9
Let o(q) be the third derivative of -3*q**5/20 - q**4/4 + q**3/2 - 13*q**2. Let o(a) = 0. What is a?
-1, 1/3
Let u(l) = -8*l + 160. Let c be u(20). Find w, given that -8/3*w**4 + 2/3*w**2 - 2*w**3 + 0*w + c = 0.
-1, 0, 1/4
Let f(s) = -s + 6. Let j be f(5). Let n be j - 5/(15/3). Find p such that 0*p + 1/4*p**3 + n - 1/4*p**2 = 0.
0, 1
Factor 1/7*j**2 - 2/7 + 1/7*j**4 + 3/7*j - 3/7*j**3.
(j - 2)*(j - 1)**2*(j + 1)/7
Let k(d) be the first derivative of -4*d**6/15 - 7*d**5/10 - d**4/3 + d**3/3 + 4*d - 6. Let r(o) be the first derivative of k(o). Factor r(b).
-2*b*(b + 1)**2*(4*b - 1)
Let v(m) = -5*m**3 - 2*m**2 - 5*m - 4. Let j(y) = -y**3 - y - 1. Let s(q) = -12*j(q) + 3*v(q). Find t, given that s(t) = 0.
-1, 0
Suppose 14*m - 16*m = -2. Let p be m*15/(-6) + 4. Find r such that 1/2*r**2 + 1/2*r**4 - 1 - 3/2*r**3 + p*r = 0.
-1, 1, 2
What is r in 0*r + 0 + 2/11*r**2 + 2/11*r**3 = 0?
-1, 0
Let b(f) = -6*f**2 - 2*f + 16. Let g(i) = 11*i**2 + 3*i - 31. Let q(p) = 7*b(p) + 4*g(p). Factor q(m).
2*(m - 3)*(m + 2)
Let m(t) be the third derivative of t**5/210 - t**4/42 - t**3/7 + 12*t**2 - 1. Factor m(r).
2*(r - 3)*(r + 1)/7
Let k(s) = -s**5 + s**3 + 3*s**2 - 3. Let c(o) = -o**2 + 1. Let v(t) = 12*c(t) + 4*k(t). Factor v(r).
-4*r**3*(r - 1)*(r + 1)
Let f(u) = -4*u**3 + 4*u**2 + 2. Let p(o) = -o**3 - o. Let n(k) = f(k) - 5*p(k). Factor n(g).
(g + 1)**2*(g + 2)
Let y(u) be the second derivative of 3*u**5/100 - u**4/20 - u**3/2 - 9*u**2/10 + 11*u. Factor y(j).
3*(j - 3)*(j + 1)**2/5
Let n(y) = -y**4 + y**3 + 4*y**2 - 4*y - 4. Let l = 7 - 11. Let j(g) = g**2 - g - 1. Let m(i) = l*j(i) + n(i). Solve m(w) = 0.
0, 1
Let f(x) = -x - 6. Let j be f(-6). Factor -2*p + 3*p + j*p**3 + p**2 - 7*p**3 + p**3.
-p*(2*p - 1)*(3*p + 1)
Suppose 3*v - 9 - 9 = 0. Let y(a) be the third derivative of -2/15*a**5 - a**2 - 1/12*a**4 + 0*a + 0*a**3 + 0 - 1/15*a**v. Solve y(j) = 0.
-1/2, 0
Let h(n) be the first derivative of 14/5*n**5 + 2*n**2 + 0*n + 9 + 2*n**3 - 6*n**4. Solve h(f) = 0.
-2/7, 0, 1
Let j(m) be the third derivative of 2*m**7/105 - 3*m**6/10 + 7*m**5/5 - 19*m**4/6 + 4*m**3 + 21*m**2. Factor j(k).
4*(k - 6)*(k - 1)**3
Let u(w) = -30*w**2 + 18*w + 6. Let m(v) = -59*v**2 + 37*v + 12. Let i(h) = -3*m(h) + 5*u(h). Solve i(c) = 0.
-2/9, 1
Suppose 2*c + 11*p - 6*p = -41, 3*c + 34 = -2*p. Let x = c - -10. Factor -2*q - q**2 + 3*q**x + 8*q - 5*q**2.
-3*q*(q - 2)
Find c, given that 3/2*c**3 + 0 + 9/2*c**4 - 5/2*c**2 + 1/2*c = 0.
-1, 0, 1/3
Let t(o) = -o. Let b be t(-3). Factor 3*a**5 + 6*a**4 - 6*a**2 + 2*a**3 - 2*a**b - 3*a.
3*a*(a - 1)*(a + 1)**3
Let i(l) be the second derivative of l**5/30 - 2*l**4/9 + 5*l**3/9 - 2*l**2/3 - 5*l. Factor i(t).
2*(t - 2)*(t - 1)**2/3
Suppose -5/3 + 1/3*t**2 - 4/3*t = 0. What is t?
-1, 5
Let q be 1335/178 - (1 - 0). Solve 0*m + 35/6*m**3 - q*m**2 + 2/3 = 0.
-2/7, 2/5, 1
Let v(a) be the second derivative of -a**5/30 - a**4/9 + 16*a. Determine o so that v(o) = 0.
-2, 0
Let p(y) be the second derivative of 0 - 3*y + 5/12*y**4 - 2*y**3 + 3/5*y**5 + 2*y**2 - 3/10*y**6. Find j, given that p(j) = 0.
-1, 2/3, 1
Let z be 2/(-7) + 264/42. Suppose 3*f - z*f = -42. Factor -2 - o**2 - f*o - o**2 + 10*o.
-2*(o + 1)**2
Let q = -7 + 12. Let g = q - 1. Suppose -3*r**4 + 5*r**4 - 4*r**5 + g*r**3 + 2*r**2 - 4*r**2 = 0. What is r?
-1, 0, 1/2, 1
Let -h - 1/2*h**2 + 3/2 = 0. What is h?
-3, 1
Let l(j) = -30*j**4 + 150*j**3 - 270*j**2 + 210*j - 25. Let s(u) = 5*u**4 - 25*u**3 + 45*u**2 - 35*u + 4. Let r(t) = -6*l(t) - 35*s(t). Factor r(m).
5*(m - 2)*(m - 1)**3
Let n(s) be the first derivative of -s**4/38 - 4*s**3/57 + 3*s**2/19 - 1. Factor n(v).
-2*v*(v - 1)*(v + 3)/19
Factor -4*u - 20 - 6*u**2 + 29*u + 2*u**2 - u**2.
-5*(u - 4)*(u - 1)
Let d(x) = 15*x**2 + 380*x + 155. Let y(a) = 4*a**2 + 95*a + 39. Let v(n) = -6*d(n) + 25*y(n). Suppose v(q) = 0. Calculate q.
-9, -1/2
Let g(x) be the third derivative of 4*x**6/165 + 4*x**5/165 + x**4/132 - 4*x**2. Find d, given that g(d) = 0.
-1/4, 0
Let s(u) = 3*u**2 - u - 10. Let f(z) = 15*z**2 - 6*z - 51. Let r(m) = 4*f(m) - 21*s(m). Factor r(v).
-3*(v - 1)*(v + 2)
Let b(t) = t + 9. Let j be b(-6). Determine k, given that 0*k**4 - j*k**5 + 2*k**5 - k**5 - 2*k**4 = 0.
-1, 0
Let l(j) be the first derivative of -1/15*j**5 + 1/3*j - 1/6*j**4 + 1/3*j**2 + 0*j**3 + 4. Factor l(w).
-(w - 1)*(w + 1)**3/3
Let m(v) be the second derivative of v**7/70 - 3*v**6/40 + v**5/10 - 3*v**2/2 + 4*v. Let i(u) be the first derivative of m(u). Find c, given that i(c) = 0.
0, 1, 2
Let t(l) be the first derivative of -2*l**6/3 + 9*l**5/5 - l**4/2 - 8*l**3/3 + 3*l**2 - l - 3. Suppose t(n) = 0. What is n?
-1, 1/4, 1
Let l be (-22)/(-8) + 10/8 + -1. Factor -1/6*w**l + 1/3 + 1/2*w**4 - 1/2*w - 3/2*w**2.
(w - 2)*(w + 1)**2*(3*w - 1)/6
Let z(a) be the third derivative of -a**6/40 + a**5/10 - a**4/8 - 9*a**2. Factor z(o).
-3*o*(o - 1)**2
Suppose -4 = -4*a + 8. Solve -3*y**2 - y**3 - y**3 + 7*y**a + 5*y**2 = 0 for y.
-2/5, 0
Let b be (18/25)/((-42)/(-140)). Factor b*j - 12/5 - 3/5*j**2.
-3*(j - 2)**2/5
Let y be (-30)/(-21) - (-16)/28. Suppose 0*k - y*k = 5*j - 6, 4*k = -3*j - 2. Factor -j*o**3 + 0*o - 8/3 + 14/3*o**2.
-2*(o - 2)*(o - 1)*(3*o + 2)/3
Let o(y) = y + 2. Let r be o(6). Let x(i) = i**2 - 26*i + 8. Let d(l) = 9*l - 3. Let c(z) = r*d(z) + 3*x(z). Find a, given that c(a) = 0.
0, 2
Let k(t) = t**2 - 6*t - 7. Let f be k(7). Suppose f*r = 3*r - 6. Factor -1/2*n + 1 - 15/2*n**r.
-(3*n - 1)*(5*n + 2)/2
Let j = 16384 - 149209/9. Let v = 195 + j. Factor -v*t**2 + 0 + 2/9*t.
-2*t*(t - 1)/9
Let c(s) = 2*s**2 - s - 1. Let x(o) = -o**3 + o**2 - o. Let q be x(1). Let p be c(q). Factor -1 + 7/2*z**p + 7/2*z - 6*z**3.
-(z - 1)*(3*z + 2)*(4*z - 1)/2
Let y be ((-2)/(-6))/(6/126). Suppose 4*v + c = 17, -2*c - y = -4*v - c. Solve -5*p + 3 - 3*p + v*p**2 + 2*p = 0.
1
Let t(z) be the second derivative of 2*z**6/15 - 6*z**5/5 + 3*z**4 + 7*z. Solve t(c) = 0 for c.
0, 3
Let i(h) be the first derivative of 10*h**6/9 + 8*h**5 + 55*h**4/4 - 85*h**3/9 - 35*h**2/2 + 15*h - 20. Solve i(j) = 0.
-3, -1, 1/2
Let g be 145/(-1260) - 3/(-21). Let n(a) be the second derivative of 0 + 1/18*a**3 - 2*a + 0*a**2 + g*a**4. Factor n(w).
w*(w + 1)/3
Factor 0*h**5 + 12*h + 32*h**2 - 36*h**3 + 60*h**3 - 4*h**5.
-4*h*(h - 3)*(h + 1)**3
Let g be (-1)/(-1) + -11 + 3. Let f = -3 - g. Factor 0*b**4 - b**4 + 0*b**f - 2*b**3 - b**2.
-b**2*(b + 1)**2
Let y = 482 - 480. Let -1/3*c - 2/3*c**y - 1/3*c**3 + 0 = 0. What is c?
-1, 0
Let p(c) be the second derivative of -c**6/135 - c**5/45 + 2*c**4/27 + 8*c**3/27 - 7*c. Find o such that p(o) = 0.
-2, 0, 2
Let g = -2 - -4. Let r be -1*(-2 + -2 + g). Factor q**3 - 3*q**3 - r*q**5 + q + 3*q**5.
q*(q - 1)**2*(q + 1)**2
Let t(h) be the third derivative of 11/1050*h**7 + 0 + 23/300*h**5 + 23/600*h**6 - h**2 + 1/15*h**3 + 11/120*h**4 + 0*h + 1/840*h**8. Factor t(s).
(s + 1)**3*(s + 2)*(2*s + 1)/5
Let -48/5*u**5 + 0 + 96/5*u**2 + 189/5*u**3 + 12/5*u - 24/5*u**4 = 0. What is u?
-2, -1/4, 0, 2
Let l(o) = -5*o**3 + 30*o**2 - 67*o + 40. Let f(x) = 6*x**3 - 30*x**2 + 66*x - 39. Let d(m) = 2*f(m) + 3*l(m). Factor d(y).
-3*(y - 7)*(y - 2)*(y - 1)
Let b(h) be the first derivative of 6 - 8/15*h**5 + 0*h + 0*h**2 - 1/6*h**4 + 0*h**3. Factor b(n).
-2*n**3*(4*n + 1)/3
Suppose 3*l - 15 = 2*a + a, 2*a + 4 = 0. Let q(h) = h**2 - h - 3. Let i be q(3). Suppose 5*j**l + 2*j**2 - 4*j + 2*j - i*j**3 - 2 + 0*j**3 = 0. Calculate j.
-1, 1
Suppose m - 2*k - 12 = 2, -3 = -3*k. Find q, given that -71*q + 7*q - m - 30*q**2 + 2*q**2 = 0.
-2, -2/7
Let v = 369/2 - 184. Factor 1/4*f - v*f**3 + 0 + 0*f**4 + 0*f**2 + 1/4*f**5.
f*(f - 1)**2*(f + 1)**2/4
Let l = 17 - 15. Suppose -6*z = -l*z - 16. Factor 2/3*k - 2/3*k**z + 0 + 2/3*k**2 - 2/3*k**3.
-2*k*(k - 1)*(k + 1)**2/3
Let n(z) be the first derivative of -z**4/24 + z**3/6 - z**2/4 + z/6 + 21. Factor n(u).
-(u - 1)**3/6
Let l(a) be the first derivative of a**6/30 + a**5/5 + 9*a**4/20 + 7*a**3/15 + a**2/5 + 7. Factor l(j).
j*(j + 1)**3*(j + 2)/5
Let v(a) be the third derivative of a**7/350 - a**6/120 + a**5/300 + a**4/120 - 4*a**2. Factor v(t).
t*(t - 1)**2*(3*t + 1)/5
Let z be -2*(2 - (5 + -1)). Factor 2*w**2 + 0*w - 2*w + z*w + 0*w.
2*w*(w + 1)
Let t(j) be the first derivative of j**5/5 + j**4/4 - j**3 - 5*j**2/2 - 2*j - 5. Suppose t(n) = 0. What is n