)**2*(d + 1)/5
Let o be 252 + 2 - (-3 + 1). Factor -4*i**2 + 256*i - o*i.
-4*i**2
Let f be (-138)/(-18) + 2/6. Factor f*a**3 - a + 10*a**2 - 2*a**4 + 5*a + 4*a**4.
2*a*(a + 1)**2*(a + 2)
Let a be 1/((-2)/(-14)) - 1. Let h be (a/(-16))/(6/(-4)). Factor 0 + 0*r**2 + 1/4*r - h*r**3.
-r*(r - 1)*(r + 1)/4
Let f(a) = -171*a**3 + 504*a**2 - 291*a + 60. Let x(s) = 49*s**3 - 144*s**2 + 83*s - 17. Let c(l) = -5*f(l) - 18*x(l). Determine v so that c(v) = 0.
1/3, 2
Let 33/4*q - 3/4*q**4 - 33/4*q**3 - 27/4*q**2 + 15/2 = 0. What is q?
-10, -1, 1
Let y(l) be the first derivative of l**5 - 5*l**4 + 20*l**3/3 - 5. Factor y(r).
5*r**2*(r - 2)**2
Let r(s) be the second derivative of s**4/16 - s**3/8 + 13*s. Find t, given that r(t) = 0.
0, 1
Let a(r) be the second derivative of 2*r**7/7 + r**6/10 - 3*r**5/5 - r**4/4 + 13*r. Solve a(y) = 0.
-1, -1/4, 0, 1
Let l be ((12/10)/(-3))/((-24)/45). Find r, given that 9/4*r**3 + 0 + 3/2*r + 3/4*r**4 - l*r**5 - 15/4*r**2 = 0.
-2, 0, 1
Find u, given that 108/5*u**4 + 21*u**3 - 6/5*u + 0 - 9/5*u**2 = 0.
-1, -2/9, 0, 1/4
Suppose 21 = 4*z + 5. Suppose -16*n**3 - 23*n**3 + 4*n + 18*n**5 - 4*n**2 + 20*n**z + 82*n**5 = 0. Calculate n.
-1/2, 0, 2/5
Let a(z) be the third derivative of -z**7/42 + z**5/6 - 5*z**3/6 - 17*z**2. Factor a(k).
-5*(k - 1)**2*(k + 1)**2
Let h(s) be the third derivative of -s**7/150 + 3*s**6/200 - s**5/150 - 9*s**2. Factor h(k).
-k**2*(k - 1)*(7*k - 2)/5
Suppose 2*h = h + 2. Let g = 2 + h. Let -a**g + 3*a**4 - a**3 + 3*a**3 = 0. Calculate a.
-1, 0
Let y(p) be the third derivative of -1/15*p**6 + 1/6*p**4 + 0*p**7 + 0*p**5 + 0*p**3 + 0 + 0*p + 5*p**2 + 1/84*p**8. Find j, given that y(j) = 0.
-1, 0, 1
Let b(p) = -p**2 + 7*p - 3. Let l be b(4). Let t(k) = 10 - 10 - l*k - 3*k**3 - 18 - 24*k**2. Let g(z) = -z**2 - 1. Let n(q) = -15*g(q) + t(q). Solve n(o) = 0.
-1
Let p be (-39)/(-18) - 4/6. Suppose 48*f - 4 = 46*f. Let 1/2*c + c**4 + 0 - c**f + p*c**5 - 2*c**3 = 0. Calculate c.
-1, 0, 1/3, 1
Let u(o) be the second derivative of o**8/2240 - o**6/80 - o**5/20 - 5*o**4/6 - 2*o. Let b(f) be the third derivative of u(f). Factor b(y).
3*(y - 2)*(y + 1)**2
Suppose -4*d = b + b - 18, -22 = -5*d - 3*b. Suppose -4*x + 30 = x. Determine n so that -d - x*n - 5*n**3 - 6*n**2 + 3 + 3*n**3 = 0.
-1
Let b be 116/28 + (-1)/7. Suppose 0 = 3*k - k - 6. Find h, given that 6*h**4 + 4*h**4 + b*h - 10*h**2 + 6*h**5 + 8*h**5 + 7*h**3 - 25*h**k = 0.
-1, 0, 2/7, 1
Let o = 87/2 - 388/9. Let u(i) be the second derivative of -2/9*i**3 - i - 4/15*i**5 - 1/15*i**6 + 0 - o*i**4 + 0*i**2. Let u(h) = 0. What is h?
-1, -2/3, 0
Let a(j) be the first derivative of -25*j**4/4 - 35*j**3/3 - 5*j**2 + 15. What is f in a(f) = 0?
-1, -2/5, 0
Let t(m) be the third derivative of m**10/10080 - m**8/2240 - m**4/24 - 3*m**2. Let z(u) be the second derivative of t(u). Solve z(c) = 0 for c.
-1, 0, 1
Let n(i) = i**3 + 17*i**2 + 6*i. Let q(d) = -d**3 - 8*d**2 - 3*d. Let a(r) = 2*n(r) + 5*q(r). Determine w, given that a(w) = 0.
-1, 0
Let g(m) = -8*m**3 + 16*m**2 + 5*m + 13. Let n(f) = 4*f**3 - 8*f**2 - 2*f - 6. Let a(u) = 6*g(u) + 13*n(u). Factor a(l).
4*l*(l - 1)**2
Let u be ((-3)/27)/(5/(-15)). Factor 25*g**2 + 5*g + 125/3*g**3 + u.
(5*g + 1)**3/3
Let o**3 - 1/5*o + 1/5 - 3/5*o**2 - 2/5*o**4 = 0. Calculate o.
-1/2, 1
Let r(y) = 18*y**3 - 59*y**2 + 24*y + 11. Suppose -5*g + 0 = 30. Let l(v) = -9*v**3 + 30*v**2 - 12*v - 6. Let z(q) = g*r(q) - 11*l(q). Factor z(t).
-3*t*(t - 2)*(3*t - 2)
Let w(p) be the second derivative of -p**6/45 + p**5/3 - 11*p**4/6 + 40*p**3/9 - 16*p**2/3 + 49*p. Solve w(f) = 0 for f.
1, 4
Factor 20*l + 550 - 212 + 2*l**2 + 32*l.
2*(l + 13)**2
Let u be (4 - 78/24)*4. Factor 0*o**u - 1/4*o**4 + 0*o + 0*o**2 + 0.
-o**4/4
Let n be (1*3)/(18 + -17). Factor 0 + 2/11*o**2 - 6/11*o**4 + 0*o + 4/11*o**n.
-2*o**2*(o - 1)*(3*o + 1)/11
Let r = 107 + -107. Let r*b**3 - 1/5*b**4 + 1/5*b**5 + 0*b + 0 + 0*b**2 = 0. What is b?
0, 1
Suppose -5*f - z = -10, -3*f - 2*f + 10 = 2*z. Let c be f/(-10) - 1/(-5). Determine l, given that l**3 - l + c*l**3 - 2*l**3 - 2*l**2 = 0.
-1, 0
Determine d, given that -15*d**4 + 3*d**4 - 2*d + 4*d**3 + 2*d = 0.
0, 1/3
Factor -6*t - 4*t + 2*t - 3*t**2 - t.
-3*t*(t + 3)
Let d(u) = 114*u**4 - 111*u**3 + 31*u**2 + 11. Let t(b) = 23*b**4 - 22*b**3 + 6*b**2 + 2. Suppose -2*p - 44 = -4*p. Let n(r) = p*t(r) - 4*d(r). Factor n(o).
2*o**2*(5*o - 2)**2
Factor -1/4 + 3/4*l**4 + 3/2*l**2 + 0*l + 2*l**3.
(l + 1)**3*(3*l - 1)/4
Factor 0 + 0*c + 2/3*c**2.
2*c**2/3
Suppose -8 = -10*n + 8*n. Let w(j) = -j**3 + j**2 - 2. Let l(y) = y**3 - y**2 - y + 1. Let b(q) = n*w(q) + 5*l(q). Let b(t) = 0. What is t?
-1, 3
Suppose 0 = -3*t - 5 + 17. Factor j**4 + j - 5*j + t*j.
j**4
Let y(q) be the third derivative of q**5/12 + 5*q**4/6 + 5*q**3/2 - 2*q**2 - 6*q. Solve y(s) = 0 for s.
-3, -1
Let g(r) be the first derivative of r**6/1440 + r**3/3 + 3. Let b(q) be the third derivative of g(q). Factor b(s).
s**2/4
Suppose 5 + 3 = 2*c. Let b = c - -1. Factor -b - 3 - 2*n**3 + 4 + 2*n - n**4 - n**4 + 6*n**2.
-2*(n - 1)**2*(n + 1)*(n + 2)
What is o in 0 + 1/3*o - 1/3*o**2 = 0?
0, 1
Let h = -423 + 2969/7. Factor h*r + 8/7 + 2/7*r**2.
2*(r + 2)**2/7
Suppose 8*v - 4*v = 8. Suppose 5*p - 4*u = 4, v*p + 2*u + 2 = -0*u. Determine y so that 0 + 2/5*y**3 + p*y - 4/5*y**2 = 0.
0, 2
Suppose -n - 8 = -3, 5*d = -n + 10. Factor -3/4*r**5 + 0*r**4 + 0 + 3/2*r**d + 0*r**2 - 3/4*r.
-3*r*(r - 1)**2*(r + 1)**2/4
Let m = -3/82 + 25/123. Factor -1/6 + 1/6*c**2 - m*c**3 + 1/6*c.
-(c - 1)**2*(c + 1)/6
Let h(y) = 7*y**5 - y**3 - 9*y**2 - 5*y + 5. Let m(r) = -4*r**5 + 5*r**2 + 3*r - 3. Let q(v) = -3*h(v) - 5*m(v). Factor q(s).
-s**2*(s - 2)*(s + 1)**2
Let i(z) be the first derivative of -z**8/8400 - z**7/1400 - z**6/600 - z**5/600 - 5*z**3/3 - 1. Let c(h) be the third derivative of i(h). Solve c(n) = 0 for n.
-1, 0
Let r(m) = 7*m**3 - 28*m**2 + 58*m - 40. Let a(x) = -190*x**3 + 755*x**2 - 1565*x + 1080. Let p(h) = -2*a(h) - 55*r(h). Find q, given that p(q) = 0.
2
Let d(z) be the third derivative of -z**5/120 - 7*z**4/48 + 2*z**3/3 - 48*z**2. Solve d(r) = 0.
-8, 1
Let z(o) be the second derivative of -1/39*o**3 + 0 + 0*o**2 - 9*o - 1/78*o**4. Determine w, given that z(w) = 0.
-1, 0
Let u be (-3 - -3)*(-5)/10. Let h be 0/(-3 + u/(-4)). Suppose -3/5*v**2 + 0 + h*v = 0. What is v?
0
Let n(q) = -q**4 + 11*q**3 + 7*q**2 + 5*q + 5. Let l(a) = -a**4 + 17*a**3 + 11*a**2 + 7*a + 7. Let p(j) = -5*l(j) + 7*n(j). Solve p(t) = 0.
-3, -1, 0
Let b(p) be the first derivative of p**6/1080 - p**5/360 - p**4/36 + p**3 + 3. Let c(n) be the third derivative of b(n). Factor c(g).
(g - 2)*(g + 1)/3
Suppose -2*h + 4 = -h. Factor -n**5 + 3*n**2 - h*n**4 + n**3 + 9*n**4 - 4*n**2 - 4*n**4.
-n**2*(n - 1)**2*(n + 1)
Let f be ((-4)/24)/(28/(-8)). Let g(d) be the second derivative of d + 0 - 1/21*d**3 + 0*d**2 - 1/70*d**5 - f*d**4. Solve g(k) = 0 for k.
-1, 0
Let f(r) be the third derivative of 1/150*r**5 + 0*r - 1/525*r**7 + 1/60*r**4 + 0*r**3 - 3*r**2 - 1/300*r**6 + 0. Factor f(k).
-2*k*(k - 1)*(k + 1)**2/5
Let n(f) be the second derivative of -1/3*f**3 - 3*f + 0 + 0*f**2 + 1/12*f**4. What is c in n(c) = 0?
0, 2
Let h(b) be the first derivative of -3*b**4/16 + 3*b**3/4 - 9*b**2/8 + 3*b/4 + 1. Factor h(p).
-3*(p - 1)**3/4
Let u(j) be the first derivative of j**2/2 + 2*j + 1. Let x be u(-2). Factor x - 2/5*k - 2/5*k**2.
-2*k*(k + 1)/5
Factor -1/2*b**4 + 0 + 0*b**3 - 1/4*b + 1/4*b**5 + 1/2*b**2.
b*(b - 1)**3*(b + 1)/4
Let f(c) be the first derivative of c**7/315 + c**6/120 + c**5/180 - 9*c**2/2 - 10. Let k(a) be the second derivative of f(a). Factor k(x).
x**2*(x + 1)*(2*x + 1)/3
Let x(n) be the third derivative of -n**5/390 + n**4/39 - 4*n**3/39 - 5*n**2. Let x(b) = 0. What is b?
2
Factor -16*t + 2*t**2 + 16*t**2 + 6*t**2 + 4 + 4*t**4 - 16*t**3.
4*(t - 1)**4
Let h(n) be the third derivative of n**8/1512 - n**7/210 + 13*n**6/1080 - n**5/108 - n**4/72 + n**3/27 - 37*n**2. Factor h(p).
(p - 2)*(p - 1)**3*(2*p + 1)/9
Let o(l) be the third derivative of 5*l**8/448 - 23*l**7/280 + 7*l**6/32 - 17*l**5/80 - l**4/8 + l**3/2 - 4*l**2. Let o(n) = 0. What is n?
-2/5, 1, 2
Let r(s) be the second derivative of -s**6/5 - s**5/10 + 5*s**4/6 + s**3/3 - 2*s**2 + 2*s. Determine a so that r(a) = 0.
-1, 2/3, 1
Let g(y) be the second derivat