
-2*c*(c + 1)**2/3
Factor 1/2*u**2 - 3/4*u + 1/4.
(u - 1)*(2*u - 1)/4
Let r(l) be the third derivative of 1/42*l**5 + 2/21*l**4 + 0 + 0*l + 4/21*l**3 + 1/420*l**6 - 4*l**2. Factor r(p).
2*(p + 1)*(p + 2)**2/7
Let q(y) be the second derivative of y**7/56 + 3*y**6/40 + 9*y**5/80 + y**4/16 + y. Determine d so that q(d) = 0.
-1, 0
Factor -38/5*z**3 - 8/5 - 14/5*z**4 - 32/5*z - 10*z**2 - 2/5*z**5.
-2*(z + 1)**3*(z + 2)**2/5
Let l(t) = -10*t**4 - 34*t**3 - 33*t**2 - 7*t + 2. Let b(x) = -19*x**4 - 67*x**3 - 66*x**2 - 14*x + 4. Let n(p) = -3*b(p) + 7*l(p). Solve n(j) = 0.
-1, 2/13
Let o(i) be the second derivative of -1/30*i**4 - 1/30*i**3 + 1/75*i**6 + 0*i**2 + 0*i**5 + 1/210*i**7 + 0 + 6*i. Solve o(k) = 0 for k.
-1, 0, 1
Let n(j) = -j**3 + 2*j**2 + 3*j - 3. Let k be n(2). Factor -13*v**4 + 16*v**k - 4*v**3 - 4*v**2 + 2*v**3 + 3*v**4.
-2*v**2*(v - 1)*(5*v - 2)
Suppose 3*p + 0*p = 18. Let v(t) be the third derivative of -t**2 - 1/100*t**p + 0 + 0*t**3 + 1/75*t**5 + 0*t + 1/60*t**4. Factor v(r).
-2*r*(r - 1)*(3*r + 1)/5
Let r(d) be the third derivative of -3*d**2 + 0*d**3 + 0*d + 0 - 1/30*d**5 - 1/24*d**4 - 1/120*d**6. Suppose r(n) = 0. What is n?
-1, 0
Let v be ((-12)/(-2))/(-1 - -2). Let -4*l**5 + 6*l**4 - v*l**5 + 2*l**5 + 5*l**5 - 3*l**3 = 0. Calculate l.
0, 1
Let n(a) be the second derivative of a**7/147 + a**6/35 + a**5/35 + 20*a. Determine m so that n(m) = 0.
-2, -1, 0
Suppose -4*b + 13 = m, 2*m = -b - m + 6. Let l(v) be the third derivative of -1/3*v**4 + 0 - 4/3*v**b - 1/30*v**5 + 0*v + v**2. Suppose l(t) = 0. Calculate t.
-2
Let w(o) = 2*o + 5. Let p(c) = -c**2 - 5*c - 9. Let t(h) = -3*p(h) - 5*w(h). Factor t(v).
(v + 1)*(3*v + 2)
Let s = 65 + -62. Let y(h) be the third derivative of -1/360*h**6 + 0*h + 2*h**2 + 0*h**s + 1/72*h**4 + 0*h**5 + 0. Suppose y(m) = 0. What is m?
-1, 0, 1
Let c(x) be the second derivative of -x**6/135 + x**5/18 - x**4/6 + 7*x**3/27 - 2*x**2/9 - 20*x. Find o such that c(o) = 0.
1, 2
Let q be 3 - (-1 + (5 - 1)). Factor q + 0*v**3 - 1/5*v**4 + 2/5*v + 3/5*v**2.
-v*(v - 2)*(v + 1)**2/5
Suppose 0 = 2*u + t + 4, -20 = -2*u + u + 5*t. Suppose 2*r + 3*r - 15 = u. Solve -1/5 - 4/5*i**r + 1/5*i**2 + 4/5*i = 0.
-1, 1/4, 1
Let p(m) = 2*m - 2. Let l(c) = 2*c + 14. Let y be l(-6). Let h be p(y). Factor 0*r + 2*r**3 - 4/5*r**h + 0.
2*r**2*(5*r - 2)/5
Factor 3/2 + 0*q - 3/2*q**2.
-3*(q - 1)*(q + 1)/2
Suppose 4*d - 4*n = -3*n + 4, -2*d + 4*n - 12 = 0. Suppose 0 = -6*i + 2*i + 8. Factor 2*v**d - 8 - v**2 + 3*v + i + 2*v**2.
3*(v - 1)*(v + 2)
Let d be (6 - 165/39) + -1. Factor 6/13*p**3 - d*p**2 + 2/13 + 2/13*p.
2*(p - 1)**2*(3*p + 1)/13
Find b such that -11*b + 5*b**3 - 10 + 26*b - 15*b**3 + 5*b**3 = 0.
-2, 1
Let h(r) = 2*r**5 - 4*r**4 + r**2 - 5*r - 3. Let c(z) = -6*z**5 + 12*z**4 - 2*z**2 + 16*z + 10. Let o(b) = -3*c(b) - 10*h(b). Find v such that o(v) = 0.
-1, 0, 1
Let l be 0 + (-5)/((-5)/2). Let m be 2 - (45/10 - 3). Factor -m*o + 1/4*o**l + 0.
o*(o - 2)/4
Let s(w) be the third derivative of w**6/720 + w**5/120 + w**4/48 + w**3/36 + 20*w**2 + 3*w. Factor s(r).
(r + 1)**3/6
Let f(u) = -5*u**5 + 6*u**4 - 5*u**3 + 4*u**2 + 4*u + 4. Let m(n) = -10*n**5 + 13*n**4 - 10*n**3 + 7*n**2 + 7*n + 7. Let c(j) = -7*f(j) + 4*m(j). Factor c(i).
-5*i**3*(i - 1)**2
Let i be (-9)/6*(-6)/27. Factor 0 + 1/3*z**3 - 1/3*z**5 - i*z**2 + 0*z + 1/3*z**4.
-z**2*(z - 1)**2*(z + 1)/3
Let c(a) be the first derivative of -a**4/14 - 41. Solve c(w) = 0 for w.
0
Let q = 29 + -27. Let r be (2/(-3))/((-5)/6). Suppose -v**q + r*v**3 + 0 + 1/5*v = 0. Calculate v.
0, 1/4, 1
Let m(g) = 11*g**3 - 16*g**2 + 23*g. Let v(h) = -10*h**3 + 16*h**2 - 22*h. Let j(a) = 6*m(a) + 7*v(a). Factor j(x).
-4*x*(x - 2)**2
Let a be (-2)/(-8) + (-3)/(4*-3). Factor 0*g + 0 + a*g**4 - 1/2*g**5 + 1/2*g**3 - 1/2*g**2.
-g**2*(g - 1)**2*(g + 1)/2
Let i(p) be the second derivative of -p**9/22680 + p**7/1890 - p**5/180 - p**4/6 - 4*p. Let w(r) be the third derivative of i(r). Factor w(y).
-2*(y - 1)**2*(y + 1)**2/3
Let u = 7 - -1. Let x = 12 - u. Find c such that 2*c**x + c**5 + 0*c**5 + c**5 = 0.
-1, 0
Let u be (8/(-10))/((-2)/5). Factor -r**3 + u*r**3 - r**2 + 0*r**3 + 0*r**2.
r**2*(r - 1)
Let x be 17/35 + (-3)/15. Let b = -5 + 5. Factor x*y**2 + b*y + 0.
2*y**2/7
Suppose -3*j - 10 = 8. Let b be j/18 + 2/6. Factor b*h**3 - 2*h + 2*h**3 + h + 2*h**4 + h**3.
h*(h + 1)**2*(2*h - 1)
Let z be 3/2 - (0 + 1). Suppose -29*k + 28*k = -2. Factor 2*g - k - z*g**2.
-(g - 2)**2/2
Let m(b) be the second derivative of 0*b**3 - b - 1/54*b**4 + 1/189*b**7 - 1/45*b**6 + 1/30*b**5 + 0 + 0*b**2. Suppose m(o) = 0. What is o?
0, 1
Let x = -9 - -14. Suppose 4*n - 4*h = 8, n - x*h + 1 = -1. Find g such that 2*g + g**2 - g**3 - 3*g - n*g**2 = 0.
-1, 0
Let w be 2/(-5)*(6 - 21) - 2. Let k(p) be the third derivative of 1/12*p**3 + 1/24*p**w + 1/120*p**5 + 3*p**2 + 0 + 0*p. Let k(r) = 0. Calculate r.
-1
Let p(v) = v**3 - v**2 - v - 1. Let i(a) = -a**3 - a**2 + 5*a + 1. Let j(o) = i(o) + 2*p(o). Factor j(w).
(w - 1)**3
Let o(s) be the second derivative of -s**9/20160 - s**8/2240 - s**7/672 - s**6/480 + s**4/3 + 4*s. Let q(x) be the third derivative of o(x). Factor q(g).
-3*g*(g + 1)**2*(g + 2)/4
Let o(f) be the second derivative of f**4/54 - 2*f**3/27 + f - 11. Let o(v) = 0. Calculate v.
0, 2
Let s(g) be the first derivative of 0*g - 5/4*g**4 - 2*g**2 - 5 - 8/3*g**3 - 1/5*g**5. Factor s(d).
-d*(d + 1)*(d + 2)**2
Let d(w) be the second derivative of w**6/900 - w**5/150 + 2*w**3/3 + w. Let z(y) be the second derivative of d(y). Find b such that z(b) = 0.
0, 2
Let q(w) be the third derivative of 0*w + 0*w**6 + 0 + 0*w**3 + 1/75*w**5 - 1/60*w**4 + 1/840*w**8 + 5*w**2 - 2/525*w**7. Suppose q(b) = 0. What is b?
-1, 0, 1
Let m(p) be the first derivative of -p**4/6 + 2*p**3/3 - 6. Factor m(a).
-2*a**2*(a - 3)/3
Let y = 33 + -33. Suppose 2*z - 8 = g, -3 = -3*z - y*g - 3*g. Suppose -1/3*i**5 + i**z + 1/3*i**4 - 1/3*i**2 - 2/3*i + 0 = 0. What is i?
-1, 0, 1, 2
Let a(z) be the second derivative of 0*z**3 + 2*z + 0 - 1/30*z**4 + 1/5*z**2. Factor a(b).
-2*(b - 1)*(b + 1)/5
Let g be (-1 - -4)/((-78)/(-65)). Determine i so that g*i**2 + 0 - i = 0.
0, 2/5
Let r = -1/81 + 169/567. Let f = 1780/7 - 254. Factor 0 - 4/7*s**2 + 4/7*s**4 + r*s + 0*s**3 - f*s**5.
-2*s*(s - 1)**3*(s + 1)/7
Let t = -40 + 201/5. Suppose t*a**2 + 0 + 2/5*a = 0. What is a?
-2, 0
Suppose 0 = 3*s - 3 - 0. Factor -7*g + 1 + 8 + 4*g**2 - s - 5*g.
4*(g - 2)*(g - 1)
Let h(l) be the third derivative of -l**5/120 - l**4/24 + 3*l**2. Factor h(a).
-a*(a + 2)/2
Let a be 57/135 - 12/54. Let l(p) be the first derivative of 1/10*p**2 + 0*p + 1/5*p**3 + 2 - a*p**4. Factor l(m).
-m*(m - 1)*(4*m + 1)/5
Let l(q) be the second derivative of 1/2*q**2 + 0*q**3 + 1/210*q**5 - q + 1/84*q**4 + 0. Let p(c) be the first derivative of l(c). Factor p(n).
2*n*(n + 1)/7
Factor 289*r + 160*r**3 + 31*r**4 + 31*r + 128 + 320*r**2 + 9*r**4 + 4*r**5.
4*(r + 2)**5
Factor 6*y**3 - y**3 + 27*y**2 - 32*y**2.
5*y**2*(y - 1)
Suppose i + 7 = 9. Suppose 9/4*m**3 - 1/4 - 15/4*m**i + 7/4*m = 0. Calculate m.
1/3, 1
Let t(p) be the first derivative of -p**6/160 - p**5/20 - p**4/8 + p**2/2 + 2. Let v(c) be the second derivative of t(c). Factor v(o).
-3*o*(o + 2)**2/4
Let t(u) be the third derivative of -u**6/180 - u**5/90 + u**4/36 + u**3/9 + u**2. Factor t(y).
-2*(y - 1)*(y + 1)**2/3
Let t(m) = -m**3 - 4*m**2 + 4. Suppose -3*f - 2 - 10 = 0. Let q be t(f). Factor w**2 + w + 5*w**2 + w**3 - q*w**2.
w*(w + 1)**2
Let x(o) be the second derivative of -o**5/230 + 7*o**3/69 + 6*o**2/23 - 16*o. Solve x(h) = 0.
-2, -1, 3
Let m = -129 + 87. Let n be ((-7)/m)/((-1)/(-4)). Find p such that 4/3*p**2 - 2/3 - 2/3*p - n*p**5 + 4/3*p**3 - 2/3*p**4 = 0.
-1, 1
Factor 54*m**3 + 16*m - 3*m**3 + 49*m**3 - 80*m**2.
4*m*(5*m - 2)**2
Let c(i) be the first derivative of 2*i**3/7 - 6*i**2 + 42*i - 22. Factor c(m).
6*(m - 7)**2/7
Let n(o) = -20*o**4 - 14*o**3 + 41*o**2 - 7*o - 5. Let z(f) = 21*f**4 + 15*f**3 - 42*f**2 + 6*f + 6. Let j(p) = 6*n(p) + 5*z(p). Factor j(u).
-3*u*(u - 1)*(u + 2)*(5*u - 2)
Let s = 8 - 4. Suppose -2*g + 15 = 3*g. Let h(k) = -k**2 + 3*k + 1. Let o(l) = l**2 - 4*l - 1. Let j(r) = g*o(r) + s*h(r). Factor j(x).
-(x - 1)*(x + 1)
Determine t so that 6/13*t + 16/13*t**2 + 6/13*t**3 - 4/13 = 0.
-2, -1, 1/3
Let r(f) be t