0
Let l(m) be the third derivative of 0 - 1/240*m**6 - 1/12*m**3 + 1/48*m**4 + 1/120*m**5 + 0*m - m**2. Factor l(c).
-(c - 1)**2*(c + 1)/2
Suppose -4*k + 7 = 2*f + 3, 3*f - 6 = -3*k. Factor 2*v**f + 1 - 4 + 3.
2*v**2
Let j be 12/24 - 2/4. Determine g so that -4*g**4 + 8*g - 12*g**4 - 2 + j*g**4 - 16*g**3 + 12*g**2 - 2 = 0.
-1, 1/2
Let l(y) be the second derivative of 0 - 1/8*y**4 + 0*y**3 + 1/4*y**2 - 2*y + 1/20*y**5. Suppose l(h) = 0. What is h?
-1/2, 1
Let v(p) = -1 + 3 + 3*p - 1 + 4*p. Let s(i) = i**2 - 27*i - 5. Let n(u) = -6*s(u) - 22*v(u). Factor n(t).
-2*(t - 2)*(3*t + 2)
Let a(t) = -t**3 + t**2 - t - 1. Let s(b) = -12*b**4 - 34*b**3 + 26*b**2 + 30*b - 14. Let v(u) = -2*a(u) + s(u). Solve v(w) = 0.
-3, -1, 1/3, 1
Let p(a) be the second derivative of a**4/32 - 3*a**2/16 - 6*a. Factor p(i).
3*(i - 1)*(i + 1)/8
Suppose -4*t = -7*t. Let z(g) be the second derivative of 3*g + t*g**2 + 0*g**3 + 1/24*g**4 + 0. Factor z(j).
j**2/2
Let z be (-84)/(-54)*-1 + 2. Let 4/9 - z*c**4 + 2/9*c**5 - 4/9*c**3 - 14/9*c + 16/9*c**2 = 0. What is c?
-2, 1
Let h = 2 - 7. Let j(w) = w**4 - w**2 + w - 1. Let g(s) = 15*s**4 - 6*s**3 - 29*s**2 - 3*s - 5. Let a(p) = h*j(p) + g(p). Suppose a(f) = 0. What is f?
-1, -2/5, 0, 2
Let f(p) be the first derivative of p**4 + 4*p**3 + 6*p**2 + 4*p - 15. Factor f(c).
4*(c + 1)**3
Suppose -4*u = -0*u - 72. Let -14*m - 4 + 0*m - 8*m**3 - 4*m**3 - u*m**2 + 2*m**3 - 2*m**4 = 0. Calculate m.
-2, -1
Let y(k) be the second derivative of -k**6/6 - k**5/2 + 55*k**4/12 + 10*k**3 - 90*k**2 + 5*k + 4. Find z such that y(z) = 0.
-3, 2
Let k = 3646/2285 + 2/457. Factor 2/5*f**2 + k*f + 8/5.
2*(f + 2)**2/5
Let s(r) be the third derivative of -2*r**2 + 0*r**3 - 1/60*r**5 + 0 + 0*r + 1/24*r**4. Determine y, given that s(y) = 0.
0, 1
Suppose 5*w - 8 = w. Let j(t) be the second derivative of 0 + w*t - 2/3*t**4 + 0*t**3 - 2/5*t**5 - 1/15*t**6 + 0*t**2. Suppose j(a) = 0. What is a?
-2, 0
Solve 28*a**3 - 544/7*a + 80/7 + 124*a**2 = 0 for a.
-5, 2/7
Find h such that 50/7 + 2/7*h**3 + 10*h + 22/7*h**2 = 0.
-5, -1
Solve 13 - 46 + 6*a**4 - 15*a + 27*a**2 + 18 + 18 - 21*a**3 = 0.
1/2, 1
Let 18/5*x - 6*x**2 - 2/5*x**4 + 0 + 14/5*x**3 = 0. What is x?
0, 1, 3
Let z be 24 - 27 - (-35)/11. Determine c so that 2/11 + 4/11*c + z*c**2 = 0.
-1
Factor 15 + 6*z + 3/5*z**2.
3*(z + 5)**2/5
Let l(g) = 34*g**3 + 6*g**2 - 20*g - 20. Let h(u) = 7*u**3 + u**2 - 4*u - 4. Let j(t) = -14*h(t) + 3*l(t). Factor j(v).
4*(v - 1)*(v + 1)**2
Let d(t) be the third derivative of t**8/840 + t**7/525 - t**6/150 - t**5/75 + t**4/60 + t**3/15 + 8*t**2. Solve d(c) = 0.
-1, 1
Let j(f) = 3*f - 25. Let n be j(10). Let o(g) be the first derivative of 0*g**2 + 2/35*g**n - 2/21*g**6 + 0*g**3 + 1/14*g**4 + 0*g + 3. Factor o(u).
-2*u**3*(u - 1)*(2*u + 1)/7
Let t(f) be the second derivative of f**10/105840 - f**8/11760 + f**6/2520 - f**4/4 + 3*f. Let a(q) be the third derivative of t(q). Factor a(s).
2*s*(s - 1)**2*(s + 1)**2/7
Let s = 14 - 8. Factor 1 + s*z**4 + 2 - 3*z**4 - 6*z**2.
3*(z - 1)**2*(z + 1)**2
Let h(w) be the first derivative of 1/2*w**4 + 1 + 3/5*w**5 + 0*w**2 - 3*w**3 + 4*w. Factor h(l).
(l - 1)**2*(l + 2)*(3*l + 2)
Let m be 4/10*(8 - -2). Factor 3*y**4 - 5*y**4 + 0*y**4 + 2*y**3 + y**m.
-y**3*(y - 2)
Let g = 15607/22 - 3710671/5236. Let c = 3/119 + g. Factor c*b**4 - 1/2*b**3 - 1/4*b**5 - 1/2*b**2 - 1/4 + 3/4*b.
-(b - 1)**4*(b + 1)/4
Let t be (12 + -2)*1*-2. Let v be (-2)/4*t/45. What is w in -2/9*w**2 + 2/9*w**3 - v*w + 0 + 2/9*w**4 = 0?
-1, 0, 1
Let k(i) = i**3 - 8*i**2 + 22*i - 9. Let s(r) = r**3 - 9*r**2 + 21*r - 9. Let n(w) = -4*k(w) + 6*s(w). Determine f so that n(f) = 0.
1, 9
Let c(z) = -z**2 + z + 1. Let u(v) = 26*v**2 + 10*v - 5. Let b(p) = -2*c(p) + u(p). Let x(a) = -14*a**2 - 4*a + 4. Let n(q) = 4*b(q) + 7*x(q). Factor n(j).
2*j*(7*j + 2)
Factor -l**2 - 2*l**2 + 18 - 3*l + 0*l + 0*l.
-3*(l - 2)*(l + 3)
Let i(k) = 4*k**3 - 3*k**2 + 4 - 5 + 3. Suppose -4 = -4*n + 6*n. Let w(y) = y**3 + y**2 + y. Let x(o) = n*w(o) + 2*i(o). Factor x(h).
2*(h - 1)**2*(3*h + 2)
Let j(o) = o + 1. Let x(q) = q**2 - 4*q - 4. Let u(z) = -4*j(z) - x(z). Solve u(w) = 0.
0
Let w(r) be the second derivative of 0 - 2*r - 1/12*r**4 + 0*r**3 + 1/20*r**5 + 0*r**2. Factor w(h).
h**2*(h - 1)
Let c be (-3)/9 - (-100)/60. Suppose c - 2/3*p**2 + 2/3*p = 0. Calculate p.
-1, 2
Let i(c) be the second derivative of 3*c + 0 + 1/20*c**4 - 1/5*c**3 + 3/10*c**2. Factor i(h).
3*(h - 1)**2/5
Let k be 9/12 + 3/(-4). Suppose -1 + 6*o - 2*o + o**2 + k*o - o**3 - 3*o**3 = 0. What is o?
-1, 1/4, 1
Let g(t) be the second derivative of 1/30*t**3 + 1/150*t**6 + 0 - t - 1/100*t**5 - 1/60*t**4 + 0*t**2. Factor g(r).
r*(r - 1)**2*(r + 1)/5
Let c(h) = 10*h + 61. Let d be c(-6). Let q(p) be the first derivative of -3/16*p**4 - d + 0*p + 0*p**2 - 1/4*p**3. Factor q(g).
-3*g**2*(g + 1)/4
Let c(v) be the first derivative of 2*v**5/35 + 9*v**4/14 + 18*v**3/7 + 27*v**2/7 - 20. Factor c(o).
2*o*(o + 3)**3/7
Suppose 3*z + 3 - 15 = 0. Let j(f) be the first derivative of 2*f**3 + 1/2*f**z + 2*f**2 + 1 + 0*f. Suppose j(y) = 0. What is y?
-2, -1, 0
Let w(c) be the third derivative of -1/2*c**3 - 2*c**2 + 1/20*c**5 - 1/8*c**4 + 0*c + 1/40*c**6 + 0. Factor w(l).
3*(l - 1)*(l + 1)**2
Let v = 3/2 + -13/10. Let 1/5 - 2/5*b**2 + v*b = 0. Calculate b.
-1/2, 1
Suppose 1/5*a**3 - 3/5*a + 0*a**2 - 2/5 = 0. Calculate a.
-1, 2
Let k(p) = 2*p**2 - 2*p - 12. Let t be k(-2). Find l such that -1/2*l**3 + 1/2*l + t + 0*l**2 = 0.
-1, 0, 1
Let r(b) be the first derivative of -1/14*b**4 - 1 - 2/7*b - 3/7*b**2 - 2/7*b**3. Determine l so that r(l) = 0.
-1
Let n(d) be the second derivative of d**7/945 + d**6/180 + d**5/90 + d**4/108 - 3*d**2/2 - 3*d. Let t(s) be the first derivative of n(s). Solve t(h) = 0.
-1, 0
Let k(z) be the third derivative of 3/70*z**7 + 2/5*z**5 + 0*z - 1/224*z**8 - 7/40*z**6 + 0 + 2*z**2 - 9/16*z**4 + 1/2*z**3. Factor k(r).
-3*(r - 2)*(r - 1)**4/2
Solve 3/2 - 1/2*s**2 + s = 0 for s.
-1, 3
Suppose 20 = t - 4*p, 30 = 3*t - 2*p - 0*p. Suppose -3*u + 4 = u, 3*z - t = 4*u. Factor -h**2 - 9/2*h**3 - 5/2*h**5 - 6*h**z + 0 + 0*h.
-h**2*(h + 1)**2*(5*h + 2)/2
Let c(p) be the first derivative of 3*p - 10 + 3/2*p**2 - 9*p**3 - 27/4*p**4. Factor c(z).
-3*(z + 1)*(3*z - 1)*(3*z + 1)
Let d(n) = -n**2 - 2*n + 3. Let o be d(-3). Let h be (-1 + o)/(1/(-4)). Find m such that 4 - h - 2*m + 2*m**3 = 0.
-1, 0, 1
Factor -10*c + 6 - 15*c**5 - 15*c**3 + 66*c**4 + 96*c**2 - 99*c**3 - 29*c + 0.
-3*(c - 1)**4*(5*c - 2)
Factor -4*t**2 + 8*t - 13 + 5*t**4 - t**4 + 13 - 8*t**3.
4*t*(t - 2)*(t - 1)*(t + 1)
Suppose 5*a - 1 - 9 = 0. Suppose -3*d - 2*d + a*j + 18 = 0, 2*j - 2 = 0. Determine c, given that -1/3 - 2/3*c + 0*c**2 + 2/3*c**3 + 1/3*c**d = 0.
-1, 1
Let l(s) be the third derivative of -s**7/168 + s**6/48 - s**5/48 - 4*s**2. Solve l(p) = 0.
0, 1
Factor 46*l - 7*l + 11*l + 5*l**2 + 125.
5*(l + 5)**2
Let j(o) = o**3 - 7*o**2 + 7*o - 4. Let m be j(6). Let h be (4/8)/(m/8). Factor 1/3*y**h - 2/3*y + 0.
y*(y - 2)/3
Suppose -b + 5 + 29 = 0. Determine k so that -32*k**2 - 2*k - 3 + b*k**2 - 1 = 0.
-1, 2
Suppose 2*k - 10 = 2. Let o = 6 - k. Factor -1/3*l**2 - 1/3*l + o.
-l*(l + 1)/3
Let t be -1*(-3)/(-6)*0. Let o = t - -2/3. Solve 0 + o*h + 2/3*h**4 + 2*h**3 + 2*h**2 = 0 for h.
-1, 0
Factor 0 - 1/2*k**2 - 1/3*k - 1/6*k**3.
-k*(k + 1)*(k + 2)/6
Let z(h) be the third derivative of h**8/112 + h**7/105 - h**6/20 - h**5/15 + h**4/8 + h**3/3 - 10*h**2. Solve z(q) = 0.
-1, -2/3, 1
Let w(j) = -2*j - 6. Let y be w(-5). Let n(z) be the second derivative of 0 + 0*z**3 + 0*z**y + 1/45*z**6 - 3*z + 0*z**2 + 0*z**5. Suppose n(b) = 0. What is b?
0
Let q(a) be the first derivative of -a**3/9 + 2*a**2/3 - a - 3. Find h, given that q(h) = 0.
1, 3
Let h(i) be the second derivative of -i**5/40 + i**3/12 + 3*i. Factor h(v).
-v*(v - 1)*(v + 1)/2
Let q(d) be the third derivative of -d**9/7560 - d**8/1680 + d**7/1260 + d**6/180 + d**4/12 + 3*d**2. Let l(g) be the second derivative of q(g). Factor l(z).
-2*z*(z - 1)*(z + 1)*(z + 2)
Suppose -103*g**2 + 12*g**4 - 3*g**5 - 48*g - 4*g**3 + 7*g**5 + 59*g**2 - 16 = 0. What is g?
-2, -1, 2
Let j(b) be the third derivative of -3*b**7/280 + b**6/160 + 23*b**5/240 + 13*b**4/96 + b**3/12 - 4*b**2. Suppose j(a) = 0. Calculate a.
-1, -1/3, 2
Let c be 21