h(d) be the first derivative of d**3/4 + 33*d**2/4 + 363*d/4 - 43. Factor h(v).
3*(v + 11)**2/4
Suppose 2*w = 4*h - 4, 4*h + 2*w = w + 10. Let n be (-1)/(-2)*(3 + -3). Factor -1/3*a + 1/3*a**h + n.
a*(a - 1)/3
Let s(g) be the third derivative of -g**7/1260 + g**6/90 - g**5/15 + g**4/8 + 3*g**2. Let h(x) be the second derivative of s(x). Factor h(f).
-2*(f - 2)**2
Let h(n) = n**2 + 16*n + 3. Let l be h(-16). Solve 0*j + 0 - 6/5*j**l - 2/5*j**2 = 0 for j.
-1/3, 0
Let m(x) be the third derivative of 0 + 1/120*x**5 + 1/480*x**6 + 2*x**2 + 0*x**3 + 0*x + 1/96*x**4. Factor m(d).
d*(d + 1)**2/4
Suppose 45*i**5 - 206*i + 1910*i**3 + 557*i**2 + 933*i + 125 + 1673*i**2 + 198*i + 525*i**4 = 0. Calculate i.
-5, -1, -1/3
Suppose -3*a = -u + 6, 3*a = -2*u - 1 + 4. Factor 14/5*x**u + 2/5*x + 0 + 11/5*x**2.
x*(2*x + 1)*(7*x + 2)/5
Factor 0*m + 1/2*m**2 - 1/2.
(m - 1)*(m + 1)/2
Suppose -2*z = -16 + 62. Let c = -23 - z. Find y, given that -2/5*y**2 + 0*y - 6/5*y**3 + c = 0.
-1/3, 0
Let d(t) be the first derivative of 2 + 0*t**2 + t + 5/12*t**4 + 1/3*t**3. Let b(w) be the first derivative of d(w). Determine g, given that b(g) = 0.
-2/5, 0
Determine q, given that 20/7*q**3 + 20/7*q**2 + 2/7 + 10/7*q + 2/7*q**5 + 10/7*q**4 = 0.
-1
Factor 2/13*l**4 + 0 - 6/13*l**2 - 4/13*l + 0*l**3.
2*l*(l - 2)*(l + 1)**2/13
Let l(o) be the first derivative of 7*o**6/780 + 8*o**5/195 + 11*o**4/156 + 2*o**3/39 + o**2/2 - 2. Let m(p) be the second derivative of l(p). Solve m(c) = 0.
-1, -2/7
Let r(i) = 7*i**3 - 14*i**2 + 2*i - 5. Let w(a) = -a - a - 11*a**3 + 7*a**2 + 4*a**3 + 6 + 8*a**2. Let s(g) = 6*r(g) + 5*w(g). Factor s(t).
t*(t - 1)*(7*t - 2)
Let a(p) = -9*p**2 - 21*p - 12. Let j(d) = 5*d**2 + 11*d + 6. Let t(z) = -6*a(z) - 11*j(z). Factor t(i).
-(i - 6)*(i + 1)
Let m(b) = -3*b**3 + 10*b**2 - 5*b + 4. Let g(n) = n - 2*n - 5*n**2 + 3*n**3 - 5 + 5*n - 6*n**2. Let q(h) = 2*g(h) + 3*m(h). Factor q(u).
-(u - 1)**2*(3*u - 2)
Solve 6*h**3 - 48*h**2 + 27*h + 27*h**3 + 3*h**5 + 9*h**3 - 18*h**4 - 6 = 0 for h.
1, 2
Let w be -2 + (332/160 - 0) - 0. Let m(c) be the third derivative of w*c**5 - 3*c**2 - 7/48*c**4 + 1/420*c**7 + 0 - 1/48*c**6 + 1/6*c**3 + 0*c. Factor m(l).
(l - 2)*(l - 1)**3/2
Let n(k) = -21*k**3 + 14*k**2 + 21*k - 14. Let q(w) = 20*w**3 - 15*w**2 - 20*w + 15. Let x(i) = 5*n(i) + 4*q(i). Factor x(s).
-5*(s - 1)*(s + 1)*(5*s - 2)
Let o be 3/2 + (-324)/110. Let a = 3/55 - o. Find k such that -9/4*k**4 - 3/2*k + 0 - a*k**3 + 21/4*k**2 = 0.
-2, 0, 1/3, 1
Suppose -12/7*i**2 - 15/7*i - 3/7*i**3 - 6/7 = 0. What is i?
-2, -1
Let r(i) = -i. Let k be r(6). Let u = -6 - k. Suppose -4/9*f - 2/9*f**4 + 2/3*f**2 + u*f**3 + 0 = 0. What is f?
-2, 0, 1
Let z(l) be the third derivative of -l**8/3696 - l**7/770 - l**6/660 + l**5/330 + l**4/88 + l**3/66 - 14*l**2. Factor z(v).
-(v - 1)*(v + 1)**4/11
Let y(m) be the second derivative of -m**5/4 + 5*m**4/6 + 5*m**3/6 - 5*m**2 - 5*m. Find z, given that y(z) = 0.
-1, 1, 2
Let v(r) be the third derivative of -r**9/90720 + r**8/15120 + r**5/20 - 6*r**2. Let f(n) be the third derivative of v(n). Suppose f(c) = 0. What is c?
0, 2
Suppose -5 = -4*f + 4*x + 7, 0 = 2*f + 5*x - 6. Let w be 0/(1/(-2)*-2). Factor f*r + w*r**2 - 2*r - 7*r**2 - 3*r.
-r*(7*r + 2)
Let h(d) = -d**4 + d**2 - 4*d - 4. Let u(g) = -9*g**4 + 9*g**2 - 33*g - 33. Let k(r) = -33*h(r) + 4*u(r). Solve k(p) = 0 for p.
-1, 0, 1
Suppose 5*f - 2*v = 4, -3*v + 0 = -f + 6. Suppose -3*k + 8*k = f. Factor -10/3*g**5 + k - 8*g**4 - 6*g**3 + 0*g - 4/3*g**2.
-2*g**2*(g + 1)**2*(5*g + 2)/3
Let r(q) be the first derivative of q**6/30 + q**5/10 + q**4/12 + 8*q - 9. Let u(l) be the first derivative of r(l). Factor u(i).
i**2*(i + 1)**2
Let s(j) be the first derivative of j**7/15 - 19*j**6/60 + 4*j**5/15 + j**4/3 - 2*j**2 + 4. Let x(h) be the second derivative of s(h). Factor x(p).
2*p*(p - 2)*(p - 1)*(7*p + 2)
Let u(n) be the first derivative of 0*n**3 + 0*n + 1/21*n**6 + 0*n**2 - 1/7*n**4 + 2/35*n**5 + 1. Factor u(y).
2*y**3*(y - 1)*(y + 2)/7
Let y(d) be the third derivative of d**5/75 + d**4/10 + 4*d**3/15 - 5*d**2. Factor y(c).
4*(c + 1)*(c + 2)/5
Let j(k) be the first derivative of 1/3*k**3 - 1 + 1/2*k**2 + 0*k. Find l, given that j(l) = 0.
-1, 0
Let z(f) = 2*f**2 - 3*f - 4. Let y be z(4). Let g(v) = -10*v**2 - 4*v + 22. Let o(h) = 3*h**2 + h - 7. Let m(n) = y*o(n) + 5*g(n). Factor m(a).
-2*(a + 1)**2
Let o be (-40)/3*6/3. Let v = 27 + o. Let -v*w**5 - w**3 + 0 + 0*w - 1/3*w**2 - w**4 = 0. What is w?
-1, 0
Let t = -121387/12735 - 4/2547. Let w = t + 51/5. Determine h so that 2/3*h**2 + w*h + 0 = 0.
-1, 0
Let u(q) be the second derivative of -1/3*q**3 - 1/6*q**4 + 0 + 2*q + 2*q**2. Let u(d) = 0. Calculate d.
-2, 1
Factor 0*b + 0*b**2 + 0 - 8/9*b**4 + 2/9*b**5 + 8/9*b**3.
2*b**3*(b - 2)**2/9
Let z(p) be the third derivative of 0*p - 27/40*p**6 - 1/4*p**4 + 3*p**2 + 0*p**3 + 0 - 13/20*p**5 - 23/70*p**7 - 1/16*p**8. Factor z(g).
-3*g*(g + 1)**3*(7*g + 2)
Let v(d) be the first derivative of -d**6/18 + 8*d**5/15 - 25*d**4/12 + 38*d**3/9 - 14*d**2/3 + 8*d/3 - 20. Let v(o) = 0. What is o?
1, 2
What is w in -1/2 + 1/4*w**2 - 1/4*w = 0?
-1, 2
Suppose -4*s + 109 = -4*h - 7, -4*s - 5*h + 152 = 0. Let t = s - 131/4. Suppose t*m + 1/2 - 1/4*m**2 = 0. What is m?
-1, 2
Suppose 6/5*o + 4/5 + 2/5*o**2 = 0. What is o?
-2, -1
Let f(p) be the first derivative of -p**4/5 - p**3/3 - p**2/10 + 7. Solve f(u) = 0.
-1, -1/4, 0
Let j(w) = -18*w**3 + 12*w**2 - 2*w + 11. Let n(m) = 9*m**3 - 6*m**2 + m - 6. Let r(f) = -6*j(f) - 11*n(f). Factor r(b).
b*(3*b - 1)**2
Solve -o**5 + 23*o**2 + 3*o**3 + 0*o - 4*o - 11*o**2 - 16*o**2 + 2*o**4 = 0 for o.
-1, 0, 2
Let 0 + y**2 + 0*y + y**4 - 3/2*y**5 + 7/2*y**3 = 0. Calculate y.
-1, -1/3, 0, 2
Let b be 1/(2/12*2). Suppose 0 = -y + b - 1. Factor 3*s**y - 4 + 3 - s**3 - 3*s + 2.
-(s - 1)**3
Let m(k) = -k - 4. Let y be m(-6). Determine r so that -11*r**2 - 7*r**3 - 3*r**4 + 2*r**y - 3*r - 2*r**3 = 0.
-1, 0
Let y(u) = u**4 - 10 + u**2 + 8 - u - 3*u**3 + 0*u**4. Let i(x) = -5*x**4 + 13*x**3 - 4*x**2 + 5*x + 9. Let s(k) = -2*i(k) - 9*y(k). Factor s(m).
m*(m - 1)*(m + 1)**2
Let h(x) = 2*x**2 + x - 7. Let k(u) = -10*u**2 - 4*u + 34. Let t(i) = 28*h(i) + 6*k(i). Solve t(z) = 0.
-1, 2
Find j, given that -3*j + 3*j - 4*j - 3 - j**2 = 0.
-3, -1
Suppose h + 54 = 4*h. Let w = 37/2 - h. Factor -3/4*z - w + 1/4*z**3 + 0*z**2.
(z - 2)*(z + 1)**2/4
Let h(i) be the third derivative of i**5/60 - i**4/6 + 2*i**3/3 + i**2. Factor h(s).
(s - 2)**2
Let c = 95 + -189/2. Factor p**2 + c*p**3 + 0 + 1/2*p.
p*(p + 1)**2/2
Let s(g) = 3*g**4 + 4*g**3. Suppose -2*b - 4 = -26. Let t(w) = -9*w**4 - 11*w**3. Let d(i) = b*s(i) + 4*t(i). Factor d(y).
-3*y**4
Let c(v) be the third derivative of v**8/1848 - v**6/220 + v**5/165 - 9*v**2. Let c(h) = 0. Calculate h.
-2, 0, 1
Factor -2 + 7/2*n - 5/4*n**2.
-(n - 2)*(5*n - 4)/4
Let k(o) = o**2 - 13*o - 9. Let p be k(14). Suppose 10*w - 15 = p*w. Factor 3/2*j**w + 0 + 1/2*j**4 + j**2 + 0*j.
j**2*(j + 1)*(j + 2)/2
Let v(o) = o**3 + 5*o**2 - 8*o - 9. Let f be v(-6). Suppose 45*p**2 - 3*p**f - 45*p**2 = 0. Calculate p.
0
Let m(a) = -2*a**2 + 17*a - 8. Let c be m(8). Factor c - 2/3*u**2 - 4/3*u.
-2*u*(u + 2)/3
Let s(k) be the first derivative of 1/12*k**4 - 2 + 0*k**3 + 1/6*k - 1/30*k**5 - 1/6*k**2. Factor s(y).
-(y - 1)**3*(y + 1)/6
Let r(k) = -7*k**5 + 15*k**4 - 9*k**3 + 7*k**2. Let i(z) = -13*z**5 + 29*z**4 - 19*z**3 + 13*z**2. Let h(l) = 3*i(l) - 5*r(l). Factor h(t).
-4*t**2*(t - 1)**3
Find q such that -12*q**2 - 16*q**2 + 27*q**2 - 4*q = 0.
-4, 0
Let y(c) be the first derivative of 7/4*c**4 + 4*c**3 + 3/2*c**2 - 2*c - 4. Suppose y(u) = 0. Calculate u.
-1, 2/7
Suppose 4*l - 10 + 30 = 0, 3*l = -3*x + 3. Let j be (-9)/x*8/(-6). Let 2/3*g**4 + 1/3*g**3 + 0*g + 0*g**j + 1/3*g**5 + 0 = 0. Calculate g.
-1, 0
Let b(c) be the first derivative of -c**3/12 + 9*c**2/8 - 7*c/2 + 51. Factor b(i).
-(i - 7)*(i - 2)/4
Let k(x) = 13*x**3 - 34*x**2 + 27*x - 4. Let v(a) = -207*a**3 + 543*a**2 - 432*a + 63. Let f(y) = 33*k(y) + 2*v(y). Suppose f(h) = 0. Calculate h.
2/5, 1
Let x be ((-3)/(-9))/(3/9). Let d be 3 - x/(-2 - -3). Let p + 12*p**3 - 2*p**2 - 7*p**4 - 3*p - p**d = 0. Calculate p.
-2/7, 0, 1
Solve -2/11*f**2 + 0 + 0*f - 6/11*f**4 + 2/11*f**5 + 6/11*f**3 = 0 for f.
0, 1
Let i(g) be the first 