 - 1/5*y**3 - 4/5*y.
-y*(y + 2)**2/5
Let p(s) be the first derivative of s**5/5 - s**4 + 5*s**3/3 - s**2 - 6. Factor p(n).
n*(n - 2)*(n - 1)**2
Factor 1/4*i**2 + 0 - 1/4*i**4 + 1/4*i**3 - 1/4*i**5 + 0*i.
-i**2*(i - 1)*(i + 1)**2/4
Factor -n + 1/2*n**2 + 1/2.
(n - 1)**2/2
Solve -2/5 - 2/5*o**2 + 4/5*o = 0.
1
Let u(h) be the second derivative of 0*h**2 + 6*h + 1/9*h**4 + 0 + 1/60*h**5 + 0*h**3. What is a in u(a) = 0?
-4, 0
Factor -22*q**3 + 28*q**2 - 5*q**4 - 50 + q**4 - 2*q**5 + q**5 - 6*q**4 + 55*q.
-(q - 1)**2*(q + 2)*(q + 5)**2
Let i(j) be the second derivative of j**7/1260 - j**6/180 + j**5/90 + j**3/2 - 3*j. Let x(v) be the second derivative of i(v). What is k in x(k) = 0?
0, 1, 2
Let v(d) be the third derivative of -d**7/420 - d**6/90 - d**5/60 - d**3/3 - 5*d**2. Let y(p) be the first derivative of v(p). Factor y(z).
-2*z*(z + 1)**2
Let x(d) be the first derivative of -d**5/5 + 2*d**4/3 - 2*d**3/3 + d/3 + 7. Factor x(n).
-(n - 1)**3*(3*n + 1)/3
Let d be 1348/672 - 1/(1/2). Let p(j) be the third derivative of -1/15*j**5 + 2/105*j**7 - 1/12*j**4 + 0*j**6 + 0*j**3 - 3*j**2 + 0*j + 0 + d*j**8. Factor p(q).
2*q*(q - 1)*(q + 1)**3
Let w = 10 + -7. Suppose 0*m**w + 0*m + 0*m - 2*m**3 = 0. Calculate m.
0
Suppose 0*q**3 + 0*q**2 + 1/7*q**5 - 1/7*q**4 + 0*q + 0 = 0. What is q?
0, 1
Let u(i) be the first derivative of -5*i**3 + 8 + 3/2*i**4 + 6*i**2 - 3*i. Determine w so that u(w) = 0.
1/2, 1
Factor 0 - 4/9*x**3 + 2/9*x**4 - 2/9*x**2 + 4/9*x.
2*x*(x - 2)*(x - 1)*(x + 1)/9
Let w be (-6)/(-180)*(62/8 - 1). Let x(c) be the second derivative of 5/84*c**7 + 1/12*c**4 + 0 + 1/5*c**6 - 3*c + 0*c**2 + 0*c**3 + w*c**5. Factor x(d).
d**2*(d + 1)**2*(5*d + 2)/2
Suppose 16 - 1 + 10 + 24*c**2 - 48*c + 7 - 4*c**3 = 0. Calculate c.
2
Find p, given that 12*p**2 + 7*p - 9*p**3 - 19*p + 6*p**3 = 0.
0, 2
Let j = 157 + -782/5. Let -6/5*d + 3/5*d**2 + j = 0. Calculate d.
1
Let i be 5/(-20) - 114/(-8). Let z(t) = t**3 - 15*t**2 + 13*t + 18. Let x be z(i). Factor -2/3*v + 4/3*v**2 - 2/3 + 4/3*v**3 - 2/3*v**5 - 2/3*v**x.
-2*(v - 1)**2*(v + 1)**3/3
Let s = -29 + 33. Suppose 1/6*m**s + 0*m**2 + 0 + 0*m + 1/6*m**3 = 0. Calculate m.
-1, 0
Suppose 2*x = 8, -128 = -4*j + x - 2*x. Suppose -3*n + 5*f + j = 0, -5*f = -0*n - 2*n + 29. Factor -o**2 + o**n - 2*o**2.
-2*o**2
Let k(f) be the first derivative of f**3/3 + 6*f**2 - 13*f + 27. Factor k(r).
(r - 1)*(r + 13)
Let l(b) be the second derivative of b**7/21 + 3*b**6/5 + 7*b**5/5 - 17*b**4/3 - 5*b**3 + 25*b**2 + 26*b. Solve l(a) = 0 for a.
-5, -1, 1
Let d(q) be the third derivative of 6*q**2 + 1/210*q**5 + 1/42*q**4 + 0 + 0*q**3 + 0*q. Solve d(o) = 0 for o.
-2, 0
Let n(d) be the first derivative of 0*d - d**3 - 1 + 21/8*d**4 + 0*d**2. Determine l, given that n(l) = 0.
0, 2/7
Let v(l) be the first derivative of -l**5/5 + l**3 + l**2 - 21. Factor v(r).
-r*(r - 2)*(r + 1)**2
Let a(w) be the second derivative of -w**10/15120 - w**9/2520 - w**8/1120 - w**7/1260 - w**4/6 - w. Let c(u) be the third derivative of a(u). Factor c(h).
-2*h**2*(h + 1)**3
Let o(b) = -5 + 0*b - b + 3*b + 2. Let h be o(3). Factor 0*w**2 + 1/4*w**h + 0*w + 0.
w**3/4
Let t(i) be the third derivative of 0*i**3 - 1/120*i**5 + 6*i**2 - 1/96*i**6 + 0*i**4 + 0 + 1/280*i**7 + 0*i. Factor t(y).
y**2*(y - 2)*(3*y + 1)/4
Let a(b) be the third derivative of b**5/15 - b**4/3 + 2*b**3/3 - 16*b**2. Factor a(c).
4*(c - 1)**2
Find x, given that 32/9*x**2 + 0*x + 16/3*x**3 + 0 + 2/9*x**5 + 2*x**4 = 0.
-4, -1, 0
Suppose -3*c - 9*c = -36. Let 3/4*t**2 - 3/4*t**4 + 0*t**c + 0 + 0*t = 0. Calculate t.
-1, 0, 1
Let k(d) be the third derivative of d**8/1344 + d**7/420 - d**6/120 - d**5/120 + d**4/32 + 8*d**2. Solve k(i) = 0 for i.
-3, -1, 0, 1
Suppose 0 = -3*d - 5*s + 29, 5*d - s - 27 = -4*s. What is q in 8*q + q**3 + 7*q + 8 + 6*q**2 - d*q = 0?
-2
Let n(j) be the third derivative of -j**5/90 + 2*j**4/3 - 16*j**3 - 41*j**2. Factor n(p).
-2*(p - 12)**2/3
Factor 27/5*z**2 + 21/5*z + 3/5*z**4 + 3*z**3 + 6/5.
3*(z + 1)**3*(z + 2)/5
Suppose 15 = t + 4*t. Let w(v) = 10*v - 60. Let m be w(6). Find p, given that -1/5*p**4 - 3/5*p**2 + m + 3/5*p**t + 1/5*p = 0.
0, 1
Solve -80*w**2 + 18*w + 10 - 20*w**4 - 33*w - 22*w**3 - 53*w**3 = 0 for w.
-2, -1, 1/4
Let g be 12/(-54) + (-536)/18. Let w be (-31)/(-15) + 12/g. Factor k**2 - 1/3 - w*k**3 + 2/3*k**4 + 1/3*k.
(k - 1)**3*(2*k + 1)/3
Suppose 4*d + 16 = -3*j + 1, -2*j - 8 = 2*d. Let q = -1 - j. Let -3*v**3 - v**5 - 3*v**4 + q*v**3 - v**2 + 0*v**2 = 0. What is v?
-1, 0
Let y(u) be the third derivative of u**8/168 - u**7/105 - u**6/30 + u**5/15 + u**4/12 - u**3/3 - u**2 + 13. Factor y(h).
2*(h - 1)**3*(h + 1)**2
Let k(i) be the first derivative of i**6/1440 + i**5/240 + 2*i**3/3 - 2. Let m(b) be the third derivative of k(b). What is l in m(l) = 0?
-2, 0
Let h(t) be the second derivative of t**6/30 - 11*t**4/12 + 3*t**3 - 4*t**2 + 27*t. Factor h(q).
(q - 2)*(q - 1)**2*(q + 4)
Let r be 2 - 2*447/(-12). Let z = r + -75. Factor z*b**2 + 1/2 - 3/2*b - 1/2*b**3.
-(b - 1)**3/2
Let t(o) be the second derivative of 125*o**7/42 + 5*o**6/6 - 33*o**5/2 + 55*o**4/3 - 20*o**3/3 + 23*o. Let t(b) = 0. Calculate b.
-2, 0, 2/5, 1
Let x(m) be the first derivative of -m**4/4 + 2*m**3/3 - 18. Factor x(r).
-r**2*(r - 2)
Let x = -23/4 - -7. What is w in 3/4*w**3 + 1/4*w + x*w**2 - 1/4 = 0?
-1, 1/3
Suppose 0 = b - 2, -s + b + 8 = 4*b. Let s*o**4 + 0 + 0*o**2 + 0*o + 1/2*o**3 + 3/2*o**5 = 0. What is o?
-1, -1/3, 0
Suppose -w - 62 = -5*l - 10, w - 14 = -l. Let j be 0 + -3 + l/3. Let 0*z**2 - j*z - 2/3*z**5 + 4/3*z**3 + 0*z**4 + 0 = 0. Calculate z.
-1, 0, 1
Let x(j) be the second derivative of j**6/10 + 3*j**5/5 + 3*j**4/2 + 2*j**3 + 3*j**2/2 - 9*j. Factor x(i).
3*(i + 1)**4
Let o(u) be the first derivative of -u**3/15 - u**2/5 - u/5 - 4. Factor o(d).
-(d + 1)**2/5
Suppose 18*g**2 - 90*g - 13*g**2 + 553 - 148 = 0. Calculate g.
9
Let b(j) be the third derivative of 4*j**2 - 1/1365*j**7 - 1/195*j**6 + 1/39*j**4 + 0 + 0*j - 1/130*j**5 + 4/39*j**3. Determine g, given that b(g) = 0.
-2, -1, 1
Suppose -2*h + 5*x + 0*x = -31, 2*x = -10. Factor i**3 + i**h + 0*i**3.
2*i**3
Factor 3*m**2 + 71*m**4 - m - 68*m**4 + m + 6*m**3.
3*m**2*(m + 1)**2
Let l(n) be the first derivative of -n**5/10 + n**4/6 + n**3/3 - n**2 + 2*n + 2. Let i(y) be the first derivative of l(y). Solve i(f) = 0 for f.
-1, 1
Let u(p) = p**2 + p + 3. Suppose 0 = -w + 9 - 3. Let m = w - 7. Let s(d) = -1. Let q(i) = m*u(i) - 5*s(i). Factor q(b).
-(b - 1)*(b + 2)
Let h = 1 - -1. Factor 2 - 6*z**3 - 6*z**2 - 2*z - 2 - h*z**4.
-2*z*(z + 1)**3
Suppose 0 = -4*p, 7*p - 2*p + 8 = 4*n. Let u be n/(-15) - (-32)/15. What is f in 1/3*f + 1/3*f**u - 2/3 = 0?
-2, 1
Let t(q) = -5*q**2 - 7*q - 2. Let p(s) be the first derivative of -s**3/3 - s**2/2 + 4. Let m(y) = 3*p(y) - t(y). Factor m(i).
2*(i + 1)**2
Let -6/7 + 9/7*v**2 + 3/7*v**3 - 3/7*v**4 - 3/7*v = 0. What is v?
-1, 1, 2
Let h(z) = 3*z - 1. Let c be h(1). Suppose 2 + 2 = 2*v. Suppose 0*r - 3 + v*r**2 + 2*r**3 - c*r + 1 = 0. Calculate r.
-1, 1
Let r(t) be the first derivative of -t**4/20 + t**3/15 + t**2/10 - t/5 + 4. Solve r(g) = 0 for g.
-1, 1
Let y(h) be the third derivative of h**8/2240 + h**7/420 + 5*h**4/24 - 4*h**2. Let i(w) be the second derivative of y(w). Determine k so that i(k) = 0.
-2, 0
Let f be (1/7)/((-22)/(-44)). Suppose 4/7 + 0*k**2 - 6/7*k + f*k**3 = 0. Calculate k.
-2, 1
Suppose 0 = 4*p + y - 8, 3*y + 3 = 2*p - 1. Factor 1 + 4*s**2 - 2*s**2 + s**2 - 2*s**p - 2*s.
(s - 1)**2
Suppose 3*o - l = 2*o + 2, 0 = 2*l + 8. Let r(n) = 6*n - 2. Let f(i) = i**2 + 13*i - 4. Let h(v) = o*f(v) + 5*r(v). Factor h(w).
-2*(w - 1)**2
Suppose 0 = -3*o + 11*o. Let i(m) be the third derivative of -m**2 + 1/27*m**3 + 0*m + 1/270*m**5 + o - 1/54*m**4. Determine l so that i(l) = 0.
1
Let v(u) be the third derivative of u**8/672 - u**7/420 - u**6/240 + u**5/120 + 20*u**2. Solve v(y) = 0.
-1, 0, 1
Let d(l) be the first derivative of l**9/2646 + l**8/1960 - l**7/2940 - 4*l**3/3 + 5. Let j(p) be the third derivative of d(p). Let j(a) = 0. What is a?
-1, 0, 1/4
Let a(v) be the third derivative of -v**5/300 - v**4/40 - v**3/15 + 7*v**2. Find u such that a(u) = 0.
-2, -1
Let j(b) = 28*b**3 + 12*b**2 - 16. Let s(y) = -y**3. Let f(c) = j(c) + 24*s(c). Suppose f(r) = 0. What is r?
-2, 1
Let i(z) 