t x(u) = u + k*u - 4*u + 2 + 10*u**2. Let b(q) = -2*r(q) + 5*x(q). Let b(w) = 0. What is w?
-2/5, 0
Let a(t) = -2*t**2 + 7*t - 3. Let x be a(3). Suppose -2/7*g + 0*g**2 + 2/7*g**3 + x = 0. What is g?
-1, 0, 1
Let w(z) = z**3 - 4*z**2 + 3*z + 4. Let m be w(3). Determine n, given that -4*n**3 - 17*n**3 - 18*n**m + 21*n**5 + 6*n**2 + 12*n**4 = 0.
-1, 0, 2/7, 1
Let f = 3/8 - -1/8. Let 1/2*a**2 + f*a**3 - 1/2 - 1/2*a = 0. What is a?
-1, 1
Factor -2*z + 2 + 1/2*z**2.
(z - 2)**2/2
Suppose -o - 5*s + 3 = 3*o, 0 = 3*s + 3. Let y(j) be the second derivative of -1/60*j**4 + 1/10*j**2 + 0 + o*j + 0*j**3. Solve y(w) = 0.
-1, 1
Suppose -25 = -m - 4*m + 2*a, -a = -m + 8. Find k, given that 0*k - 1/2*k**4 + 1/4*k**5 + 1/2*k**2 + 0 - 1/4*k**m = 0.
-1, 0, 1, 2
Factor -4*l - 20/7*l**3 + 4/7*l**4 + 36/7*l**2 + 8/7.
4*(l - 2)*(l - 1)**3/7
Let q = -174 + 177. Let u(d) be the second derivative of -1/3*d**3 + 0*d**4 + 0*d**2 + 0 - q*d + 1/10*d**5. Factor u(a).
2*a*(a - 1)*(a + 1)
Let j be 13/(-52) + 18/8. Let u(y) be the first derivative of -4/21*y**3 + 3 - 1/14*y**4 - 1/7*y**j + 0*y. Solve u(p) = 0 for p.
-1, 0
Suppose v = -5*d + 6, -3*v + 4*d - 2 = -v. Factor -v + 5*q**3 + 0*q**2 + 5*q**4 + 3/2*q**5 - 5/2*q.
(q + 1)**4*(3*q - 2)/2
Suppose -3 = -2*c + 3*p + 1, 4*c + 28 = -3*p. Let o(f) = -f**2 - 4*f. Let n be o(c). Let -1/3 + n*u + 1/3*u**2 = 0. Calculate u.
-1, 1
Let s(v) be the third derivative of -v**5/300 + v**4/120 + v**3/15 - 11*v**2. Factor s(w).
-(w - 2)*(w + 1)/5
Let q(j) be the third derivative of -1/72*j**6 - 1/630*j**7 + 0 - 1/20*j**5 + 3*j**2 + 0*j - 1/9*j**3 - 7/72*j**4. Determine s so that q(s) = 0.
-2, -1
Let b(r) be the third derivative of -r**5/40 + r**3/4 + 22*r**2. Find f, given that b(f) = 0.
-1, 1
Let x be ((-4)/(-6))/(15/(-10) - -2). Let k(n) be the first derivative of -1/2*n**4 + 0*n**2 + 0*n - 2 - x*n**3. Suppose k(b) = 0. What is b?
-2, 0
Let i be 0*((-4)/4 - 0)/(-1). Suppose z**2 + i - 1/2*z**3 - 1/2*z = 0. Calculate z.
0, 1
Suppose -4*a - k + 5 = -0*a, -3*a = 3*k + 3. Suppose 9*s**3 - 24*s**3 - 24 + 0*s**4 + 12*s - 2*s**4 + 18*s**a + 5*s**4 = 0. Calculate s.
-1, 2
Let f be (-151)/51 - 3/(-1). Let a = f + 41/255. Factor -a*n - 2/5*n**2 - 1/5*n**3 + 0.
-n*(n + 1)**2/5
Let f = 1437 + -2621. Let j = f + 5938/5. Suppose -26/5*o**3 + 0 - 12/5*o**4 - 4/5*o - j*o**2 = 0. What is o?
-1, -2/3, -1/2, 0
Let r be (5 + 1)*(-4)/(-8). Factor -2*q**3 + r*q**3 - 3*q**3.
-2*q**3
Let o(i) = i + 13. Let m be o(-7). Factor -3*l**3 + 5*l**2 - l**3 + l**3 - l**5 + 2*l - l**4 + m*l**3.
-l*(l - 2)*(l + 1)**3
Let j(d) = 2*d**3 - 9*d**2 - 12*d - 1. Let r(v) = -v**3 + 9*v**2 + 11*v + 1. Suppose 0*c + 2*c = -12. Let o(z) = c*r(z) - 5*j(z). Factor o(x).
-(x + 1)**2*(4*x + 1)
Let h be 2/(-6)*(-13 + -2). Suppose x = -2*x + 9, 5*x - 27 = -4*w. Factor -12*q**w - 5*q**4 - h*q**4 - 4*q**4 - 4*q**2 - 6*q**3.
-2*q**2*(q + 1)*(7*q + 2)
Determine k so that 3/5*k - 3/5 - 3/5*k**3 + 3/5*k**2 = 0.
-1, 1
Let u(f) be the first derivative of -f**4/42 + 2*f**3/21 - 2*f**2/21 + 14. Find d, given that u(d) = 0.
0, 1, 2
Let l(j) = -8*j**4 + 14*j**3 + 11*j. Let t(w) = 3*w**4 - 5*w**3 - 4*w. Suppose 0 = h - 0*h + 4. Let g(a) = h*l(a) - 11*t(a). Factor g(p).
-p**3*(p + 1)
Let p(m) be the first derivative of 0*m + 1/5*m**2 - 4 + 1/15*m**3. Factor p(u).
u*(u + 2)/5
Let h(o) be the first derivative of o**2 + 4/3*o + 2/9*o**3 - 4. Factor h(j).
2*(j + 1)*(j + 2)/3
Let c = 216 + -216. Factor 3/5*w**3 - 3/5*w**5 + c + 0*w + 0*w**2 + 0*w**4.
-3*w**3*(w - 1)*(w + 1)/5
Let h be -1 + 7 + -8 + 5. Suppose -1 + h*d**2 - 6*d - 9 + 13 = 0. What is d?
1
Suppose 3*d - 46 = -5*m, -5*m + 4*d + 0*d + 67 = 0. Let r = m + -11. Solve 0 + r*b - 1/2*b**3 - b**2 = 0.
-2, 0
Let o(j) be the first derivative of 0*j + 0*j**5 + 1/1440*j**6 - 2 + 0*j**2 + 0*j**4 + 2/3*j**3. Let x(t) be the third derivative of o(t). Factor x(k).
k**2/4
Suppose -9 = z + 3*l, -3*l = 4*z - 8*l - 15. Suppose z*m - 4 = -2*m. Factor -1 + 2 + 2*v**3 + v - v**m - 3*v**3.
-(v - 1)*(v + 1)**2
Let v(w) = 9*w**4 + 12*w**3 + w**2 + 17*w - 13. Let k(x) = 2*x**4 + 3*x**3 + 4*x - 3. Let i(b) = 26*k(b) - 6*v(b). Factor i(l).
-2*l*(l - 1)**3
Let v(w) be the third derivative of w**5/30 + 5*w**4/6 + 25*w**3/3 - 11*w**2. Factor v(c).
2*(c + 5)**2
Let y(r) = -r**2 - 1. Let a(m) = 4*m**3 - 28*m**2 + 32*m - 24. Let u(b) = a(b) - 8*y(b). Factor u(t).
4*(t - 2)**2*(t - 1)
Suppose 0*y + 5*y = 0. Determine m, given that y - 2*m**3 + 2*m**5 + 0 = 0.
-1, 0, 1
Let m(p) be the second derivative of -p**8/5880 - p**7/1470 + p**5/210 + p**4/84 + p**3/6 + 3*p. Let h(v) be the second derivative of m(v). Factor h(o).
-2*(o - 1)*(o + 1)**3/7
Let x(l) = l**2 + l + 1. Let p(f) = -f**2 - 3*f - 4. Suppose 0 = -3*c + 2*c + 4. Let g(j) = c*x(j) + 2*p(j). Factor g(b).
2*(b - 2)*(b + 1)
Let s(m) be the second derivative of 2*m - 1/12*m**5 - 1/18*m**4 + 0 + 0*m**2 + 0*m**3. Factor s(v).
-v**2*(5*v + 2)/3
Suppose 0*v - 4 = v, 0 = 5*c + 4*v - 9. Factor -4*r + 3*r + 4*r**2 + 9*r**3 + 3*r**2 + r**5 + c*r**4 + 3*r.
r*(r + 1)**3*(r + 2)
Let m(s) be the third derivative of 6*s**2 + 1/150*s**5 - 1/300*s**6 + 0*s**3 - 1/525*s**7 + 0*s + 0*s**4 + 0 + 1/840*s**8. Factor m(u).
2*u**2*(u - 1)**2*(u + 1)/5
Let m(b) be the second derivative of -7*b**4/20 - 9*b**3/10 - 3*b**2/5 + 11*b. Let m(n) = 0. What is n?
-1, -2/7
Let t(w) be the second derivative of 1/30*w**5 - 2/3*w**3 - 4*w + 0 - 1/2*w**2 + 1/12*w**4. Let m(i) be the first derivative of t(i). Let m(c) = 0. What is c?
-2, 1
Let k = 7 - -6. Let l = -1 + 13. Factor 7*m**4 - 5*m**2 + 2*m + m**4 + l*m**3 + k*m**2 + 2*m**5.
2*m*(m + 1)**4
Suppose 0 = 13*r - 15*r. Let o(x) be the second derivative of 0 + 1/3*x**3 + r*x**4 + 1/2*x**2 - 1/10*x**5 - 2*x - 1/30*x**6. Factor o(t).
-(t - 1)*(t + 1)**3
Solve -3/7*v**3 - 3/7*v**4 + 0 - 1/7*v**5 + 0*v - 1/7*v**2 = 0.
-1, 0
Suppose 5*m = 10, -2 = y + 2*m - 8. Suppose -2*c + 2 = -y. Factor -2*o - o**4 + 2*o + o**c.
-o**2*(o - 1)*(o + 1)
Let t be 6/8*(4 - 6). Let a = t - -2. Factor a*y**3 + 0*y**2 + 0 + 0*y.
y**3/2
Suppose -4*b = -2*o - 0*o - 16, 3*o = 5*b - 19. Solve -8/9 + 8/9*z - 2/9*z**o = 0.
2
Let v(r) be the second derivative of -r**5/30 + r**4/9 + r + 19. Suppose v(q) = 0. What is q?
0, 2
Let o(r) be the first derivative of 0*r**2 - 1/20*r**5 + 0*r - 1/12*r**3 + 1 + 1/8*r**4. Factor o(g).
-g**2*(g - 1)**2/4
Factor 1/2*s - 1/2*s**3 + s**2 - 1/4*s**4 - 3/4.
-(s - 1)**2*(s + 1)*(s + 3)/4
Suppose 0 = -4*d - 11 + 31. Factor 5*a**2 + 0*a - 4 + 3*a + d*a.
(a + 2)*(5*a - 2)
Let y(c) be the second derivative of c**4/16 + 7*c**3/8 + 5*c. Factor y(n).
3*n*(n + 7)/4
Determine o so that 0 + 0*o - o**2 - 3/2*o**3 - 1/2*o**4 = 0.
-2, -1, 0
Determine g so that 4 - 7*g + 3*g**2 + 2 - 2*g = 0.
1, 2
Let d(p) be the first derivative of -p**5/20 - p**4/16 + p**3/12 + p**2/8 + 6. Suppose d(x) = 0. Calculate x.
-1, 0, 1
Let p(h) = -h**2 - 9*h - 14. Let t be p(-7). Let q(m) be the second derivative of 1/3*m**2 + m - 1/9*m**4 + 0*m**3 + 0*m**5 + 1/45*m**6 + t. Solve q(g) = 0.
-1, 1
Let m be (-14)/16*(-12)/14. Let o(k) be the second derivative of 0 - m*k**2 - 1/72*k**4 + 2*k - 1/6*k**3. Factor o(c).
-(c + 3)**2/6
Let m be 2 + -1 - (-2 - 1). Factor a**m - 3*a**2 + 3*a**5 - 6*a**4 - 8*a**3 - 4*a**4 + 17*a**3.
3*a**2*(a - 1)**3
Let v(j) be the first derivative of -5*j**6/12 + 4*j**5/5 + 3*j**4 - j**3/3 - 19*j**2/4 - 3*j - 8. Find q such that v(q) = 0.
-1, -2/5, 1, 3
Suppose 0*a - 4 = -a. Solve i**4 - i + 9*i**2 + i**2 - 8*i**3 - 3*i + i**a = 0.
0, 1, 2
Let c(x) be the third derivative of -x**6/24 + x**5/6 - 5*x**4/24 + 10*x**2. Factor c(u).
-5*u*(u - 1)**2
Let l be (-4)/16 - (-77)/84. Factor 1/3*j**2 + j + l.
(j + 1)*(j + 2)/3
Let p(x) = -3*x**3 + 4*x**2 - 3*x. Let d be 4/(-14) - 20/28. Let r(v) = -v**3 + v**2 - v. Let c(z) = d*p(z) + 2*r(z). Solve c(l) = 0.
0, 1
Let p(n) = n - 3. Suppose 2*q = -4*s, 4*s + 0 = -5*q + 18. Let z be p(q). Factor 5*j**2 + 2*j**4 - 5*j**2 - 2*j**z.
2*j**3*(j - 1)
Let t be ((-2)/1 - 0) + 1 + 5. Let w(m) be the second derivative of -1/5*m**2 + 0 + 1/30*m**t + 4*m + 0*m**3. Suppose w(n) = 0. What is n?
-1, 1
Factor 2/15*h + 4/15 - 2/15*h**3 - 4/15*h**2.
-2*(h - 1)*(h + 1)*(h + 2)/15
Let l be (-13)/104 - 263/(-56). Let -2/7*n**5 + l*n**2 - 18/7*n - 4*n**3 + 12/7*n**4 + 4/7 = 0. What is n?
1, 2
Let m(s) be t