1, -2/5, 0, 1
Let w(v) = v**2 - v - 2. Let o(a) = -48*a**2 + 83*a + 26. Let c(h) = o(h) + 3*w(h). Factor c(q).
-5*(q - 2)*(9*q + 2)
Let k(a) be the second derivative of -a**7/42 + 2*a**6/15 - a**5/5 + 34*a. Factor k(y).
-y**3*(y - 2)**2
Let r(u) be the second derivative of -u**5/120 - u**4/36 - u**3/36 - 9*u**2/2 - 8*u. Let c(m) be the first derivative of r(m). Suppose c(f) = 0. Calculate f.
-1, -1/3
Let p(j) be the first derivative of 5*j**3/12 - 5*j/4 - 27. Factor p(l).
5*(l - 1)*(l + 1)/4
Let b(k) be the third derivative of -k**6/30 + 2*k**5/15 - k**4/6 - 31*k**2. Find w, given that b(w) = 0.
0, 1
Let o be 4/(-10) - 15/25. Let h be 0 - o*(-1)/(-2). Let 1/2 + 2*c**3 + 3*c**2 + h*c**4 + 2*c = 0. What is c?
-1
Suppose c = -4*c + 10. Factor 2 - 4*t**2 - 7 + 3*t + 3*t**c + 3.
-(t - 2)*(t - 1)
Suppose 0 = w - 6 + 24. Let n be -5*3/w*2. Find t, given that -t**3 + 0 - 2/3*t - n*t**2 = 0.
-1, -2/3, 0
Suppose 84*h + 15 = 89*h. Factor -4/7*k**2 + 2/7 + 0*k**h + 2/7*k**4 + 0*k.
2*(k - 1)**2*(k + 1)**2/7
Let b = -5/2 - -27/10. Let s(v) be the second derivative of 1/6*v**4 + 1/12*v**6 - 1/84*v**7 - 3*v + 0*v**2 + 0 + 0*v**3 - b*v**5. Determine k so that s(k) = 0.
0, 1, 2
Let j(h) be the third derivative of -1/120*h**6 + 0 - 1/6*h**3 + 0*h + 1/60*h**5 - h**2 + 1/24*h**4. Determine r, given that j(r) = 0.
-1, 1
Suppose 8 = 3*b - 1. Let z(t) be the third derivative of 1/72*t**4 + 1/120*t**6 + 0*t + 3*t**2 + 0*t**b + 0 + 1/45*t**5. Suppose z(f) = 0. What is f?
-1, -1/3, 0
Let h(w) be the second derivative of w**6/20 - 3*w**5/40 - 3*w**4/8 + 5*w**3/4 - 3*w**2/2 - 6*w. Factor h(q).
3*(q - 1)**3*(q + 2)/2
What is q in -2/9*q**3 - 4/9*q**4 - 4/9*q + 0 + 10/9*q**2 = 0?
-2, 0, 1/2, 1
Let u be (-2)/(2/(-8)*2). Suppose -2*p + 13 = 3. Factor -p*i**u + 3*i**3 - 3*i**4 + 2*i**4 + 3*i**5.
3*i**3*(i - 1)**2
Let i(a) be the third derivative of -a**6/30 + 7*a**4/6 - 4*a**3 + 5*a**2. Factor i(o).
-4*(o - 2)*(o - 1)*(o + 3)
Let t(i) = i**4 + 8*i**3 + 18*i**2 - 26. Let y(w) = -1. Let x(k) = -t(k) - y(k). Factor x(h).
-(h - 1)*(h + 3)**3
Let y be 0/2*(-1 - -3)/(-2). Factor -2/3*r + y + 3*r**2 - 7/3*r**3.
-r*(r - 1)*(7*r - 2)/3
Let r(d) = -d**2 + 0*d**2 + 1 + 0*d - d**3 + d. Let c(f) = -2*f**3 + 10*f**2 - 10*f + 2. Let i(z) = c(z) + r(z). Solve i(v) = 0.
1
Let r(j) be the second derivative of j**8/5040 + j**7/2520 - j**6/540 - j**3/3 - 3*j. Let c(n) be the second derivative of r(n). Factor c(q).
q**2*(q - 1)*(q + 2)/3
Let c(u) = -u**3 - u**2 + 2. Let y be c(0). Let k be -8*((-12)/10 + 1). Factor -k + 0*l + 6/5*l**y - 2/5*l**3.
-2*(l - 2)**2*(l + 1)/5
Let r = -1 + 4. Suppose 5*m - 13 = -r. Factor m*k**2 - 2*k**3 + 6 - 2*k**4 - 6 + 2*k**5.
2*k**2*(k - 1)**2*(k + 1)
Factor -2/3*i**2 - 2/3*i**3 + 0 + 2/3*i**4 + 2/3*i.
2*i*(i - 1)**2*(i + 1)/3
Let w be (12 - 12)/(-2 - 1). Let u(z) be the third derivative of -1/6*z**4 + 0*z + w*z**3 + 0 - z**2 - 1/30*z**5. Factor u(q).
-2*q*(q + 2)
Let h(v) be the first derivative of v**6/54 - v**5/45 - v**4/36 + v**3/27 - 12. Factor h(m).
m**2*(m - 1)**2*(m + 1)/9
Let t(r) = r**2 - r + 2. Let f be t(1). Let -1/3*m**f - 1/3 - 2/3*m = 0. What is m?
-1
Factor -1/4*y**2 + 1 + 0*y.
-(y - 2)*(y + 2)/4
Let j = 7 - 15. Let p be -1*(0 + j/28). Factor 0 - 8/7*r - 8/7*r**2 - p*r**3.
-2*r*(r + 2)**2/7
Let u = -90 - -90. Factor 0 + u*y + 1/3*y**3 - 1/3*y**2.
y**2*(y - 1)/3
Factor 2*z**4 + z + 2 + 4*z**3 - 4 - 5*z.
2*(z - 1)*(z + 1)**3
Let d(j) be the first derivative of j**6/9 + 4*j**5/5 + 2*j**4/3 - 4*j**3/3 - 5*j**2/3 - 3. Determine g so that d(g) = 0.
-5, -1, 0, 1
Let d(y) be the second derivative of y**7/168 - y**6/60 + y**5/80 - 21*y. Factor d(a).
a**3*(a - 1)**2/4
Suppose -5*r = y - 27, 2 = 2*r + 2*y - 4. Find c, given that 7 - c**3 - 6 - 3*c + r*c**2 - 3*c**2 = 0.
1
Let k(l) be the first derivative of l**4/16 + 6. Find z, given that k(z) = 0.
0
Suppose 3*l + l = 16. Let b(m) = 2*m - 5. Let s be b(l). Factor 5*d**5 - 5*d**3 - 2*d**5 + d**3 + d**s.
3*d**3*(d - 1)*(d + 1)
Let g = 472 - 469. Factor -13/4*u**2 + 0 + 7/4*u**5 - 23/4*u**4 + 27/4*u**g + 1/2*u.
u*(u - 1)**3*(7*u - 2)/4
Let d be 378/135 + 1/5. Let 2/7*f + 0 + 2/7*f**d - 4/7*f**2 = 0. What is f?
0, 1
Suppose -2*m = z + 3 - 19, 5*z - 26 = -m. Suppose -m*p + 9*p - 9 = 0. Factor 4/3*o**p - 4/3*o + 0 - 2/3*o**4 + 2/3*o**2.
-2*o*(o - 2)*(o - 1)*(o + 1)/3
Find l such that -4 - 5 - l**2 + 4 - 4*l + 1 = 0.
-2
Let s(k) be the first derivative of 1/14*k**4 - 2/35*k**5 - 10 + 0*k + 0*k**2 + 4/21*k**3. Let s(f) = 0. What is f?
-1, 0, 2
Let u(q) = 4*q**4 + 11*q**3 - 11*q**2 - 9*q - 9. Let n(r) = -2*r**4 - 5*r**3 + 5*r**2 + 4*r + 4. Let h(y) = 9*n(y) + 4*u(y). Factor h(f).
-f**2*(f + 1)*(2*f - 1)
Factor -8/13*p - 2/13*p**2 + 0.
-2*p*(p + 4)/13
Factor -2*n**2 + 3*n**2 - 2*n**2 + 3 + 2*n.
-(n - 3)*(n + 1)
Suppose 8*d - 5*d = 0. Let k(w) be the first derivative of 1 + 4/21*w**3 + d*w**2 - 2/35*w**5 + 0*w**4 - 2/7*w. Factor k(b).
-2*(b - 1)**2*(b + 1)**2/7
Suppose -26 + 2 = -2*m. Let z be 6/(-2)*m/(-18). Solve 0 + 4/3*t - z*t**2 = 0 for t.
0, 2/3
Let o(l) be the third derivative of -l**10/15120 + l**9/7560 + l**8/3360 - l**7/1260 - l**4/12 - 2*l**2. Let r(z) be the second derivative of o(z). Factor r(f).
-2*f**2*(f - 1)**2*(f + 1)
Let q(i) be the first derivative of -9*i**4 + 88*i**3 - 152*i**2 + 96*i - 49. Let q(j) = 0. Calculate j.
2/3, 6
Let q(z) be the third derivative of z**8/1512 + 8*z**7/945 - 19*z**6/540 + z**5/27 - 8*z**2 + 2. Factor q(m).
2*m**2*(m - 1)**2*(m + 10)/9
Let t(f) = 2*f**3 + f**2. Let w(o) = 2*o**3 + 2*o**2. Let r(i) = -4*t(i) + 3*w(i). Factor r(g).
-2*g**2*(g - 1)
Let a(m) be the third derivative of -m**8/336 - 2*m**7/105 - m**6/30 + m**5/30 + 5*m**4/24 + m**3/3 - 3*m**2. Solve a(u) = 0.
-2, -1, 1
Let a be (-1)/6 - 176/(-192). Factor a*x**2 + 0 + x**3 - 1/4*x.
x*(x + 1)*(4*x - 1)/4
Let c(x) be the first derivative of x**6/15 - x**5/5 + x**4/6 - x - 6. Let g(u) be the first derivative of c(u). Factor g(a).
2*a**2*(a - 1)**2
Suppose -3*w - 2*i = -i - 13, -w - 2*i + 11 = 0. Find y such that 15*y**2 - 3*y - 4*y**w - 4 - 7*y - 2*y = 0.
-1/4, 2
Factor 0 + 0*y - 1/3*y**3 - 4/3*y**2.
-y**2*(y + 4)/3
Let r(j) = -j**2 - 12*j + 13. Let t be r(-13). Factor 5 + t + 60*q**2 + 60*q - 10*q**2 + 13.
2*(5*q + 3)**2
Let r(f) = -2*f**2 + 20*f - 6. Let l(i) = i**2 - 21*i + 6. Let n(h) = -3*l(h) - 4*r(h). Factor n(x).
(x - 3)*(5*x - 2)
Let a be (-6)/4*(-8)/6. Factor v - a*v**2 + v**3 + 2*v - 4*v + 2.
(v - 2)*(v - 1)*(v + 1)
Let 40/3*p - 16/3 - 1/3*p**4 + 10/3*p**3 - 11*p**2 = 0. What is p?
1, 4
Let m(j) be the first derivative of -j**4/16 + j**2/8 - 11. Suppose m(o) = 0. Calculate o.
-1, 0, 1
Suppose -15 = -g + 3*h, 5 = 3*g - h - 0. Let z be 10/15 - g/2. Suppose -z*o**2 + 2/3*o + 0 = 0. What is o?
0, 1
Let h(f) be the second derivative of f**5/50 + f**4/6 + 8*f**3/15 + 4*f**2/5 + 3*f. Factor h(p).
2*(p + 1)*(p + 2)**2/5
Let n = 1548/5 + -308. Solve n - 16/5*i + 14/5*i**4 - 6*i**2 - 6/5*i**5 + 14/5*i**3 = 0.
-1, 1/3, 2
Let n be (-14)/(-4) + 1*(5 - 8). Let 2*w**3 + 1 - 3/2*w + 0*w**4 - w**2 - n*w**5 = 0. Calculate w.
-2, -1, 1
Find u, given that 0*u**4 + 0*u**2 + 2/5*u**3 - 1/5*u + 0 - 1/5*u**5 = 0.
-1, 0, 1
Let u(b) be the first derivative of 4*b + 3 + 3/2*b**4 - 3*b**2 - 2/3*b**3 - 2/5*b**5. Factor u(h).
-2*(h - 2)*(h - 1)**2*(h + 1)
Let z be 4*(-4 + (-86)/(-20)). Find b such that 0*b**2 + 9/5*b - 3/5*b**3 - z = 0.
-2, 1
Let q(i) be the first derivative of -1/6*i**3 + 1 + 0*i - 1/4*i**2 + 1/8*i**4 + 1/10*i**5. Factor q(p).
p*(p - 1)*(p + 1)**2/2
Let l(v) = -7*v**5 + 16*v**4 - 24*v**3 + 13*v**2 - v. Let c(i) = 8*i**5 - 16*i**4 + 24*i**3 - 12*i**2. Let r(k) = 3*c(k) + 4*l(k). Factor r(f).
-4*f*(f - 1)**4
Let p(q) be the first derivative of q**4/9 + 12. Find j such that p(j) = 0.
0
Determine t, given that -7/2 + 1/4*t**2 - 13/4*t = 0.
-1, 14
Let d(h) = -h**3 + 8*h**2 - 6*h - 8. Let c be d(7). Let i = 3 + c. Factor 3*m**2 - m**2 - m**i - m**3.
-m**2*(m - 1)
Let z = 32 + -32. Suppose z = 10*m - 7*m. Factor -8/3*o + m - 1/3*o**4 - 2*o**3 - 4*o**2.
-o*(o + 2)**3/3
Let n(q) be the first derivative of 2/3*q**3 + 1/2*q**4 - 2/5*q**5 - q**2 + 1 + 0*q. Factor n(l).
-2*l*(l - 1)**2*(l + 1)
Factor 0*y - 32/3*y**3 - 2*y**4 + 32/3 - 16*y**2.
-2*(y + 2)**3*(3*y - 2)/3
Factor 0 - 2/5*w**4 - 1/5*w + 2/5*w**2 + 1/5*w**5 + 0*w**3.
