et i(s) = 11*s**3 - 36*s**2 + 77*s - 43. Let k(j) = -18*i(j) + 5*l(j). Factor k(w).
-3*(w - 2)**3
Let f = 145 + -144. What is h in -3/2*h + f + 1/2*h**3 + 0*h**2 = 0?
-2, 1
Suppose -8 - 1 = x - 2*g, 5*g = -3*x + 17. Let a = 3/2 + x. Solve -a*b + 0*b**2 - 1/2*b**5 + b**3 + 0*b**4 + 0 = 0 for b.
-1, 0, 1
Let k(f) = f**4 - f**3 - 2*f**2 + f. Let t(y) = y**4 + y**3 - y. Let g(j) = k(j) + t(j). Factor g(c).
2*c**2*(c - 1)*(c + 1)
Let x(a) = a**2 + 4*a - 3. Let d be x(-5). Factor 0*u + 3*u + u**2 - u**2 - 3*u**d.
-3*u*(u - 1)
Let z(w) = -w - 2. Let d be z(-6). Factor -d*g**2 - g + 5*g - 1 + 3*g**2 - 3.
-(g - 2)**2
Let t(w) = 4*w**2 + 9*w - 9. Let u(m) = -5*m**2 - 10*m + 10. Let i = -3 + 6. Let s be (-1)/((i/18)/(-1)). Let a(x) = s*t(x) + 5*u(x). Factor a(d).
-(d - 2)**2
Let a(o) = 3*o - 30. Let l be a(11). Let q(z) be the third derivative of 0*z + 0 - 4/15*z**l + z**2 - 1/300*z**6 + 1/50*z**5 + 0*z**4. Factor q(s).
-2*(s - 2)**2*(s + 1)/5
Let w = 3 - 4. Let d be (-4 + (1 - -1))*w. Factor 2*b + 2 - 2*b - 2*b**d.
-2*(b - 1)*(b + 1)
Let c(q) be the second derivative of 1/36*q**4 - 3*q + 1/9*q**3 + 1/6*q**2 + 0. Determine l so that c(l) = 0.
-1
Let x be (-4)/10 - (-66)/15. Factor 8*q**3 + 0*q**3 - q**3 + x*q**4 - q + 2*q**2.
q*(q + 1)**2*(4*q - 1)
Let w(z) be the second derivative of 1/9*z**4 + z + 0 + 4/9*z**3 + 8/9*z**2 + 1/90*z**5. Let w(k) = 0. Calculate k.
-2
Let c(d) = -d - 11. Suppose w = g - 2*w - 2, 6 = -2*g + 4*w. Let z be c(g). Determine k so that 1/3*k**3 + 0 + 0*k**z + 0*k + 0*k**4 - 1/3*k**5 = 0.
-1, 0, 1
Let o(u) be the first derivative of u**7/210 - u**6/40 + u**5/20 - u**4/24 + u**2 + 8. Let p(n) be the second derivative of o(n). Let p(r) = 0. What is r?
0, 1
Let b(x) be the first derivative of 4*x**3/3 + 2*x**2 - 8*x - 5. Find t such that b(t) = 0.
-2, 1
Let b(p) be the third derivative of 8*p**7/21 + 5*p**6/3 - 29*p**5/4 + 175*p**4/24 - 10*p**3/3 + 31*p**2. Determine t so that b(t) = 0.
-4, 1/4, 1
Let f = 9 - 3. Let q(x) be the second derivative of 1/135*x**f + 0*x**2 + 1/54*x**4 + 1/45*x**5 + 0*x**3 + 0 - 2*x. Let q(g) = 0. What is g?
-1, 0
Let m(u) be the first derivative of 5*u**3/4 - 55*u**2/8 - 5*u + 14. Factor m(n).
5*(n - 4)*(3*n + 1)/4
Let u(n) be the first derivative of -2*n**6/3 - 8*n**5/5 - n**4 - 6. Factor u(l).
-4*l**3*(l + 1)**2
Let k be 0 + -3 - (1 + -4). Let p(q) be the third derivative of k*q**3 + 0*q**5 + 2*q**2 + 1/180*q**6 + 0*q + 0 + 0*q**4. Suppose p(m) = 0. What is m?
0
Let p be -2 + (-32)/(-18) + 8/36. Factor 0 + 2/5*a**5 + 0*a + p*a**4 - 2/5*a**3 + 0*a**2.
2*a**3*(a - 1)*(a + 1)/5
Suppose 32 = 8*m + 8*m. Let h(v) be the second derivative of 2*v + 1/20*v**4 + 0 - 3/10*v**m + 0*v**3. Factor h(u).
3*(u - 1)*(u + 1)/5
Let r(c) = -4*c**2 - 8. Let j(g) = g**2 - g. Let n(z) = -6*j(z) - r(z). Solve n(l) = 0.
-1, 4
Suppose o + 7*c - 4*c + 21 = 0, 0 = -3*c. Let m = -19 - o. Let 0 + 1/5*z**m + 1/5*z = 0. Calculate z.
-1, 0
Let l(j) be the third derivative of j**8/16800 + j**7/12600 - j**6/900 + j**5/20 - j**2. Let p(r) be the third derivative of l(r). Let p(g) = 0. What is g?
-1, 2/3
Let u(r) be the third derivative of r**7/11340 + r**6/810 + r**5/135 + r**4/3 - 4*r**2. Let d(i) be the second derivative of u(i). Solve d(h) = 0.
-2
Suppose -5*a - 2*q - 6 = -6*a, -3*a - 2*q = -2. Factor -o - 1/3*o**3 - o**a - 1/3.
-(o + 1)**3/3
Let j(w) be the third derivative of 0*w - 5*w**2 - 1/180*w**5 - 1/18*w**3 + 1/36*w**4 + 0. Suppose j(m) = 0. What is m?
1
Let p(v) be the first derivative of 1/360*v**6 + 1/24*v**4 + 1/60*v**5 + 0*v**2 - 1/3*v**3 + 2 + 0*v. Let s(y) be the third derivative of p(y). Factor s(l).
(l + 1)**2
Suppose -4*j = -2*u - 78, -8 = 5*u - 3. Factor -2*h**3 - 24*h + h**2 + 16 + j*h**2 - 8*h**2.
-2*(h - 2)**3
Factor 1 + x - 3/4*x**2.
-(x - 2)*(3*x + 2)/4
Let r(z) = -36*z**3 - 39*z**2 + 12*z - 15. Let f(m) = 9*m**3 + 10*m**2 - 3*m + 4. Let h(v) = 15*f(v) + 4*r(v). Factor h(s).
-3*s*(s + 1)*(3*s - 1)
Let t(u) be the second derivative of -u**6/10 + 9*u**5/20 + u**4/4 - 3*u**3/2 + 6*u. Factor t(i).
-3*i*(i - 3)*(i - 1)*(i + 1)
Suppose -24 = -b - b. Find h such that -5*h**2 + 13*h + 2*h**3 - b*h**3 - 2*h**4 - h**2 + 5*h = 0.
-3, 0, 1
Let i be 1 - 0 - (-2 - 0). Suppose -i*v + t = -3*t + 8, -8 = v - 4*t. Factor v + 4/9*j**2 - 2/9*j - 2/9*j**3.
-2*j*(j - 1)**2/9
Let t(h) be the third derivative of 2/1155*h**7 + 0*h**6 + 0*h - 1/165*h**5 - 1/132*h**4 + 0 + 1/1848*h**8 + 0*h**3 + 5*h**2. Suppose t(s) = 0. What is s?
-1, 0, 1
Let t = -61 - -17. Let p be 3/(-12) + (-11)/t. Determine b, given that 9/4*b**3 + 5/4*b**5 - 1/2*b**2 - 3*b**4 + p + 0*b = 0.
0, 2/5, 1
Let x = -20 - -26. Let u = x + -4. Factor 4/7*y**3 + 0*y - 2/7*y**4 - 2/7*y**u + 0.
-2*y**2*(y - 1)**2/7
Suppose -f - 4*f + c = -2, -2*c = 4. Factor -1/4*g + f - 1/4*g**2.
-g*(g + 1)/4
Let y = -69 - -211/3. Factor 0 - y*j - 4/3*j**2.
-4*j*(j + 1)/3
Let 3/2*q**2 + 0*q + 0 + 1/2*q**3 = 0. What is q?
-3, 0
Let x(f) be the first derivative of -3*f**5/20 + 3*f**4/16 + f**3/8 - f + 4. Let u(m) be the first derivative of x(m). Solve u(w) = 0.
-1/4, 0, 1
Let x(d) be the third derivative of d**7/70 + d**6/10 + d**5/5 + 5*d**2. Factor x(v).
3*v**2*(v + 2)**2
Let o = -1 - -7. Suppose 3*b - 2*k - o = 0, -2*b + 3*b + 6 = -2*k. Factor 2/3*t**2 + 1/3*t**3 + 1/3*t + b.
t*(t + 1)**2/3
Let f = 2/131 - -248/917. Factor -f*y**2 + 1/7*y + 0.
-y*(2*y - 1)/7
Let q = 29/8 - 601/168. Let k(t) be the first derivative of 16/7*t + q*t**6 + 4*t**2 + 25/14*t**4 + 16/35*t**5 + 2 + 76/21*t**3. Find n such that k(n) = 0.
-2, -1
Let k(x) be the third derivative of x**7/735 - x**6/420 - x**5/210 + x**4/84 - 12*x**2. Find w such that k(w) = 0.
-1, 0, 1
Let p(c) be the first derivative of -2/21*c**3 - 2/7*c - 2/7*c**2 - 1. Suppose p(f) = 0. What is f?
-1
Suppose -2*y - 40 = 3*y. Let l be y/20*(-30)/3. Solve -5/3*k**3 + 3*k**2 + 2/3 - 7/3*k + 1/3*k**l = 0.
1, 2
Let 15/4 + 3/4*j**2 - 9/2*j = 0. Calculate j.
1, 5
Let z(t) be the third derivative of t**6/300 + 2*t**5/75 + t**4/20 - 11*t**2. Factor z(m).
2*m*(m + 1)*(m + 3)/5
Suppose 4*m = m + 9. Suppose m*v = 2*v. Solve 1/2*z - 1/2*z**2 + v = 0.
0, 1
Let -19*o**2 + 2 + 5*o**3 - 11*o**2 - 2 + 25*o = 0. Calculate o.
0, 1, 5
Let w = -5256/17 + 1261559/4080. Let c(t) be the third derivative of 0*t**3 + 0 - w*t**5 - 1/48*t**4 + t**2 + 0*t. Find g such that c(g) = 0.
-2/7, 0
Let m(o) = -3*o - 5 + 1 + 2*o - 2. Let j be m(-8). Suppose 2*p - 4*p**2 + 3*p**2 + 1 - j*p = 0. What is p?
-1, 1
Suppose -2*s - k = -6, 4*s - 3*k - 2*k = 12. Factor -4*n**3 - n**s + 0*n**3 + 3*n**3 + 2*n**2 + 4*n.
-2*n*(n - 2)*(n + 1)
What is d in -1/4*d**3 + 0*d + 1 - 3/4*d**2 = 0?
-2, 1
Factor 1/6*t + 0 + 8/3*t**4 + 4/3*t**3 - 7/6*t**2.
t*(t + 1)*(4*t - 1)**2/6
Suppose 4*k - 34 = -3*y + 41, 0 = 3*k - 5*y - 49. Suppose 4*p - 3*q - 13 - k = 0, 3*p - 2*q - 23 = 0. Solve -7*n + 2*n**4 + p*n - 2*n**3 = 0.
0, 1
Let q be 122/240 + ((-9)/(-6))/(-3). Let j(t) be the third derivative of 0*t + 0 - q*t**5 + 3*t**2 + 1/12*t**3 + 1/240*t**6 - 1/48*t**4. Factor j(p).
(p - 1)**2*(p + 1)/2
Let n(s) be the second derivative of s**5/20 + s**4/6 - s**3/6 - s**2 - 7*s. Factor n(y).
(y - 1)*(y + 1)*(y + 2)
Let h(u) be the first derivative of -2*u**3/15 + 5*u**2/3 - 16*u/15 + 66. Solve h(d) = 0.
1/3, 8
Let u(t) be the third derivative of -5*t**8/336 + 5*t**7/42 - t**6/3 + t**5/3 - 11*t**2. Factor u(m).
-5*m**2*(m - 2)**2*(m - 1)
Factor 10*w**4 - 15*w**4 - 29*w + 5*w**3 + 20*w**2 + 9*w.
-5*w*(w - 2)*(w - 1)*(w + 2)
Let 0 + 2/7*d**2 - 2/7*d = 0. What is d?
0, 1
Let m be 10/15 + 4/(-6). Suppose -r + 4 + 0 = m. Suppose -2/7*j**3 + 0 - 2/7*j**r + 0*j + 0*j**2 = 0. Calculate j.
-1, 0
Let k(x) = 2*x. Let r be k(1). Let i(g) be the first derivative of -2 - 4/7*g - 2/21*g**3 + 3/7*g**r. Determine q so that i(q) = 0.
1, 2
Let f(s) be the second derivative of -s**5/170 + 2*s**4/51 - 5*s**3/51 + 2*s**2/17 + 8*s. Determine b so that f(b) = 0.
1, 2
Let w(p) be the first derivative of -4*p**5/5 - 2*p**4 - 4*p**3/3 - 10. Factor w(j).
-4*j**2*(j + 1)**2
Suppose 2*v + 7*v = 198. Let w = v + -22. Factor 0 - 2/9*d**4 + w*d**3 + 2/9*d**2 + 0*d.
-2*d**2*(d - 1)*(d + 1)/9
Suppose -6 = -4*o + 2. Let i = -18 + 22. Factor -9*z**i - 3*z**2 + o*z**5 + z**5 + 0*z**5 + 9*z**3.
3*z**2*(z - 1)**3
Let k(j) be the second derivative of 0 + 1/35*j