Let o + 0*o - o**2 - o**4 + 0*o**4 - o**u + 2*o**4 = 0. What is o?
-1, 0, 1
Let x(m) be the first derivative of m**7/105 + m**6/60 - m**5/30 - m**4/12 - m**2/2 + 1. Let r(i) be the second derivative of x(i). Factor r(s).
2*s*(s - 1)*(s + 1)**2
Let q = -1 + 3. Factor 2*l**3 + 4*l**4 - q*l**2 + 3*l - 2*l**2 + 0*l - 5*l.
2*l*(l - 1)*(l + 1)*(2*l + 1)
Let 0 + 2/3*d**2 - 4/3*d = 0. Calculate d.
0, 2
Let d = -1405 + 1409. Factor -2/3 + 0*n**2 + 2/3*n**d - 4/3*n**3 + 4/3*n.
2*(n - 1)**3*(n + 1)/3
Let c(t) be the third derivative of -t**5/12 + 5*t**4/24 + 13*t**2. Suppose c(u) = 0. Calculate u.
0, 1
Factor -6*m**2 - 4*m + 0*m - 2*m**2 + 10*m**2 + 2.
2*(m - 1)**2
Find u such that -4*u**2 + 4*u**2 + u**3 + 3*u**3 = 0.
0
Suppose -5*a = 6 - 36. Determine m so that 2*m + m + 0*m**3 + a*m**2 + 6*m**3 - 3*m**3 = 0.
-1, 0
Let d(m) = -m**3 + 27*m**2 - 47*m - 73. Let g be d(25). Let 3/5*u**3 - 6/5*u**g - 3/5*u + 6/5 = 0. What is u?
-1, 1, 2
Let p(c) be the first derivative of -c**4/28 + c**3/21 + 4*c**2/7 - 12*c/7 - 3. Factor p(f).
-(f - 2)**2*(f + 3)/7
Let h(n) be the third derivative of -n**6/200 - 2*n**5/25 - 2*n**4/5 - 21*n**2. Factor h(t).
-3*t*(t + 4)**2/5
Factor -6*v**3 - 5*v**3 + 3*v**3 - 4*v**5 + 0*v**4 + 12*v**4.
-4*v**3*(v - 2)*(v - 1)
Factor -63/4*g**2 + 3/4*g**4 - 6 - 15/4*g**3 - 69/4*g.
3*(g - 8)*(g + 1)**3/4
Let q(x) be the third derivative of 1/2520*x**7 - 2*x**2 + 0*x**5 - 1/3*x**3 + 0*x**6 + 0*x + 0 + 0*x**4. Let w(n) be the first derivative of q(n). Factor w(s).
s**3/3
What is n in 8/5*n + 4*n**2 + 0 - 26/5*n**3 + 7/5*n**4 = 0?
-2/7, 0, 2
Let q(v) be the second derivative of v**5/40 - v**3/4 - v**2/2 + 9*v. What is t in q(t) = 0?
-1, 2
Let w(l) be the first derivative of l**6/18 + l**5/5 + l**4/12 - l**3/3 - l**2/3 + 6. Find f such that w(f) = 0.
-2, -1, 0, 1
Let k = -4 - -6. Let q(j) be the first derivative of 1/2*j**4 + 3*j**k - 2 + 2*j + 2*j**3. Suppose q(w) = 0. What is w?
-1
Solve -1/2*v + 1/2*v**2 + 1/2*v**3 - 1/2 = 0 for v.
-1, 1
Let b be (10/(-25))/((-2)/4). Let r = 65/3 - 313/15. Factor -2/5*k**3 + 2/5*k + b*k**2 - r.
-2*(k - 2)*(k - 1)*(k + 1)/5
Let z = 4 - 1. Let y be 6*(2 + (-15)/9). Factor -2*g**z + 0*g**3 + g**y + 2*g**4 - g**4.
g**2*(g - 1)**2
Let h(l) be the third derivative of l**9/60480 + l**8/10080 + l**7/5040 - l**5/30 - l**2. Let t(s) be the third derivative of h(s). Find y, given that t(y) = 0.
-1, 0
Let g be (-4)/14 + (-1296)/(-4928). Let b = 437/132 - g. Find z such that 4/3 + b*z**2 + 14/3*z = 0.
-1, -2/5
Let l(v) = v**4 + 15*v**3 - 9*v**2 + 5*v + 6. Let m(a) = -15*a**3 + 10*a**2 - 5*a - 5. Let r(z) = -5*l(z) - 6*m(z). Factor r(d).
-5*d*(d - 1)**3
Suppose -2*x = -2*u - 2, 4*x - 2*u - 7 = 3. Determine i so that 2*i**x + 0 +