*5/10 + p**4/4 - p**3/3 - 3*p**2/4 - p/2 - 14. Factor f(j).
(j - 1)*(j + 1)**4/2
Let s be 1 + (-6 + 3)/(-1). Factor 12*c**2 - 2 - 2 - s*c**3 + 4*c - 8.
-4*(c - 3)*(c - 1)*(c + 1)
Factor -1 + 16*z - 14 - 3*z**2 + 3 - z**2.
-4*(z - 3)*(z - 1)
Let p(r) = -4*r + 3. Let m be p(-1). Suppose w + 25 = 6*w. Factor 12*g - m - 4*g**2 + g**2 - w.
-3*(g - 2)**2
Let m(b) = -b**3 - 6*b**2 - 5*b + 2. Suppose -4*g = 19 + 1. Let r be m(g). Determine j, given that j**5 - j**4 - 2*j**4 + j**2 + 1 - 3*j + r*j**3 + j**2 = 0.
-1, 1
Factor -6*k**2 + k**5 - 11*k**2 + 16*k**2 - 3*k**4 + 3*k**3.
k**2*(k - 1)**3
Suppose 4*r - 86 = -4*n + 2*n, -20 = 4*n. Factor r + l**2 + l - 24.
l*(l + 1)
Let o(s) be the second derivative of 2*s**6/5 + s**5/5 - 5*s**4/3 - 2*s**3/3 + 4*s**2 + 23*s. Factor o(m).
4*(m - 1)*(m + 1)**2*(3*m - 2)
Let l(t) be the first derivative of -1/2*t**2 - 2*t**3 + 11*t + 2. Let o(i) = -i**2 + 2. Let m(w) = 2*l(w) - 11*o(w). Find f such that m(f) = 0.
-2, 0
Let c(u) be the second derivative of -u**6/165 + u**5/55 - 2*u**3/33 + u**2/11 - 8*u. Factor c(o).
-2*(o - 1)**3*(o + 1)/11
Let m = 185 + -2033/11. Determine w, given that -m*w**2 + 0 + 2/11*w = 0.
0, 1
Let l(m) be the second derivative of m**4/84 - 2*m**2/7 - 17*m. Factor l(r).
(r - 2)*(r + 2)/7
Let f = 11/35 + 4/35. Factor 3/7*a**2 + 6/7*a + f.
3*(a + 1)**2/7
Let h(n) = 3*n + n + n**3 + 1 - 3*n. Let k(y) = -27*y**4 - 12*y**3 - 6*y - 6. Let g(m) = -6*h(m) - k(m). Factor g(p).
3*p**3*(9*p + 2)
Suppose 3*r = -2*r + 20. Determine d, given that -32*d**3 - 10*d + 7*d + 28*d**2 - 5*d + 12*d**r = 0.
0, 2/3, 1
Factor -7*o**4 - 4*o**4 + 9*o**4.
-2*o**4
Let x(i) = 0*i**2 + 2*i + 2 - i**3 - 3 - i - 3*i**2 - 2*i**4. Let b(c) = 5*c**4 + 2*c**3 + 8*c**2 - 2*c + 3. Let w(t) = -3*b(t) - 8*x(t). Factor w(k).
(k - 1)*(k + 1)**3
Let b(q) be the third derivative of q**5/510 - 5*q**4/204 - 2*q**3/17 - 6*q**2. Factor b(a).
2*(a - 6)*(a + 1)/17
Let p be (-114)/15 - (-8)/(-20). Let g = p - -10. Factor -1/2 + 5*c - 25/2*c**g.
-(5*c - 1)**2/2
Let a(j) be the second derivative of j**4/16 + 11*j**3/8 - 6*j + 4. Let a(p) = 0. Calculate p.
-11, 0
Factor -1/3*a**2 - 10/3*a - 25/3.
-(a + 5)**2/3
Suppose -12*h - 2 = -14*h. Suppose 3*r - h = 8. Find a such that 1/4*a**5 + 9/4*a + 3/2*a**4 + 1/2 + 7/2*a**r + 4*a**2 = 0.
-2, -1
Suppose 15 - 5 = 2*t. Suppose 4*c + 19 = t*r, -3*r + 3*c + 0 = -9. Find s such that 0*s + r*s**3 - 2*s - s**2 + 0*s - 6*s**3 = 0.
-1, 0, 2
Factor 5*d**3 + 2*d + 7 - 25*d**2 + 32 + 6 + 13*d.
5*(d - 3)**2*(d + 1)
Let z(c) = c**2. Let s(m) = -2*m**3 + 3*m**2. Let n(d) = -2*s(d) - 2*z(d). Factor n(w).
4*w**2*(w - 2)
Let s(t) = -t**2 + 8*t + 12. Let x be s(9). Suppose -2*a + x + 1 = 0. Suppose 1/5*o - 2/5 + 3/5*o**a = 0. What is o?
-1, 2/3
Factor -4/3*z**2 - 2/3*z**3 + 2/3*z + 4/3.
-2*(z - 1)*(z + 1)*(z + 2)/3
Let y(c) be the third derivative of -c**8/23520 - c**7/4410 - c**6/2520 - c**4/6 - 2*c**2. Let i(f) be the second derivative of y(f). Find l such that i(l) = 0.
-1, 0
Suppose -4*f + 9 = -3. Solve m**2 + 3*m - 4*m**2 + f*m**3 - 2*m**3 - 1 = 0.
1
Suppose -3*m = -8*m + 100. Suppose -4*l - 4 = -m. Factor 2*g**4 + 4*g**2 - g**2 - l*g**3 - g**2.
2*g**2*(g - 1)**2
Let n(t) be the second derivative of t**6/540 - t**5/90 + t**4/36 - t**3/6 - 3*t. Let b(i) be the second derivative of n(i). Factor b(j).
2*(j - 1)**2/3
Let a = -4/275 + 1442/825. Factor -2/15*v + 4/15 - 6/5*v**2 - 2/3*v**4 + a*v**3.
-2*(v - 1)**3*(5*v + 2)/15
Let u be 1/(4/(-3) + 1). Let k(o) = -5*o**3 - 2*o**2 - 2*o + 2. Let n(i) = 2*i**3 + i**2 + i - 1. Let b(z) = u*k(z) - 7*n(z). Factor b(g).
(g - 1)**2*(g + 1)
Let k(r) = 3*r**4 - 2*r**3 - 15*r**2 - 10*r. Let v(y) = y**2 - y. Let z(a) = 3*k(a) - 12*v(a). Factor z(d).
3*d*(d - 3)*(d + 2)*(3*d + 1)
Let b(v) be the first derivative of v**6/27 - 2*v**5/45 - v**4/18 + 2*v**3/27 - 68. Factor b(u).
2*u**2*(u - 1)**2*(u + 1)/9
Let n = 94/75 + 2/25. Factor 2*j - n - 2/3*j**2.
-2*(j - 2)*(j - 1)/3
Let a(z) be the first derivative of 14*z**6/3 - 124*z**5/25 - 78*z**4/5 - 16*z**3/15 + 16*z**2/5 - 2. Suppose a(w) = 0. Calculate w.
-1, -2/5, 0, 2/7, 2
Let n(k) be the first derivative of -3/4*k**3 - 1/4*k**2 - 1 - 9/16*k**4 + 0*k. Factor n(x).
-x*(3*x + 1)*(3*x + 2)/4
Let i(x) = -x**2 + 5*x - 4. Let q(y) = -3*y**2 + 14*y - 11. Suppose 2*j + 12 = -0*j. Let g = -3 - j. Let z(d) = g*q(d) - 8*i(d). Determine h so that z(h) = 0.
1
Let u(v) be the third derivative of 0*v - 6*v**2 + 77/480*v**6 + 7/120*v**7 + 0 + 2/15*v**5 + 0*v**3 + 1/24*v**4. Let u(t) = 0. Calculate t.
-1, -2/7, 0
Let r(q) be the third derivative of q**8/112 - 3*q**7/70 + q**6/20 + q**5/10 - 3*q**4/8 + q**3/2 - 29*q**2. Solve r(g) = 0.
-1, 1
Suppose 0 = -5*x - 2*c + 8, -5*x + 5*c - 4*c - 4 = 0. Let f = x - -2. Solve -4 - s**f + 5 - 2*s + s**3 + s = 0 for s.
-1, 1
Let b = -10 - -13. Let a(c) be the second derivative of 0 + 20/3*c**b - 25/6*c**4 - 4*c**2 + c. Factor a(p).
-2*(5*p - 2)**2
Let w(a) be the second derivative of -2/75*a**6 + 0 + a - 2/5*a**3 + 3/25*a**5 - 1/60*a**4 - 2/5*a**2. Factor w(b).
-(b - 2)**2*(2*b + 1)**2/5
Suppose 4*p - 40 = 3*k - 8*k, 4*p = 2*k + 12. Factor -6/5*m**2 - 2/5*m - 2/5*m**k - 6/5*m**3 + 0.
-2*m*(m + 1)**3/5
Let d = -5 - -7. Factor 6*i**3 - d*i**2 + 4*i**3 - 10*i + 6*i**4 - 4 + 0*i**2.
2*(i - 1)*(i + 1)**2*(3*i + 2)
Let p(q) be the first derivative of -q**6/1260 + q**5/420 - q**3/3 - 3. Let v(i) be the third derivative of p(i). What is d in v(d) = 0?
0, 1
Let c(u) be the second derivative of 0 + 8/7*u**2 + 1/84*u**4 + u + 4/21*u**3. Factor c(g).
(g + 4)**2/7
Let q(p) = 3*p**3 - p**2 - p - 1. Let t be q(-1). Let w be -6*2*4/t. Suppose w - 12 + a - a**2 = 0. What is a?
0, 1
Let a = 3/182 - -2337/182. Determine u, given that -8*u + 8/7 + 8*u**3 - 14*u**4 + a*u**2 = 0.
-1, 2/7, 1
Let z(r) be the first derivative of -r**7/126 - r**6/90 - 7*r - 1. Let q(a) be the first derivative of z(a). Factor q(w).
-w**4*(w + 1)/3
Factor -13/2*w**4 + 1/2*w**2 + 0 + w - 9/2*w**3 - 5/2*w**5.
-w*(w + 1)**3*(5*w - 2)/2
Let t be 1 + 0 - (-1 + (1 - 1)). Find h, given that -h**3 + 1/3*h**t + 0 - 1/3*h**5 + h**4 + 0*h = 0.
0, 1
Let o be (-72)/(-60)*(-10)/(-6). Let d(m) be the first derivative of -1 - 2/3*m**3 - o*m - 2*m**2. Find s, given that d(s) = 0.
-1
Let r(t) = 2*t + 20. Let b be r(-9). Let j be (-10)/(-4)*(-8)/(-70). Let 2/7 - j*i**b + 0*i = 0. Calculate i.
-1, 1
Factor 0 + 19/2*s**3 + 15*s**4 + s**2 + 0*s.
s**2*(2*s + 1)*(15*s + 2)/2
Let c = 15 - 16. Let m be 12/(-48)*1*c. Factor -1/4*h**5 + 0*h - 1/4*h**4 + 1/4*h**2 + m*h**3 + 0.
-h**2*(h - 1)*(h + 1)**2/4
Let k = -8 + 15. Suppose -6*o + 0*o**2 - 3 + k + 2*o**2 = 0. What is o?
1, 2
Let l(h) = -h**3 + 7*h**2 + 6*h - 7. Let m(c) = c**3 - 8*c**2 - 7*c + 8. Let q(w) = -6*l(w) - 5*m(w). Factor q(v).
(v - 2)*(v - 1)*(v + 1)
Let g be (8/28)/(5/105). Let u(b) be the first derivative of -2 + 0*b**2 + 2/15*b**5 + 1/6*b**4 - 2/9*b**3 - 1/9*b**g + 0*b. Factor u(q).
-2*q**2*(q - 1)**2*(q + 1)/3
Let g be (-110)/(-100) + (-2)/((-10)/(-3)). Suppose -5*a + 12 = 4*i, 1 = a - 2*i + 7. Factor -m**3 + 0*m**2 + 0 + g*m**5 + 1/2*m + a*m**4.
m*(m - 1)**2*(m + 1)**2/2
Let c be 3/2*4/(-168)*-8. Factor 4/7*p - 2/7*p**2 - c*p**3 + 0.
-2*p*(p - 1)*(p + 2)/7
Let n = 9 + -9. Let f(u) be the second derivative of 1/30*u**4 + 0 - 1/5*u**2 - u + n*u**3. Factor f(y).
2*(y - 1)*(y + 1)/5
Let k(q) = -2*q + 18. Let u be k(9). Let z(m) be the third derivative of 0*m - 1/36*m**4 + u*m**3 - 1/90*m**5 + 0 - 3*m**2. Find s such that z(s) = 0.
-1, 0
Let r = 18 + -66. Let x = r - -193/4. Factor 3/2*q + x*q**2 + 9/4.
(q + 3)**2/4
Suppose -5957*t - 35 = -5964*t. Factor -8/5*j**2 - 6/5*j**3 + 8/5*j + 4/5*j**4 + 2/5*j**t + 0.
2*j*(j - 1)**2*(j + 2)**2/5
Let y = 1/310 - -3/31. Let w(n) be the second derivative of -y*n**5 - n**2 + 1/6*n**4 + 0 + 1/3*n**3 + n. Factor w(z).
-2*(z - 1)**2*(z + 1)
Let k(g) = 2*g**3 - 4*g**2 - 2*g. Let h = 5 + -10. Let j(a) = a**4 - 5*a**3 + 8*a**2 + 5*a + 1. Let i(r) = h*k(r) - 2*j(r). Determine p so that i(p) = 0.
-1, 1
Let u(w) be the first derivative of 7/30*w**6 + 4/5*w - 12/5*w**2 - 9/25*w**5 - 5 + 41/15*w**3 - 19/20*w**4. Factor u(j).
(j - 1)**3*(j + 2)*(7*j - 2)/5
Let v(q) be the first derivative of 16/7*q + 12/7*q**2 + 1/14*q**4 - 11 + 4/7*q**3. Factor v(p).
2*(p + 2)**3/7
Let v be (3 - 4)*(1 + -3). Solve