ate r.
-1, 0
Let m(l) = -l**3 + l**2 + 2*l. Let h(d) = -d**3 + 28*d**2 - 49*d + 30. Let n(y) = -h(y) + 4*m(y). Factor n(x).
-3*(x - 1)**2*(x + 10)
Let t(o) be the second derivative of o**6/10 - 9*o**5/20 + 2*o**3 - o. Factor t(m).
3*m*(m - 2)**2*(m + 1)
Factor -2*a**3 - 26/9*a - 16/3*a**2 - 4/9.
-2*(a + 2)*(3*a + 1)**2/9
Let c(l) = l**2 - 3*l + 2. Let o be c(1). Let z(d) be the first derivative of -2/3*d**3 + 4 - 1/2*d**4 + 1/3*d**6 + 2/5*d**5 + o*d**2 + 0*d. Factor z(r).
2*r**2*(r - 1)*(r + 1)**2
Factor -1/3*r**2 + 1/3*r + 0.
-r*(r - 1)/3
Suppose 3*c - 21 - 18 = 0. Let m(j) = 4*j**2 - 13*j - 13. Let x(q) = -2*q**2 + 6*q + 6. Let d(v) = c*x(v) + 6*m(v). Factor d(l).
-2*l**2
Suppose -b - 3 = -3*m, -2*b - 6 = -3*m - 0*b. Suppose m*a = -a + 2. Factor -2/3*y**a + 0*y - 2/3*y**3 + 0.
-2*y**2*(y + 1)/3
Let k(t) be the second derivative of -t**4/3 + 10*t**3/3 - 12*t**2 - 42*t. Determine x, given that k(x) = 0.
2, 3
Let a(m) be the first derivative of -m**3 + 5/2*m**2 - 2 + 0*m. Let l(j) = -25*j**2 + 41*j + 1. Let d(y) = 51*a(y) - 6*l(y). Factor d(w).
-3*(w - 2)*(w - 1)
Let n(u) be the first derivative of 0*u**3 + u**2 + 1/180*u**5 - 1 - 1/36*u**4 + 0*u. Let y(b) be the second derivative of n(b). Find l such that y(l) = 0.
0, 2
Let f = -1828 + 3723/2. Let h = -33 + f. Factor 5/2*b + h + 2*b**2.
(b + 1)*(4*b + 1)/2
Let u(m) be the third derivative of m**5/120 - 7*m**4/48 + 5*m**3/6 - 19*m**2. Factor u(a).
(a - 5)*(a - 2)/2
Let h(c) = c**3 - c**2 - 9*c - 3. Let w(k) = -k**3 + k**2 + 10*k + 3. Let x(b) = 5*h(b) + 4*w(b). Determine a so that x(a) = 0.
-1, 3
Suppose 2*g - 3*g + 5 = 0, 0 = -5*j - 2*g - 40. Let f = j + 14. Find v, given that -1/4*v**f + 0*v + 0 + 0*v**3 + 1/4*v**2 = 0.
-1, 0, 1
Suppose -5 = 3*a - 8*a. Let j(x) = -4*x**2 - 3*x - 4. Let g(l) = l**2 + l + 1. Let o(y) = a*j(y) + 5*g(y). Factor o(u).
(u + 1)**2
Let k(y) be the first derivative of 2*y**5/55 + 2*y**4/11 + 10*y**3/33 + 2*y**2/11 - 32. Let k(p) = 0. Calculate p.
-2, -1, 0
Let t(m) be the first derivative of m**6/8 + 21*m**5/20 + 3*m**4 + 2*m**3 - 6*m**2 - 12*m + 1. Determine u so that t(u) = 0.
-2, 1
Let c(l) be the first derivative of -4 + 8/11*l + 4/11*l**2 + 2/33*l**3. Solve c(w) = 0.
-2
Let h be 1/(-3*(-1)/9). Let i(c) be the second derivative of -2*c - 1/15*c**h + 0*c**2 + 1/30*c**4 + 0. Factor i(u).
2*u*(u - 1)/5
Suppose -3/5*u**4 - 27/5 - 72/5*u - 66/5*u**2 - 24/5*u**3 = 0. What is u?
-3, -1
Let r = -7 - -4. Let s be r/12 - (-45)/20. Factor 0*j + 0 - 1/2*j**s + 1/2*j**3.
j**2*(j - 1)/2
Let w(r) be the third derivative of 0*r + 1/120*r**6 + 0*r**3 + 0 + 1/84*r**4 + 6*r**2 - 1/60*r**5 - 1/735*r**7. Factor w(s).
-s*(s - 2)*(s - 1)*(2*s - 1)/7
Let f(r) = -r + 8. Let s be f(7). Let q = 7 + -5. Factor 3*v**2 + s - 2*v - q*v**2 + 0.
(v - 1)**2
Suppose b = -4*x + 17, 2*x + 0*b - 1 = -3*b. Let k be 3/(-15) + 16/x. Let -2*u**5 + u**5 + 4*u**5 - u**k - 2*u**3 = 0. What is u?
-1, 0, 1
Factor 0 + 1/4*r**3 + 1/4*r**4 - 1/4*r**2 - 1/4*r.
r*(r - 1)*(r + 1)**2/4
Let a(r) be the first derivative of r**6/360 - r**5/40 + r**4/12 - 4*r**3/3 - 3. Let k(i) be the third derivative of a(i). Factor k(u).
(u - 2)*(u - 1)
Let s(k) = 10*k**5 - 3*k**4 - 12*k**3 - 2*k**2 - 3*k + 5. Let p(t) = 9*t**5 - 3*t**4 - 11*t**3 - t**2 - 2*t + 4. Let o(n) = 5*p(n) - 4*s(n). Factor o(d).
d*(d - 1)**2*(d + 1)*(5*d + 2)
Let r(f) be the second derivative of 2*f**6/15 - f**5/5 - 5*f**4/3 - 2*f**3 + 21*f. Suppose r(i) = 0. Calculate i.
-1, 0, 3
Let -1/2 + 1/2*g + 1/2*g**2 - 1/2*g**3 = 0. What is g?
-1, 1
Let j(n) be the second derivative of -1/24*n**3 + 1/120*n**6 + 1/80*n**5 + 0 + 1/4*n**2 - 1/16*n**4 - 3*n. Suppose j(y) = 0. Calculate y.
-2, -1, 1
Let t = -63 + 68. Factor 0 - 98/11*c**t + 0*c + 0*c**2 - 8/11*c**3 - 56/11*c**4.
-2*c**3*(7*c + 2)**2/11
Factor 2*d**3 - 2*d**4 - 14*d**2 + 4*d**4 + 1 + d - 27*d - 13.
2*(d - 3)*(d + 1)**2*(d + 2)
Let q = 6 + 3. Let d be (1/(-3))/(q - 10). Factor 0 + 2/3*v**4 + 0*v**3 + 1/3*v - 2/3*v**2 - d*v**5.
-v*(v - 1)**3*(v + 1)/3
Let a(m) = 21*m**3 - 39*m**2 + 36*m - 15. Let r(s) = s**4 + 22*s**3 - 39*s**2 + 36*s - 16. Let n(t) = 4*a(t) - 3*r(t). Factor n(q).
-3*(q - 2)**2*(q - 1)**2
Let c be 116/(-14) + 14/49. Let a = 10 + c. Suppose a*i**2 - 3*i + 3*i - 4*i = 0. What is i?
0, 2
Let w(y) = 4*y**4 + 4*y**3 - 9*y**2 - 9*y - 9. Let t(c) = -2 + c**3 + 4*c - 2*c**2 + c**4 - 4*c - 2*c. Let i(b) = -9*t(b) + 2*w(b). Let i(q) = 0. Calculate q.
-1, 0
Determine r so that r**3 - 20*r + 4*r**2 + 3*r**3 - 4*r**3 + 12 + 4*r**3 = 0.
-3, 1
Let j(m) = -2*m. Suppose -3*z = 9 - 6. Let c be j(z). Solve f**c + 1/3*f - 2/3 = 0 for f.
-1, 2/3
Determine o, given that -300 + o**3 + 300 - 3*o**2 = 0.
0, 3
Let w = 62/3 + -20. Factor -w - 7/3*b + 4/3*b**2.
(b - 2)*(4*b + 1)/3
Suppose 2*x - 4*w = 6*x + 168, -3*x = -5*w + 150. Let f be 4/6 + (-276)/x. Solve 8/5*r + 0 - 2*r**4 - 32/5*r**2 + f*r**3 = 0.
0, 2/5, 1, 2
Let z(k) = 4*k**2 + 5*k**2 - 8*k**2. Let s(b) = -2 + 4*b**2 + 0*b + b**2 + 7*b. Let y(i) = s(i) - z(i). Find t such that y(t) = 0.
-2, 1/4
Suppose 5 = -u - v - 2*v, -v = -4*u + 19. Suppose u*l + 4 = 12. Factor -2*g**3 + 3*g**l - 5*g + 5*g - g**3.
-3*g**2*(g - 1)
Let p = 0 + 3. Let f(u) be the first derivative of -4*u + 3/2*u**4 - u**2 + 8/3*u**p + 3. Solve f(r) = 0.
-1, 2/3
Let t(u) be the second derivative of -u**4/4 - u**3/2 - 31*u. Factor t(r).
-3*r*(r + 1)
Factor -4/11*t**2 - 2/11*t**3 - 2/11*t + 0.
-2*t*(t + 1)**2/11
Let f(h) = 3*h**3 - 2*h**2 + 4*h + 1. Let t(l) = -4*l**3 + 2*l**2 - 5*l - 2. Let y(z) = 3*f(z) + 2*t(z). Let p be y(1). Factor -m**2 + p*m**3 - 2*m**3 + m**3.
-m**2*(m + 1)
Suppose -5*k + 90 = 530. Let r be -4 + (k/5)/(-4). Find x, given that -12/5*x**2 - 24/5*x - 16/5 - r*x**3 = 0.
-2
Let y(x) be the third derivative of -x**7/315 + x**6/90 - x**5/90 + 7*x**2. Factor y(r).
-2*r**2*(r - 1)**2/3
Let m(x) = x + 15. Let z be m(-5). Factor 2 - z + 4 + 4*c**2.
4*(c - 1)*(c + 1)
Let f(d) be the second derivative of -d**5/4 - 10*d**4/3 - 40*d**3/3 - 22*d. Find z such that f(z) = 0.
-4, 0
Let f(r) be the third derivative of -r**6/780 + r**5/65 - r**4/13 + 8*r**3/39 + 9*r**2. Let f(v) = 0. What is v?
2
Let k = 259 - 257. Factor 1/5*g**k - 6/5*g + 9/5.
(g - 3)**2/5
Let y(o) = -o**3. Let h(d) = -d**3 - 2*d**2 + d. Let n(w) = -h(w) + 2*y(w). Factor n(t).
-t*(t - 1)**2
Let o(y) = -3*y**3 - 25*y**2 + 8*y. Let x(j) = -j**3 - j**2. Let z(l) = -2*o(l) + 18*x(l). Factor z(c).
-4*c*(c - 2)*(3*c - 2)
Factor 6/5*w**3 - 3/5*w**5 + 6/5*w**2 - 3/5 - 3/5*w - 3/5*w**4.
-3*(w - 1)**2*(w + 1)**3/5
Let h(w) be the first derivative of -w**6/2 - 3*w**5/5 + 3*w**4/4 + w**3 + 3. Factor h(j).
-3*j**2*(j - 1)*(j + 1)**2
Let l be ((-4 - -3) + 1)*-1. Let i(p) be the second derivative of p + l + 2*p**2 - 2/3*p**3 + 1/12*p**4. Factor i(a).
(a - 2)**2
Suppose -4*l + 37 = 3*v, -4*v = 5*l - 10*l + 23. Let i be -2 + l/(21/6). Determine s, given that i + 2/3*s**2 - 4/3*s = 0.
0, 2
Factor 1/4*b + 1/4*b**2 - 1/2.
(b - 1)*(b + 2)/4
Let f(j) be the third derivative of -j**7/560 + j**6/160 - j**4/32 + j**3/16 - j**2. Factor f(v).
-3*(v - 1)**3*(v + 1)/8
Let k = -19 - -17. Let c be 8/(-6)*k/8. Let c*g**3 + 0*g + 1/3*g**5 - 2/3*g**4 + 0 + 0*g**2 = 0. What is g?
0, 1
Factor 4*n**4 + n**2 - n**4 + n**5 - 7*n**3 + 10*n**3.
n**2*(n + 1)**3
Let q(r) be the second derivative of r**5/120 - r**4/12 + 11*r**3/36 - r**2/2 - 15*r. Factor q(w).
(w - 3)*(w - 2)*(w - 1)/6
Let b(g) = g**3 + g + 1. Let u(z) be the third derivative of z**6/40 + z**5/2 + 4*z**4/3 + 2*z**3/3 + 4*z**2. Let s(k) = -4*b(k) - u(k). Factor s(l).
-(l + 2)**2*(7*l + 2)
Suppose -3*q - 12 = -3. Let d(p) = 13*p**3 + 6*p**2 - 7*p + 5. Let h(g) = 7*g**3 + 3*g**2 - 4*g + 3. Let z(l) = q*d(l) + 5*h(l). Factor z(u).
-u*(u + 1)*(4*u - 1)
Let q(i) be the second derivative of i**5/40 - 7*i**4/24 + 4*i**3/3 - 3*i**2 - 18*i. Factor q(b).
(b - 3)*(b - 2)**2/2
Let b be ((-36)/(-24))/((-3)/(-8)). Factor -4/5*i**3 + 6/5*i**b - 2/5*i**5 + 0 + 0*i + 0*i**2.
-2*i**3*(i - 2)*(i - 1)/5
Let o(t) be the third derivative of t**5/180 - 5*t**4/36 + 25*t**3/18 + 25*t**2. Factor o(l).
(l - 5)**2/3
Let w(y) be the third derivative of y**8/336 + y**7/42 + y**6/12 + y**5/6 + 5*y**4/24 + y**3/6 - 41*y**2. Factor w(j).
(j + 1)**5
Let x(n) = -n**2 + 7*n - 9. Let v be x(4). Suppose 0 + 0*o + 2/5*o**2 - 7/5*o**v - 