2*c**2. Factor z(a).
5*(6*a - 1)**2
Let z(w) be the second derivative of w**4/48 - w**2/8 + 3*w. Factor z(c).
(c - 1)*(c + 1)/4
Let o(w) = -15*w**2 - 3*w + 6. Let i be 1/(-6) + 206/12. Let q(a) = 44*a**2 + 9*a - 17. Let f(p) = i*o(p) + 6*q(p). Factor f(d).
3*d*(3*d + 1)
Let s(y) be the third derivative of y**5/60 - y**4/24 - y**3/3 + 5*y**2. Find h, given that s(h) = 0.
-1, 2
Solve -25/7*b**4 + 29/7*b**2 - 9/7*b**5 - 4/7 - 3/7*b**3 + 12/7*b = 0 for b.
-2, -1, 2/9, 1
Let s = -9 + 15. Solve 27*b**3 + 60*b**2 + s + 5 - 5 + 39*b = 0.
-1, -2/9
Let q(a) be the first derivative of a**6/57 - 2*a**5/95 - 3*a**4/19 - 4*a**3/57 + 5*a**2/19 + 6*a/19 + 20. Suppose q(l) = 0. What is l?
-1, 1, 3
Let z be (12/(-9))/((-2)/(-1)). Let a = z + 7/6. Factor x**3 - 1/2*x**5 + x**2 - a*x**4 - 1/2*x - 1/2.
-(x - 1)**2*(x + 1)**3/2
Let f(a) = a**3 + 3*a**2 + 5*a + 15. Let l be f(-3). Let o(d) be the second derivative of -27/4*d**2 + l - 4*d - 1/8*d**4 - 3/2*d**3. Factor o(r).
-3*(r + 3)**2/2
Let c(d) be the third derivative of d**7/525 + d**6/100 - d**5/30 - d**4/20 + 4*d**3/15 - d**2 + 2. Factor c(u).
2*(u - 1)**2*(u + 1)*(u + 4)/5
Let j be (-2667)/(-8820) - 2/7. Let a(f) be the third derivative of 0 + 0*f + j*f**5 + 0*f**3 + f**2 + 1/24*f**4. Factor a(u).
u*(u + 1)
Let m = 10 - 9. Let -r**5 - m + r**3 + 1 + 4*r**2 + r**4 - 5*r**2 = 0. What is r?
-1, 0, 1
Let u = -15 + 31/2. Suppose y + 29*k = 26*k + 18, 4*k - 14 = 2*y. Factor 0 + 3/2*z**2 + 1/2*z**4 - u*z - 3/2*z**y.
z*(z - 1)**3/2
Let g(d) be the second derivative of -d**6/135 + d**4/54 + 6*d. Factor g(f).
-2*f**2*(f - 1)*(f + 1)/9
Let q = 11 + -7. Factor -2*r**q + 3*r - 2*r + 2*r**2 - 3*r + 2*r**3.
-2*r*(r - 1)**2*(r + 1)
Factor 0 + 3/5*g - 6/5*g**2 + 3/5*g**3.
3*g*(g - 1)**2/5
Find d such that -4*d**2 + 4/3*d**4 + 32/3*d - 16/3 - 8/3*d**3 = 0.
-2, 1, 2
Let q = -8 + 13. Suppose -4*y + 28 = q*w, -3*y - 4 = -10. Determine z so that w + 1 - 5 + 2*z - 4*z**2 + 2*z**3 = 0.
0, 1
Let i(t) = 6*t**4 + 14*t**3 - 2*t - 2. Let y(v) = v**4 - v**3 - v + 1. Let n(w) = i(w) + 2*y(w). Solve n(b) = 0.
-1, 0, 1/2
Let y be (-4 - 148/(-32))*3/90. Let d(z) be the second derivative of 0 - z + 1/8*z**2 + 1/24*z**3 - 1/80*z**5 - y*z**4. Find g, given that d(g) = 0.
-1, 1
Let k be 28/16 + 3/(-12). Suppose 3/2 - 3/2*c**2 - 3/2*c**3 + k*c = 0. Calculate c.
-1, 1
Find o such that 1 + 1/2*o - 3/2*o**2 = 0.
-2/3, 1
Let f be (-3 + -2)*18/(-10). Suppose -u = -4*u + f. Factor -5*p**2 - u*p**4 + 8*p**2 - 3*p + 3*p.
-3*p**2*(p - 1)*(p + 1)
Let o be 25/6 - (0 - -4). Let i(t) be the second derivative of 0 - o*t**4 + 3*t + 0*t**2 - 2/3*t**3. Factor i(v).
-2*v*(v + 2)
Let f(w) = -12*w**3 + 60*w**2 - 84*w + 22. Let y(c) = -4*c**3 + 20*c**2 - 28*c + 7. Let p(j) = 5*f(j) - 14*y(j). Factor p(d).
-4*(d - 3)*(d - 1)**2
Suppose d + 2 = 3*d. Factor -16 - u - 17 - 15*u - 2*u**2 + d.
-2*(u + 4)**2
Let r(o) be the third derivative of o**7/1365 + o**6/780 - o**5/130 - o**4/156 + 2*o**3/39 + o**2. Solve r(q) = 0 for q.
-2, -1, 1
Let x(j) be the third derivative of -5*j**8/672 - j**7/28 + 11*j**6/24 - 19*j**5/12 + 45*j**4/16 - 35*j**3/12 + 21*j**2. Factor x(c).
-5*(c - 1)**4*(c + 7)/2
Suppose n = -2*n + 15. Suppose 5*u = -t - 10 - 3, 2*u = -n*t + 4. Solve 0*m + 2/9*m**t + 0 - 2/9*m**3 = 0.
0, 1
Let z(s) = 2*s**4 + 2*s**3 - 3*s. Let o(h) = -5*h**4 - 5*h**3 + 8*h. Let i(d) = 8*d**3 - d**2 + d. Let v be i(1). Let g(l) = v*z(l) + 3*o(l). Factor g(a).
a**3*(a + 1)
Let k(a) be the second derivative of -a**5/60 + a**4/12 - 2*a**2 + 2*a. Let s(o) be the first derivative of k(o). Factor s(m).
-m*(m - 2)
Let y(z) be the first derivative of 2*z**3 - 1/2*z**4 + z**2 + 0*z - 6/5*z**5 - 3. Factor y(l).
-2*l*(l - 1)*(l + 1)*(3*l + 1)
Factor -1/12*n**2 + 0 - 1/6*n.
-n*(n + 2)/12
Let k(t) be the second derivative of -t**6/10 - 3*t**5/5 - 5*t**4/4 - t**3 - t. Factor k(o).
-3*o*(o + 1)**2*(o + 2)
Let r be (-9)/(-3 - (-1 - 1)). Suppose -4*f + r*f - 10 = l, -5*f - 2*l + 25 = 0. Find a, given that -a**3 - a**3 - 10*a - 8*a**2 - 4 - f*a**3 + 3*a**3 = 0.
-2, -1
Suppose 5*a - p - 7 = -4*p, a - 4*p = 6. Factor 6/5*o - 9/5*o**3 + 0 + 3/5*o**a.
-3*o*(o - 1)*(3*o + 2)/5
Let h(n) be the second derivative of n**5/90 - n**4/54 - 2*n**3/27 - n. Let h(b) = 0. What is b?
-1, 0, 2
Let u(n) be the second derivative of 0*n**4 + 1/3*n**3 + 0 + 0*n**2 - 3/10*n**5 + 5*n + 2/15*n**6. Factor u(z).
2*z*(z - 1)**2*(2*z + 1)
Factor 4/5*y**2 - 12/5 - 8/5*y.
4*(y - 3)*(y + 1)/5
Let v(f) be the third derivative of 0 - 1/420*f**6 + 1/1176*f**8 + 0*f - 2*f**2 + 0*f**3 - 1/735*f**7 + 0*f**4 + 1/210*f**5. Factor v(o).
2*o**2*(o - 1)**2*(o + 1)/7
Let q = -471 - -22609/48. Let j(x) be the second derivative of -x - 1/12*x**3 + 0 + 1/8*x**2 + q*x**4. Factor j(y).
(y - 1)**2/4
Let p(t) be the first derivative of -t**4/14 + 2*t**3/21 + 2*t**2/7 - 1. Factor p(o).
-2*o*(o - 2)*(o + 1)/7
Let x(f) be the first derivative of -3*f**4/4 + 6*f**3 - 27*f**2/2 + 12*f - 13. Factor x(p).
-3*(p - 4)*(p - 1)**2
Let d(p) = -4*p - 4. Let g be d(-2). Factor g*i**4 - 4*i**2 + 22*i - 12*i - 3*i**5 + i**5 - 8*i.
-2*i*(i - 1)**3*(i + 1)
Factor 0*u**4 + 1/5*u**5 + 0*u**2 + 1/5*u - 2/5*u**3 + 0.
u*(u - 1)**2*(u + 1)**2/5
Suppose -14*g**4 - 16*g - 40*g**2 + 23*g**3 - 59*g**3 + 22*g**5 - 24*g**5 = 0. What is g?
-2, -1, 0
Let y(k) be the second derivative of -k**7/42 + 17*k**6/150 - 21*k**5/100 + 11*k**4/60 - k**3/15 - 34*k. Factor y(c).
-c*(c - 1)**3*(5*c - 2)/5
Let p(z) = 11*z**3 - 12*z**2 + z - 5. Let d(n) = 27*n**3 - 30*n**2 + 3*n - 12. Let g(m) = 5*d(m) - 12*p(m). Solve g(v) = 0.
0, 1
Suppose 3*h = 4*h. Suppose -5*u = -3*u - 5*l - 24, 5*u - 3*l - 22 = h. Find y such that -5/2*y**3 + 0 + 4*y**u + 2*y = 0.
-2/5, 0, 2
Suppose 0 = -2*g - g. Let m(s) be the first derivative of 1/2*s**2 + 1/4*s**4 - 1 + g*s + 2/3*s**3. Solve m(l) = 0.
-1, 0
Solve 11*k**2 + 11*k**2 - 18*k + 162 - 18*k - 20*k**2 = 0.
9
Determine x so that 243/2 + 3/2*x**2 + 27*x = 0.
-9
Let c(p) be the first derivative of -7*p**6/30 + p**5/4 + p**4/6 - 5*p - 5. Let n(z) be the first derivative of c(z). Solve n(h) = 0.
-2/7, 0, 1
Let k(m) be the second derivative of m**7/2940 - m**6/420 + m**5/140 - m**4/84 - 5*m**3/6 + 6*m. Let n(l) be the second derivative of k(l). Factor n(q).
2*(q - 1)**3/7
Let g(w) = w + 3. Let x be g(0). Determine i so that 0*i**2 - 2*i**2 - 3*i + i**x + 5*i**2 - 2*i**3 + 1 = 0.
1
Let v(i) be the third derivative of -i**7/840 + i**6/160 - i**5/120 + 3*i**2. Suppose v(q) = 0. Calculate q.
0, 1, 2
Factor 4*n**2 - 4*n**4 + 2*n**3 - 3*n + 0*n + 87*n**5 - 86*n**5.
n*(n - 3)*(n - 1)**2*(n + 1)
Let d(o) = 2*o**3 - 13*o**2 - 6*o - 16. Let y be d(7). Let h be (y - -5)*4/(-14). Let -h + 6/7*w**2 + 20*w**3 - 14*w**4 - 40/7*w = 0. What is w?
-2/7, 1
Let i(y) be the second derivative of y**4/30 + 4*y. Solve i(j) = 0.
0
Let l(x) be the first derivative of x**8/3360 - x**7/1120 - x**6/1440 + x**5/160 - x**4/96 - x**3 - 5. Let d(t) be the third derivative of l(t). Factor d(i).
(i - 1)**2*(i + 1)*(2*i - 1)/4
Let i(w) = -w**2 + 5*w + 3. Let t be (-8)/((-3 + 2)*2). Let c be i(t). Find l, given that 4*l + 3 - c + 5*l**2 - 6*l**2 = 0.
2
Let d(w) be the second derivative of 1/6*w**4 - 6*w + 0 - 1/6*w**3 + 0*w**2 - 1/20*w**5. Factor d(f).
-f*(f - 1)**2
Solve 26*p**2 - 35*p**4 - 5*p - 5*p + 35*p**5 + 19*p**2 - 10*p**4 - 25*p**3 = 0.
-1, 0, 2/7, 1
Factor 1/4 + 0*g - 1/4*g**2.
-(g - 1)*(g + 1)/4
Let h(j) = 3*j**2 - 24*j + 38. Let a be h(6). Factor 2/7 + 4/7*f**a + 6/7*f.
2*(f + 1)*(2*f + 1)/7
Let q be 2 + 0 + 0/3. Factor -2/7 + 2/7*u**q + 2/7*u**3 - 2/7*u.
2*(u - 1)*(u + 1)**2/7
Let g(k) be the first derivative of 1/7*k**2 + 0*k + 0*k**3 + 3 - 1/14*k**4. Solve g(i) = 0.
-1, 0, 1
Solve 7*a + 4*a**2 + 10*a**2 - 4*a**2 + 9*a - 8 = 0 for a.
-2, 2/5
Let q(v) = -v**5 - v**4 - v**2 - v. Let c(s) = -8*s**5 - 14*s**4 + 7*s**3 - 12*s**2 - 9*s. Let i(n) = 4*c(n) - 36*q(n). Factor i(o).
4*o**2*(o - 3)*(o - 1)**2
Let c(g) be the third derivative of g**6/420 - g**5/70 + g**4/28 - g**3/21 + 6*g**2. Find s such that c(s) = 0.
1
Let o(p) = -p + 12. Let n be o(8). Let x be 0 + n + (1 - 3). Factor 0 + 1/3*u**x + 1/3*u.
u*(u + 1)/3
Suppose 5*v = 2*k - 28, 4*v + 8 + 4 = -k. Let l be 9/2*v/(-6). Factor -4/7*f**2 + 2/7*f**l + 0 + 2/7*f.
2*f*(f - 1)**2/7
Let q(t) = -2*t**2 - 9*t + 7. Let f be q(-5). Let a be (