ppose -z*d + 3 = -d. Factor 1/3 + 1/3*p**d - 1/3*p**2 - 1/3*p.
(p - 1)**2*(p + 1)/3
Suppose -53 + 17 = -9*r. Let p(c) be the first derivative of 0*c**3 - 1/8*c**r - 1/4*c + 1/4*c**2 + 1/20*c**5 - 2. Determine i so that p(i) = 0.
-1, 1
Let c(m) = m**4 - m**3 - m. Suppose -2 = 11*o - 9*o. Let x(i) = 3*i**5 - 15*i**4 + 12*i**3 + 12*i. Let z(p) = o*x(p) - 12*c(p). Factor z(a).
-3*a**4*(a - 1)
Let 11/7*s**2 - 24/7*s - 36/7 - 1/7*s**3 = 0. Calculate s.
-1, 6
Let u(q) be the third derivative of q**6/80 - q**5/6 + 9*q**4/16 - 5*q**3/6 + 8*q**2. Let u(y) = 0. Calculate y.
2/3, 1, 5
Let n(a) = -5*a**2 - 6*a - 1. Let t(x) = -2*x**2 - 3*x - 1. Let p(s) = 6*n(s) - 14*t(s). Factor p(m).
-2*(m - 4)*(m + 1)
Let v(q) be the third derivative of 24*q**7/35 - 14*q**6/5 + 61*q**5/15 - 7*q**4/3 + 2*q**3/3 + 2*q**2 + 30*q. Factor v(x).
4*(x - 1)**2*(6*x - 1)**2
Let l(o) be the second derivative of o**5/70 + o**4/14 + 2*o**3/21 - 4*o - 4. Find i, given that l(i) = 0.
-2, -1, 0
Let h(s) be the third derivative of s**8/504 + s**7/315 - s**6/30 + s**5/45 + 5*s**4/36 - s**3/3 - 15*s**2. Suppose h(a) = 0. What is a?
-3, -1, 1
Let -3/4*g + 0 - 27/8*g**2 = 0. Calculate g.
-2/9, 0
Factor -2*s - 12*s**2 - 8*s**4 - 494*s**3 + 4*s**2 - 2*s**5 + 482*s**3.
-2*s*(s + 1)**4
Suppose -4*g = g - 20. Factor 71*y**2 - g*y - 77*y**2 + y + 3.
-3*(y + 1)*(2*y - 1)
Find w such that 4/5*w**2 - 4/5 - 2/5*w**3 + 2/5*w = 0.
-1, 1, 2
Let x(z) be the first derivative of -z**3/3 - 3*z**2 + 3*z - 1. Let y be x(-5). Factor -6*j**2 - 8 - y*j + 3*j**2 + j**2.
-2*(j + 2)**2
Suppose 11 = -3*a + 2*h, a - 3*h + 8 = -5. Let n be (a/(-4)*0)/1. Factor 0*f**3 - 2/5*f**2 + 0*f + n + 2/5*f**4.
2*f**2*(f - 1)*(f + 1)/5
Factor 3/4*k**3 + 9/4*k + 9/4*k**2 + 3/4.
3*(k + 1)**3/4
Let d(r) be the second derivative of r**5/60 - r**4/36 - r**3/9 + 2*r. Find y such that d(y) = 0.
-1, 0, 2
Let c be 2*5/16*(-336)/(-280). Determine z so that c*z**2 + 0 + 9/4*z = 0.
-3, 0
Let i(p) = -5*p**2 + p - 9*p - 7 + p**3 - 3*p**2. Let u be i(9). Let 0*a + 0*a**u + 0*a**4 + 1/4*a**5 + 0 - 1/4*a**3 = 0. Calculate a.
-1, 0, 1
Let j(y) = -5*y**4 - 55*y**3 + 60*y**2 + 105*y - 105. Let g(o) = o**4 + 14*o**3 - 15*o**2 - 26*o + 26. Let c(i) = 25*g(i) + 6*j(i). Factor c(b).
-5*(b - 2)**2*(b - 1)*(b + 1)
Let z(s) be the third derivative of -7*s**6/1440 + s**5/240 + s**3/6 + 2*s**2. Let h(a) be the first derivative of z(a). Factor h(u).
-u*(7*u - 2)/4
Let y(h) = 2*h**2 + h - 1. Let b be y(1). Find g, given that -6*g**2 + 12 - b*g - 13 + 5 = 0.
-1, 2/3
Let x(b) be the second derivative of 3*b**8/560 + b**7/350 - b**6/100 + b**2 - 3*b. Let c(l) be the first derivative of x(l). Factor c(d).
3*d**3*(d + 1)*(3*d - 2)/5
Factor 2/17*r + 2/17*r**2 - 4/17.
2*(r - 1)*(r + 2)/17
Let l = -29 + 35. Let x(s) be the third derivative of 0 + s**2 - 1/945*s**7 + 0*s + 0*s**3 - 1/270*s**l + 0*s**4 - 1/270*s**5. Factor x(d).
-2*d**2*(d + 1)**2/9
Suppose -3*a = 8 - 8. Let w(n) be the second derivative of -1/10*n**4 - 2/15*n**3 + 0*n**2 + 2*n + a. What is c in w(c) = 0?
-2/3, 0
Suppose 1780 = 2*x - 7*x. Let s = x + 1431/4. Factor 1/2*a - 1/2*a**3 + 0 + s*a**2 - 7/4*a**4.
-a*(a - 1)*(a + 1)*(7*a + 2)/4
Suppose -3*i + o + 3 = 2*o, 5*i + 3*o = 9. Let u(m) be the third derivative of -1/210*m**5 + 1/84*m**4 + 0 + m**2 + 0*m + i*m**3. Suppose u(k) = 0. Calculate k.
0, 1
Factor 1/7*o**2 + 9/7*o + 8/7.
(o + 1)*(o + 8)/7
Let k(j) be the first derivative of -1 + 1/10*j**2 + 1/30*j**6 - 1/10*j**4 + 0*j**5 + 0*j + 0*j**3. Factor k(i).
i*(i - 1)**2*(i + 1)**2/5
Let z(k) be the first derivative of -3*k**4/4 - 12. Factor z(s).
-3*s**3
Let h(z) = -z. Let t be h(-2). Suppose 11*p**4 + t*p**4 + 2*p + 8*p**5 + 14*p**2 + 30*p**3 + 13*p**4 = 0. What is p?
-1, -1/4, 0
Let l(t) be the first derivative of 2*t**5/55 + 5*t**4/22 + 6*t**3/11 + 7*t**2/11 + 4*t/11 - 7. Let l(u) = 0. Calculate u.
-2, -1
Factor 0*n**3 + 3/2*n**5 + 0*n + 0*n**2 + 0 - 3/2*n**4.
3*n**4*(n - 1)/2
Let k be (-2 - 2 - -5)/(1/2). Factor -4/3 - 2*r + k*r**3 + 2/3*r**4 + 2/3*r**2.
2*(r - 1)*(r + 1)**2*(r + 2)/3
Let b(q) be the second derivative of -1/120*q**6 + 0*q**2 - 1/6*q**3 - 1/8*q**4 + q - 1/20*q**5 + 0. Let f(v) be the second derivative of b(v). Factor f(p).
-3*(p + 1)**2
Let c(j) be the first derivative of -2*j**6/5 + 3*j**5/25 + 3*j**4/5 - j**3/5 + 8. What is h in c(h) = 0?
-1, 0, 1/4, 1
Let o(a) be the second derivative of 5*a**4/12 - 5*a**3/3 + 6*a. Let o(t) = 0. What is t?
0, 2
Let r(h) be the second derivative of -h**5/70 + h**4/6 - 5*h**3/7 + 9*h**2/7 - 2*h. Factor r(x).
-2*(x - 3)**2*(x - 1)/7
Let b(i) be the second derivative of i**7/1260 - i**6/360 + i**4/3 + i. Let f(l) be the third derivative of b(l). Let f(k) = 0. Calculate k.
0, 1
Let r be 1/((-4)/8) + 2. Let k(t) = t**3 + 4*t**2. Let u be k(-4). Find q, given that u*q + r - 2/3*q**2 = 0.
0
Let u = 107/1425 + -2/57. Let z(t) be the second derivative of 1/105*t**7 + 1/30*t**4 + 0*t**3 + 3/50*t**5 + 0 + 0*t**2 - 2*t + u*t**6. Factor z(q).
2*q**2*(q + 1)**3/5
Let y(g) = g**5 - g**4 - g - 1. Let v = -6 - -5. Let t(a) = 3*a**5 - 5*a**4 + 2*a**3 - a - 1. Let h(p) = v*y(p) + t(p). Factor h(z).
2*z**3*(z - 1)**2
Let z(h) = 29*h**5 + 49*h**4 + 20*h**3 + 8*h**2 - 4*h - 4. Let x(p) = -p**5 - p**4 + p**3 - p**2 + p + 1. Let t(v) = -4*x(v) - z(v). Factor t(c).
-c**2*(c + 1)*(5*c + 2)**2
Find w such that -5*w + 3*w**3 + 7*w + 3*w**2 - 2*w**3 = 0.
-2, -1, 0
Let q(v) be the first derivative of 196/45*v**5 + 8/3*v**3 + 0*v - 4/9*v**2 - 35/6*v**4 - 5. Factor q(u).
2*u*(2*u - 1)*(7*u - 2)**2/9
Let w = 4 + -3. Suppose 5*q + w = 11. Factor 11*n**2 - 8*n**3 - 13*n**2 + 4 - 10*n - 20*n**q.
-2*(n + 1)*(n + 2)*(4*n - 1)
Factor -d**2 - 2*d + 6 - d + 5 - 13.
-(d + 1)*(d + 2)
Factor 25*g**2 + 35*g + 223*g**3 + 0 + 15 - 218*g**3.
5*(g + 1)**2*(g + 3)
Determine v so that -1/9*v**3 - 1/9*v + 0 + 2/9*v**2 = 0.
0, 1
Let a(p) be the third derivative of p**5/270 - p**4/27 + 4*p**3/27 + 2*p**2. Factor a(n).
2*(n - 2)**2/9
Let t(h) be the second derivative of -9*h**5/40 + 3*h**4/8 - h**3/4 + h**2/12 - 19*h. Factor t(q).
-(3*q - 1)**3/6
Let h(l) be the first derivative of l**6/9 - 4*l**5/15 + l**4/6 - 1. Let h(w) = 0. Calculate w.
0, 1
Factor -18*a**2 + 120*a - 101*a**4 - 24*a**3 - 19 + 195*a**4 - 97*a**4 - 56.
-3*(a - 1)**2*(a + 5)**2
Let l(x) be the first derivative of 9*x**5/5 + 3*x**4/2 - 11*x**3/3 - 2*x**2 + 4*x - 2. Let l(m) = 0. What is m?
-1, 2/3
Let b be (4/(-70))/(2 - (-11)/(-5)). Factor 0 - 2/7*t - b*t**2 + 2/7*t**4 + 2/7*t**3.
2*t*(t - 1)*(t + 1)**2/7
Let r be (-2)/(4/24*-4). Factor -7*q**3 + 6*q**4 - 5*q**4 - q**2 - q**5 + 8*q**r.
-q**2*(q - 1)**2*(q + 1)
Suppose -3*j = -2*u - 16, 0 = -9*j + 8*j - 5*u - 23. Factor 0 + i - 1/2*i**j.
-i*(i - 2)/2
Let x(m) = -m**3 - 7*m**2 + 12*m - 15. Let l be x(-11). Let p = 2363/7 - l. Factor p + 6/7*b + 2/7*b**2.
2*(b + 1)*(b + 2)/7
Let r(t) = -3*t - 6. Let c be r(-6). Let q be (c/(-15))/(2/(-5)). Suppose -s - s**3 - 5*s**4 + 5*s**5 + 5*s**2 - q*s**3 - s**5 = 0. What is s?
-1, 0, 1/4, 1
Let i be 0 - (-5 + 3) - 5. Let l = 2 - i. Factor -2*v**3 + 0*v**4 + v**4 + v**l + v**3 - v**3.
v**3*(v - 1)*(v + 2)
Let n = 37/240 + -1/48. Let g(o) be the second derivative of 2*o - n*o**3 + 1/30*o**4 + 0 + 1/5*o**2. Factor g(m).
2*(m - 1)**2/5
Suppose -33 = -4*w - 9. Let l(s) be the second derivative of 0*s**3 - 1/168*s**7 + 0*s**2 + 0 + 0*s**4 - 1/80*s**5 - 1/60*s**w + 2*s. Let l(m) = 0. What is m?
-1, 0
Let a(z) = -z**3 + z**2. Let b(n) = 16*n**3 - 18*n**2 + 6*n + 4. Let l(d) = 36*a(d) + 2*b(d). Factor l(w).
-4*(w - 2)*(w + 1)**2
Let t be 39/33 + 4/(-22). Let o(f) be the first derivative of 1/6*f**2 + t - 2/9*f**3 + 1/3*f. Let o(l) = 0. Calculate l.
-1/2, 1
Suppose -2*w = -l, 0*w + 2*w = -l - 4. Let z be (-8)/(-24) - w/6. Solve -1/2 - j**3 - z*j**4 + 1/2*j + j**2 + 1/2*j**5 = 0.
-1, 1
Let l(v) be the first derivative of v**6/24 - v**5/20 - v**4/16 + v**3/12 - 3. Factor l(y).
y**2*(y - 1)**2*(y + 1)/4
Suppose 9 = 3*k + 5*j, -1 = 5*k + 4*j - 3. Let i be k/(-6)*3 - -6. Factor 3*y**3 + 2*y + y**2 - i*y**3 + 3*y**3.
-y*(y - 2)*(y + 1)
Let u(j) = 1. Let h(v) = 2*v**2 - 8*v + 6. Let c(i) = -2*h(i) - 4*u(i). Factor c(s).
-4*(s - 2)**2
Let h(b) be the first derivative of b**5/5 + b**4 + 2*b**3 + 2*b**2 + b - 12. Determine q so that h(q) = 0.
-1
Let b(h) be the 