3)*(h + 1)**2
Let p = 87 + -83. Let y(c) be the first derivative of 1/16*c**p - 1/4*c**3 + 1/4*c**2 + 2 + 0*c. Suppose y(w) = 0. What is w?
0, 1, 2
Let a = -7 - -13. Suppose q + a = 4*q. Factor 0 + 14/5*r**q + 6/5*r**4 + 16/5*r**3 + 4/5*r.
2*r*(r + 1)**2*(3*r + 2)/5
Let a(g) be the third derivative of g**5/210 + g**4/42 + 15*g**2 - 2*g. What is h in a(h) = 0?
-2, 0
Factor 3/2*w**2 - 2*w + 1/2.
(w - 1)*(3*w - 1)/2
Let x(i) be the second derivative of 5/4*i**3 + 0 + 3/2*i**2 + 1/4*i**4 + 5*i. Suppose x(g) = 0. Calculate g.
-2, -1/2
Let f be 24/30*(-10)/(-4). Let l(y) be the third derivative of 0*y**6 + 0*y**4 + 1/672*y**8 + 0*y**5 + 3*y**f + 0*y + 0 - 1/420*y**7 + 0*y**3. Factor l(c).
c**4*(c - 1)/2
Find r such that -45*r - 38*r**3 - 334*r**2 + 4 - r + 414*r**2 = 0.
2/19, 1
Let o(u) be the first derivative of -4 - 27/16*u**4 + 0*u - 7/4*u**3 - 1/8*u**6 - 3/4*u**2 - 3/4*u**5. Factor o(c).
-3*c*(c + 1)**3*(c + 2)/4
Let u be -4 + 1 + (-147)/(-35). Factor -u - 2/5*y**3 - 14/5*y - 2*y**2.
-2*(y + 1)**2*(y + 3)/5
Suppose 5/2*c**4 + 5/4*c**3 + 0*c**2 + 5/4*c**5 + 0 + 0*c = 0. What is c?
-1, 0
Suppose -18 = -4*h - 2*o, -24 = -4*h + h + 2*o. Let k = -4 + h. Factor -2*g**2 - k + 0*g - 3*g - g.
-2*(g + 1)**2
Suppose 3*k + 12 = 6*k. Suppose -o = -k*o. What is z in 8*z**2 + 4 - 21*z + 2 + z**2 + o = 0?
1/3, 2
Factor -6*t**2 - 21*t**3 + t**2 + 5*t**4 + 16*t**3 + 5*t.
5*t*(t - 1)**2*(t + 1)
Let l(o) = -o**3 - 6*o**2 + 2. Let f be l(-6). Factor -3/2 + 1/2*s**f - s.
(s - 3)*(s + 1)/2
Let h(d) be the first derivative of -d**5/180 - d**4/18 - 2*d**3/9 + 7*d**2/2 + 4. Let z(c) be the second derivative of h(c). Factor z(j).
-(j + 2)**2/3
Let o(d) = -105*d**2 + 72*d. Let r(z) = 21*z**2 - 14*z. Let m(v) = -4*o(v) - 21*r(v). Factor m(y).
-3*y*(7*y - 2)
Suppose 0*m - 9760 = -61*m. Solve m*b + 200*b**2 + 250/3*b**3 + 128/3 = 0.
-4/5
Suppose -10 = -48*s + 43*s. What is p in -s*p - 3 - 1/3*p**2 = 0?
-3
Let d be (-8)/(1/1 + 1). Let s be ((-3)/d)/(7/28). Solve -9/4*b**2 + 27/4*b + 1/4*b**s - 27/4 = 0.
3
Factor -1/2*m + 0 - 1/2*m**2.
-m*(m + 1)/2
Let l(j) = -20*j**4 - 38*j**3 - 18*j**2 + 6*j + 6. Let d(r) = 13*r**4 + 25*r**3 + 12*r**2 - 4*r - 4. Let y(h) = -8*d(h) - 5*l(h). Solve y(n) = 0 for n.
-1, 1/2
Let g = -1 + 5. Let d(m) = 5*m**3 - 5*m**2 - 4*m - 4. Let u(b) = -b**3 + b**2 + b + 1. Let o(l) = g*u(l) + d(l). Factor o(w).
w**2*(w - 1)
Factor h**2 - 1 + 3*h**2 - 4 + h**2.
5*(h - 1)*(h + 1)
Let y(c) be the first derivative of 2*c**5/5 - 2*c**3/3 + 4. Determine l, given that y(l) = 0.
-1, 0, 1
Let l(u) = u**2 - 8*u + 6. Let b be l(6). Let c = b + 8. Find k, given that -c*k**3 + 0 + 14/5*k**2 - 4/5*k = 0.
0, 2/5, 1
Let m(p) be the third derivative of -2*p**7/105 + p**5/5 + p**4/3 + 12*p**2. Factor m(r).
-4*r*(r - 2)*(r + 1)**2
Let s(u) = -u - 9. Let c be s(10). Let k = 21 + c. Factor 4/7 + 6/7*i - 10/7*i**k.
-2*(i - 1)*(5*i + 2)/7
Suppose -6*u - 5*u - 2*u = 0. Factor u + 1/6*g**2 - 1/3*g.
g*(g - 2)/6
Let d(j) be the second derivative of -j**4/12 + j**3/3 - j**2/2 + 6*j. Let i be d(1). Factor -1/3*o**3 - 1/3*o**2 + 0 + i*o.
-o**2*(o + 1)/3
Let r(n) be the second derivative of 0 - 1/24*n**4 + 13/48*n**3 - 3/160*n**5 + 4*n - 3/8*n**2. Factor r(k).
-(k - 1)*(k + 3)*(3*k - 2)/8
Let r be 8/44 + (-106)/(-22). Let d(i) be the third derivative of 0*i + 1/120*i**6 + 0*i**3 + 0 + 2*i**2 + 0*i**4 + 1/60*i**r. What is u in d(u) = 0?
-1, 0
Let h = -8 - -13. Suppose -4*m + 6 = h*r, 3*r - 3 = -0*r - 3*m. Let 0 + 0*c**r - 2/9*c**3 + 0*c = 0. What is c?
0
Let m(z) = z**3 + z**2 - 8*z - 4. Let i be m(-3). Factor 2/9 + 2/9*u**i + 4/9*u.
2*(u + 1)**2/9
Let z(v) be the third derivative of -v**9/3024 - v**8/560 - v**7/420 - 2*v**3/3 + 9*v**2. Let p(g) be the first derivative of z(g). Factor p(t).
-t**3*(t + 1)*(t + 2)
Let t be ((-2)/(-4) + 1)*-6. Let o = -5 - t. Factor -2/3*m**o + 2/3*m**5 + 2/3*m - 4/3*m**3 + 4/3*m**2 - 2/3.
2*(m - 1)**3*(m + 1)**2/3
Let k(c) be the second derivative of 0 + 7/3*c**3 - 7/10*c**5 + 2*c**2 - 1/3*c**4 - c. Let k(h) = 0. What is h?
-1, -2/7, 1
Let m(f) = -6*f**3 - 6*f**2 + 4*f. Let n(l) = -l**3 - l**2. Let p(b) = m(b) - 4*n(b). Factor p(x).
-2*x*(x - 1)*(x + 2)
Let o = -18049/3 - -5949. Let t = o - -68. Factor -2/9*v**2 + 0*v - 2/9*v**5 - t*v**3 + 0 - 2/3*v**4.
-2*v**2*(v + 1)**3/9
Let n(u) be the third derivative of u**8/17280 - u**7/15120 - u**5/30 - 3*u**2. Let o(i) be the third derivative of n(i). Determine a, given that o(a) = 0.
0, 2/7
Let l(b) = -3*b**4 - 26*b**3 - 72*b**2 - 54*b + 27. Let a(r) = 3*r**4 + 26*r**3 + 72*r**2 + 54*r - 27. Let g(z) = 4*a(z) + 3*l(z). Factor g(f).
(f + 3)**3*(3*f - 1)
Let -4/3*m**3 + 2/3*m**4 + 4/3*m - 2/3 + 0*m**2 = 0. What is m?
-1, 1
Factor -x**2 + x**4 - 3*x**2 + 4*x**3 + 5*x**2 - 2*x**3.
x**2*(x + 1)**2
Let k(q) = -q**3 + 6*q**2 - 4*q - 3. Let r be k(5). Suppose -r*p = p. Suppose 0*u + 1/4*u**2 + p = 0. Calculate u.
0
Let r be (3 - 2) + (1 - -1). Let o(p) be the second derivative of -1/18*p**4 - 1/30*p**5 + 0*p**2 + 2*p + 1/45*p**6 + 1/9*p**r + 0. Factor o(h).
2*h*(h - 1)**2*(h + 1)/3
Let z be 1 - (-1)/(2/8). Factor 2*p**3 - p**4 - p**3 - p**z - 2*p**2 + 3*p**2.
-p**2*(p - 1)*(p + 1)**2
Let m(n) = -6*n**2 - 2*n - 4. Let d(x) be the first derivative of 11*x**3/3 + 2*x**2 + 7*x - 1. Let j(y) = -4*d(y) - 7*m(y). Find l, given that j(l) = 0.
-1, 0
Let b(y) be the first derivative of y**4/36 + y**3/3 - 43. Factor b(u).
u**2*(u + 9)/9
Let d = 15 - 12. Let l = -2 - -4. Factor -n**4 + d + 0*n + n + n**l - 3 - n**3.
-n*(n - 1)*(n + 1)**2
Let k(g) = 3*g**2 + 12*g + 12. Let o(s) = -s**2 - 4*s - 4. Let l be ((-8)/10)/((-2)/(-10)). Let r(j) = l*k(j) - 14*o(j). Factor r(b).
2*(b + 2)**2
Let w(h) = -h**4 - 17*h**3 + 24*h**2 + 22*h - 13. Let p(m) = 3*m**4 + 60*m**3 - 84*m**2 - 78*m + 45. Let i(r) = 5*p(r) + 18*w(r). Factor i(j).
-3*(j - 1)**2*(j + 1)*(j + 3)
Let u(x) be the first derivative of -3/4*x**3 - 4 + 1/4*x**4 + 3/4*x**2 - 1/4*x. Factor u(h).
(h - 1)**2*(4*h - 1)/4
Suppose 0 = 4*c + 23 - 31. Factor -1 + 0*y**4 + y**c - 2*y**3 + 1/2*y**5 + 3/2*y.
(y - 1)**3*(y + 1)*(y + 2)/2
Let h be ((-4)/(-6))/((-4)/48). Let s(n) = 53*n**3 + 13*n**2 - 32*n + 11. Let w(o) = -158*o**3 - 38*o**2 + 96*o - 32. Let l(c) = h*s(c) - 3*w(c). Factor l(z).
2*(z + 1)*(5*z - 2)**2
Let p(w) = -5*w**3 + 29*w**2 - 15*w - 45. Let i(k) = 5*k**3 - 30*k**2 + 15*k + 45. Let d(q) = 4*i(q) + 5*p(q). Factor d(t).
-5*(t - 3)**2*(t + 1)
Suppose 2*z - w = 6, 5*z - 4*z = 3*w + 3. Factor 3*m**3 - 11*m**4 - 6*m**3 + m**z + 12*m**4.
m**3*(m - 2)
Let a be (2 - 1) + 8/16*-2. Let z(f) = 2*f - 4. Let m be z(3). What is q in -10/3*q**m - 4/3*q + a = 0?
-2/5, 0
Let j(p) be the second derivative of 2/3*p**4 + 3/10*p**5 - 6*p + 0*p**2 + 0 - 1/21*p**7 - 2/45*p**6 + 4/9*p**3. Find u, given that j(u) = 0.
-1, -2/3, 0, 2
Let m(h) = h**2 - 1. Let c(f) = -f**2 + 1. Let b(p) = -5*c(p) - 2*m(p). Solve b(u) = 0 for u.
-1, 1
Let v(k) be the second derivative of k**6/10 + 21*k**5/80 + k**4/8 - k**3/8 - 3*k. Find y such that v(y) = 0.
-1, 0, 1/4
Suppose -5*f = -5, -3*b + 5*f - f + 8 = 0. Find l such that -2/9 + 0*l - 2/9*l**b + 0*l**3 + 4/9*l**2 = 0.
-1, 1
Suppose -7*z + 13 = -15. Let k(d) be the first derivative of 1 + 1/5*d**3 - 1/5*d + 1/10*d**z + 0*d**2. What is h in k(h) = 0?
-1, 1/2
Let h be 43/9 - (-8)/36. Factor -14*z**3 + 0*z**2 + h*z**3 + 11*z**2 - 2*z.
-z*(z - 1)*(9*z - 2)
Let j = 4 + -4. Let n(w) be the third derivative of 0*w + 0 - w**2 - 1/240*w**6 + j*w**4 + 0*w**3 + 0*w**5. Factor n(k).
-k**3/2
Let h(t) = -46*t**2 - 25*t + 21. Let l(o) = 15*o**2 + 5*o + 2. Let s(c) = -c**2 - 1. Let q(g) = l(g) + 6*s(g). Let j(f) = -2*h(f) - 11*q(f). Factor j(m).
-(m + 1)*(7*m - 2)
Let g = 3 + -1. Let c(y) be the first derivative of -1/9*y**3 + 1 - 2/3*y - 1/2*y**g. Factor c(z).
-(z + 1)*(z + 2)/3
Factor -1/4 - 1/4*j**2 + 1/2*j.
-(j - 1)**2/4
Let r(c) be the first derivative of -1/3*c**3 + 0*c**2 + c - 1 + 1/6*c**4. Let x(t) be the first derivative of r(t). Find k, given that x(k) = 0.
0, 1
Let p(w) be the first derivative of w**5/90 + w**4/36 - 2*w**3/9 - 3*w**2 + 5. Let o(y) be the second derivative of p(y). Find f, given that o(f) = 0.
-2, 1
Let t(a) be the first derivative of -44*a**3/9 - 26*a**2/3 - 8*a/3 + 5. Factor t(j).
-4*(j + 1)*(11*j + 2)/3
Let h(s) = 7*s**3 - 7*s - 4. Let j = 69 - 36. L