 1
Suppose -3*z + 2*u = -0 - 13, -4*z + 10 = u. Factor -3 + 8*w - 3*w**2 - 9*w + z.
-w*(3*w + 1)
Factor -2*z**4 + 4*z**5 + 2*z**3 - 5*z**5 - z**5 + 2*z**2.
-2*z**2*(z - 1)*(z + 1)**2
Suppose -44 + 76*x - 12 + 20*x**3 + 166*x**2 + 0 - 14*x**2 = 0. Calculate x.
-7, -1, 2/5
Let d(o) be the first derivative of 0*o - 3 - 1/16*o**4 + 0*o**2 + 1/4*o**3. Solve d(u) = 0.
0, 3
Let y be 1*(-15)/9*-3. Let l = y - 2. Suppose 7 + l*i**2 - 7 = 0. Calculate i.
0
Let v(m) be the second derivative of 1/36*m**4 + 0 + 1/18*m**3 - 1/3*m**2 + 4*m. Suppose v(b) = 0. What is b?
-2, 1
Determine t, given that 6/7*t + 3/7*t**3 - 9/7*t**2 + 0 = 0.
0, 1, 2
Let l(u) be the third derivative of u**7/11340 + u**6/1080 + u**5/270 - u**4/12 + u**2. Let n(f) be the second derivative of l(f). Solve n(j) = 0 for j.
-2, -1
Let d(f) be the first derivative of 0*f**2 + 4 + 0*f + 2/15*f**3 - 1/10*f**4. Find v such that d(v) = 0.
0, 1
Let h(d) be the second derivative of d**6/30 - d**5/10 + d**4/12 - 3*d. Find t such that h(t) = 0.
0, 1
Let q(o) be the first derivative of o**4/3 + 4*o**3/3 + 3*o**2/2 + 2*o/3 + 4. Factor q(x).
(x + 2)*(2*x + 1)**2/3
Let u(k) = -7*k**2 + 2*k - 7. Let z(j) = j**2 + 1. Let b(w) = -w**3 + 5*w**2 + 7*w - 5. Let c be b(6). Let y(a) = c*u(a) + 6*z(a). Solve y(g) = 0.
1
Let k(w) = 3*w**4 + 36*w**3 - 72*w**2 + 57*w - 9. Let s(t) = -t**4 - 18*t**3 + 36*t**2 - 28*t + 4. Let m(a) = -4*k(a) - 9*s(a). Factor m(j).
-3*j*(j - 2)**3
Suppose -2*m - 4*b + 24 = 0, 0 = -3*m + 3*b - 2*b + 1. Suppose 4 = -m*c, 2*s = -c - c. Factor -2/5*t**3 + 0*t - 2/5*t**s + 0.
-2*t**2*(t + 1)/5
Let d(i) be the first derivative of -i**5/50 + i**3/5 - 2*i**2/5 + 10*i + 9. Let j(s) be the first derivative of d(s). Find z, given that j(z) = 0.
-2, 1
Let p be (1/(-2))/(6/24). Let m(j) = -j**5 + j**4 - 3*j**3 + 3. Let c(g) = g**5 + 2*g**3 - 2. Let a(q) = p*m(q) - 3*c(q). Factor a(s).
-s**4*(s + 2)
Suppose 0 = -4*h + 2*h. Let c = 4 - h. Factor -6*d + 6*d**3 - c*d + 4*d**3 + 6*d**4 - 2*d**2 - 4.
2*(d - 1)*(d + 1)**2*(3*d + 2)
Let n be (6/(-4))/((-1)/2). Suppose -n*v - 6 = -6*v. Solve -2*d**v + 2*d**3 - 2 + 0*d**3 + 4 - 2*d = 0 for d.
-1, 1
Let s(r) be the second derivative of r**7/462 + 2*r**6/165 + 3*r**5/110 + r**4/33 + r**3/66 - 20*r. Let s(h) = 0. Calculate h.
-1, 0
Factor 2*x**4 - 6*x**3 + 0*x**4 + 105*x**2 - 101*x**2.
2*x**2*(x - 2)*(x - 1)
Let h(g) be the second derivative of g**7/294 + g**6/105 - g**5/140 - g**4/42 - 6*g. Factor h(d).
d**2*(d - 1)*(d + 1)*(d + 2)/7
Let d be (6/(-18))/((-10)/12). Let r(x) be the first derivative of 0*x**2 + 1 + 0*x**3 + 0*x - x**4 + d*x**5. Solve r(h) = 0.
0, 2
Factor -77*z**2 + 12 + 36*z**2 + 38*z**2 + z**3 - 12*z + 2*z**3.
3*(z - 2)*(z - 1)*(z + 2)
Let o(v) be the third derivative of 0*v**4 + 0*v - 5/336*v**8 - 31/630*v**7 + 3*v**2 - 1/18*v**6 + 0*v**3 + 0 - 1/45*v**5. Suppose o(y) = 0. Calculate y.
-1, -2/3, -2/5, 0
Let z(s) be the first derivative of -3 + 1/18*s**4 + 1/3*s**2 - 2/9*s**3 - s. Let h(l) be the first derivative of z(l). Let h(t) = 0. What is t?
1
Let d = 0 + -6. Let y(b) = -b**3 - 1. Let k(v) = -v**4 - v**3 - 4*v**2 + 3. Let r(g) = d*y(g) - 2*k(g). Factor r(h).
2*h**2*(h + 2)**2
Let q = 4186184/373989 + 50/33999. Let g = -120/11 + q. Factor g*a**3 - 2/7*a + 2/7 - 2/7*a**2.
2*(a - 1)**2*(a + 1)/7
Let u(g) be the third derivative of 1/315*g**7 + 0*g**3 - 2/135*g**6 + 7/270*g**5 - 1/54*g**4 + 0*g + 0 + 4*g**2. Factor u(n).
2*n*(n - 1)**2*(3*n - 2)/9
Let m(y) be the third derivative of 0*y**5 + 0 + 0*y**4 + 1/280*y**6 + 1/784*y**8 - 1/245*y**7 + 0*y**3 + 0*y - 4*y**2. Determine v, given that m(v) = 0.
0, 1
Let x(m) = 12*m**4 - 4*m**3 + 16*m**2 + 4*m + 14. Let a(f) = -f**4 - f**2 - 1. Let c(z) = -28*a(z) - 2*x(z). Factor c(q).
4*q*(q - 1)*(q + 1)*(q + 2)
Let a(j) = 0 + 6*j**2 - 1 + 2*j**3 + 4*j - j**3. Let m be a(-5). Factor -2*n**2 + 98/3*n**m + 140/3*n**3 + 8/3 - 40/3*n.
2*(n + 1)**2*(7*n - 2)**2/3
Suppose -4*d + 21 = 5. Let r(z) = -6*z**2 - z + 1. Let v(b) = -3*b**2 + b + 8*b**2 - b. Let s(t) = d*r(t) + 5*v(t). Factor s(w).
(w - 2)**2
Determine z, given that 2 - 1/2*z**2 + 3/2*z = 0.
-1, 4
Suppose 5*i - 65 = -10. Factor -3*m**3 + 12 - i + 0*m**3 - m**2 + 3*m.
-(m - 1)*(m + 1)*(3*m + 1)
Let i(v) be the first derivative of -3*v**5/25 + 3*v**4/20 + v**3/5 - 3*v**2/10 - 4. Factor i(a).
-3*a*(a - 1)**2*(a + 1)/5
Let x(u) be the first derivative of -u**3 + 3*u**2 - 3*u - 5. Factor x(f).
-3*(f - 1)**2
Suppose -2*u + 6 = u. Let r(c) = -c**2 - 5*c. Let f be r(-5). Factor -14/3*z**3 - 16/3*z**4 + f + 32/3*z**5 - 2/3*z**u + 0*z.
2*z**2*(z - 1)*(4*z + 1)**2/3
Determine f, given that -1/4*f**2 + 1/2 + 1/4*f = 0.
-1, 2
Suppose -2*l + c - 43 = -4*c, -5*l - 3*c = 30. Let x be l/(-6)*4/2. Factor 0*s**3 - 2*s**x - 2*s**2 + 2*s**5 - 5*s**4 + 7*s**4.
2*s**2*(s - 1)*(s + 1)**2
Suppose -2*r = -5*f + 28, -3*f + f + 12 = -r. Let g(l) be the third derivative of 0*l**f + 1/60*l**5 - 1/120*l**6 + 0*l + 0 + 0*l**3 - l**2. Factor g(b).
-b**2*(b - 1)
Suppose -6 = -8*u + 5*u. Let t(h) be the first derivative of 2/3*h**2 - 2/9*h**3 + u - 2/3*h. Find f, given that t(f) = 0.
1
Let u be (-1)/(-5)*(-15)/(-48). Let z(k) be the second derivative of k + 0 - 1/3*k**3 + u*k**5 + 7/48*k**4 - 1/2*k**2. Factor z(l).
(l - 1)*(l + 2)*(5*l + 2)/4
What is a in 20*a**2 + 4*a**5 + 24*a**4 + 28*a**2 - 48*a - 40*a**2 - 32 + 44*a**3 = 0?
-2, -1, 1
Let o = 8 + -5. Suppose -b - 5*s + 8 = o*b, -3*s = 2*b - 4. Factor -5*i**2 - i - i**b + 4*i**2 - i**3.
-i*(i + 1)**2
Solve 3*x**2 + x**4 - 15*x**4 + 0*x**2 + x**2 - 10*x**3 = 0.
-1, 0, 2/7
Factor 1/5*q**2 + 4/5*q + 4/5.
(q + 2)**2/5
Suppose -2*a = -12*a. Let o(n) be the first derivative of -2/5*n**5 + a*n**4 - 2 + 2/3*n**3 + 0*n + 0*n**2. Factor o(w).
-2*w**2*(w - 1)*(w + 1)
Let a(s) be the second derivative of -s**6/315 + s**5/210 + s**4/126 - s**3/63 + 3*s. Suppose a(f) = 0. Calculate f.
-1, 0, 1
Suppose 37 = 6*y + 19. Let u(w) be the second derivative of -4*w + 1/10*w**4 + 1/15*w**y + 0 + 1/25*w**5 + 0*w**2. Determine p, given that u(p) = 0.
-1, -1/2, 0
Determine y, given that 24*y + 2*y**2 + 4*y**3 - 3*y**4 + y**4 - 28*y = 0.
-1, 0, 1, 2
Suppose -2*j - 5*p = -p, -4*j + 5 = 3*p. Factor -2/3 + 2/3*f**j + 0*f.
2*(f - 1)*(f + 1)/3
Let i(m) be the first derivative of m**6/2340 - m**5/195 + m**4/52 - 2*m**3/3 + 3. Let r(y) be the third derivative of i(y). Factor r(l).
2*(l - 3)*(l - 1)/13
Let z(p) be the first derivative of 4/21*p**3 - 2/7*p - 2/35*p**5 + 7 - 1/7*p**2 + 1/7*p**4 - 1/21*p**6. Suppose z(w) = 0. What is w?
-1, 1
Let a be (0/2)/(4/1). Let v(g) be the second derivative of 0 - 1/6*g**4 - 2*g + 0*g**3 + a*g**2. Suppose v(t) = 0. What is t?
0
Let p = 2282/5 + -456. Solve p*u**2 - 2/5*u**3 + 0*u + 0 = 0.
0, 1
Let v be (-12)/(-8) - (2 - (-4 + 6)). Factor 0 - 3*u**3 + 0*u + v*u**4 + 3/2*u**2.
3*u**2*(u - 1)**2/2
Let n(m) = -m**4 + m**3 - m**2 + m. Let k(p) = -3*p**5 - 3*p**4 - 12*p**3 + 12*p**2 + 3*p + 3. Let d(b) = -k(b) + 18*n(b). What is t in d(t) = 0?
1
Let p = -13 + 7. Let x be (p/4)/(1/(-2)). Factor 2/3*j**x + 0*j + 4/3*j**2 - 2/3*j**4 + 0.
-2*j**2*(j - 2)*(j + 1)/3
Let v(z) be the third derivative of -z**5/210 + 6*z**2. Factor v(x).
-2*x**2/7
Let m(w) be the second derivative of -1/42*w**7 + 5/6*w**3 + w + 1/6*w**4 + 0 + w**2 - 2/15*w**6 - 1/5*w**5. Factor m(d).
-(d - 1)*(d + 1)**3*(d + 2)
Let g(z) be the first derivative of 1/6*z**4 + 1 - 1/3*z**2 - 2/3*z + 2/9*z**3. Find u such that g(u) = 0.
-1, 1
Let 0 + 0*k + 2/5*k**4 - 2/5*k**2 + 0*k**3 = 0. Calculate k.
-1, 0, 1
Let n(x) be the second derivative of -x**6/15 - 2*x**5/5 - x**4/2 + 4*x. Factor n(c).
-2*c**2*(c + 1)*(c + 3)
Let q(c) be the first derivative of 3*c**4/16 - 7. Factor q(f).
3*f**3/4
Let q(k) be the second derivative of -1/120*k**6 - 1/12*k**3 + 1/40*k**5 + 0 + 0*k**4 - k + 1/8*k**2. Factor q(s).
-(s - 1)**3*(s + 1)/4
Let v = 14 + -23. Let m(j) = -1 + 20*j + 37*j**2 - 2 + 7 + 21*j**3 + 9*j. Let h(r) = 5*r**3 + 9*r**2 + 7*r + 1. Let y(t) = v*h(t) + 2*m(t). Factor y(b).
-(b + 1)**2*(3*b + 1)
Suppose 0 = -5*d - 4*s + 24, d + 2*s = -3*d + 18. Factor -22/3*q**3 - 14/3*q**5 + 4/3*q**2 + 32/3*q**d + 0 + 0*q.
-2*q**2*(q - 1)**2*(7*q - 2)/3
Let z(r) = 4*r**2 + r + 5. Let d(k) be the first derivative of -2*k**3 - k**2 - 8*k - 1. Let t = -3 - 2. Let b(j) = t*d(j) - 8*z(j). Let b(a) 