 Let l = b + 44. Find z such that 0 + 12/5*z**l + 2/5*z**2 - 2*z**4 - 4/5*z**3 + 0*z = 0.
-1/2, 0, 1/3, 1
Let -2*r**2 + 3*r**3 + 0*r**5 - r**4 + r**4 - r**5 = 0. What is r?
-2, 0, 1
Factor -2*u**2 + 10 + 13 - 18 + 3 - 6*u.
-2*(u - 1)*(u + 4)
Factor -2*b - 4*b**4 - 31*b**3 + 32*b**3 + b**5 - 8 + 10*b**2 - 2*b.
(b - 2)**3*(b + 1)**2
Let l(r) be the first derivative of r**6/120 - r**5/20 + 5*r**4/48 - r**3/12 + 6*r + 2. Let b(z) be the first derivative of l(z). Factor b(c).
c*(c - 2)*(c - 1)**2/4
Let j = 1/105 - -62/105. Let b(f) be the first derivative of -2/5*f**4 - j*f**2 - 1 - 4/5*f**3 - 1/5*f. Factor b(s).
-(2*s + 1)**3/5
Let h(v) = v**3 - 2*v**2 - 5*v - 1. Let p be h(4). Suppose p = 4*l - 17. Factor 7*q**2 - 2*q**4 - l*q**2 + 0*q**5 + 2*q**5.
2*q**4*(q - 1)
Let f(l) = -4 + 2*l - 1 - 2 + 4. Let z be f(3). Let 2*m**5 - 2*m**2 - m**5 + m**5 + 3*m**3 + 2*m**4 - 5*m**z = 0. Calculate m.
-1, 0, 1
Let y(i) be the first derivative of -i**8/720 + i**7/504 + i**6/540 - 4*i**3/3 + 6. Let h(g) be the third derivative of y(g). Factor h(w).
-w**2*(w - 1)*(7*w + 2)/3
Let r(h) = -h**2 + 1. Let l be r(2). Let o be 1*-3*2/l. Solve -3*g**5 + 5*g + o*g**4 - 2*g - 8*g**4 + 6*g**2 = 0.
-1, 0, 1
Let h be (-4)/(-10)*(-3)/(-291). Let o = h + 1926/3395. Factor -6/7*c**3 + 0 - 10/7*c**2 - o*c.
-2*c*(c + 1)*(3*c + 2)/7
Let z(q) be the first derivative of q + 0*q**3 + 1 - 1/30*q**4 + 0*q**2. Let y(m) be the first derivative of z(m). Solve y(i) = 0.
0
Let t be (-3)/(2 + (-11)/4). Suppose 19 + 13 = t*n. Solve n*r**2 - r**4 - 8*r**2 = 0.
0
Let u(p) be the third derivative of -p**5/270 + 5*p**4/108 - 5*p**2. Determine d, given that u(d) = 0.
0, 5
Suppose -7*q = j - 2*q - 22, -j = -4*q + 14. Let r(d) be the second derivative of d + 0 - 1/5*d**j - 1/30*d**4 + 2/15*d**3. Factor r(c).
-2*(c - 1)**2/5
Let z(t) be the third derivative of t**8/42 - t**7/21 + t**6/60 - 15*t**2. Factor z(h).
2*h**3*(h - 1)*(4*h - 1)
Let z be (16/(-28))/(-2)*-7. Let m be 11/3 + 6/z. Factor -m - 2/3*v + 2/3*v**2 + 2/3*v**3.
2*(v - 1)*(v + 1)**2/3
Let c(l) be the first derivative of 4/7*l - 2/21*l**3 + 3 - 1/7*l**2. Factor c(y).
-2*(y - 1)*(y + 2)/7
Let a(x) be the first derivative of 125*x**6/2 + 210*x**5 - 405*x**4 + 232*x**3 - 48*x**2 - 46. Find s, given that a(s) = 0.
-4, 0, 2/5
Suppose 0 = -4*i + 3*i. Let z(c) be the second derivative of 0*c**2 - 1/60*c**5 + i + 0*c**3 - 1/36*c**4 - 2*c. Determine h, given that z(h) = 0.
-1, 0
Let z(d) be the second derivative of d**5/30 - d**4/9 + d**3/9 + d. Factor z(g).
2*g*(g - 1)**2/3
Let t(p) be the first derivative of p**7/735 + p**6/420 - 5*p**2/2 + 7. Let u(j) be the second derivative of t(j). Factor u(r).
2*r**3*(r + 1)/7
Suppose 4*h + 2*h**2 - 12*h + 196 - 188 = 0. Calculate h.
2
Let d(f) = f**4 + f**3 + f**2. Let l(k) = 3*k**4 + k**3 + 2*k**2. Let u(p) = 4*d(p) - 2*l(p). Find a such that u(a) = 0.
0, 1
Let -85*z**3 - z**2 - 4*z + 4 + 86*z**3 + 0 = 0. Calculate z.
-2, 1, 2
Suppose -21 - 9 = -5*f - 4*k, -5*k = -2*f - 21. Let r = f - -1. Let 3*b**3 - 2 - b**r - 2*b + 2*b**2 + 0 = 0. What is b?
-1, 1
Let q(x) = 2*x**5 + x**4 + 3*x**3 - 7*x**2 + x. Let b = -1 + -4. Let u(p) = -2*p**5 - p**4 - 2*p**3 + 6*p**2 - p. Let c(v) = b*q(v) - 6*u(v). Factor c(t).
t*(t - 1)*(t + 1)**2*(2*t - 1)
Let w be (-8)/(-28) - 2/7. Let w*n**4 - 2*n**5 + n**3 + n**5 + 0*n**2 - n**4 + n**2 = 0. Calculate n.
-1, 0, 1
Let o(m) be the first derivative of -3*m**4/4 + 3*m**3 - 9*m**2/2 + 3*m + 8. What is r in o(r) = 0?
1
Suppose 17*c**2 + 694*c**4 - 660*c**3 - 10*c - 6*c + 175*c**2 - 210*c**4 = 0. Calculate c.
0, 2/11, 1
Factor 11 + a - 3 - 3 + a**2 - 7.
(a - 1)*(a + 2)
Let k = 2185/4 + -546. Determine g, given that k*g**2 - 3/4*g + 1/2 = 0.
1, 2
Let g(o) = 2*o**4 - 6*o**3 + 12*o**2 - 2*o + 6. Let q(j) = -3*j**4 + 7*j**3 - 12*j**2 + j - 7. Let b(i) = 7*g(i) + 6*q(i). Let b(d) = 0. Calculate d.
-2, 0, 1
Let i(s) be the second derivative of -3*s**7/56 + s**6/4 - 9*s**5/20 + 3*s**4/8 - s**3/8 - 17*s. Factor i(b).
-3*b*(b - 1)**3*(3*b - 1)/4
Let j(l) be the second derivative of -l**6/1440 - l**5/240 - l**4/96 + l**3/6 - 3*l. Let q(b) be the second derivative of j(b). Factor q(f).
-(f + 1)**2/4
Let u(b) be the first derivative of -b**8/1512 - b**7/315 + 2*b**5/135 - 3*b**2/2 - 2. Let k(h) be the second derivative of u(h). Factor k(c).
-2*c**2*(c - 1)*(c + 2)**2/9
Suppose -4*x - 2*j = -5 - 3, 4*x = 2*j - 8. Factor w**3 + 1/2*w**2 + x*w + 0 + 1/2*w**4.
w**2*(w + 1)**2/2
Let c(y) = 19*y**3 - 2*y**2 + 4*y + 8. Let u(s) = 5*s**3. Let m(d) = 5*c(d) - 20*u(d). Factor m(p).
-5*(p - 2)*(p + 2)**2
Find j such that -44*j - 112*j**3 + 8 + 31*j**3 + 11*j**4 - 49*j**2 + 139*j**2 + 16*j**4 = 0.
2/3, 1
Let i(b) be the second derivative of -b**9/5040 - 3*b**8/2240 - b**7/280 - b**6/240 + 7*b**4/12 + b. Let z(k) be the third derivative of i(k). Factor z(p).
-3*p*(p + 1)**3
Let t = 16 - 10. Suppose -7*u + t*u = -3*s + 12, 5*s - 28 = -u. Factor 4*l**3 - 3*l**5 + l**5 - 2*l**u.
-2*l**3*(l - 1)*(l + 1)
Let u(i) be the first derivative of 7/12*i**3 - 5/2*i**4 + 11 + 0*i - 36/5*i**5 + 1/4*i**2. Factor u(h).
-h*(4*h + 1)**2*(9*h - 2)/4
Let f(o) be the second derivative of -7*o**4/6 - 3*o**3 - 2*o**2 - 6*o. Determine p so that f(p) = 0.
-1, -2/7
Let k(t) be the third derivative of -t**8/840 + t**7/210 - t**6/180 + t**3/3 - 3*t**2. Let s(f) be the first derivative of k(f). Factor s(g).
-2*g**2*(g - 1)**2
Let a(g) be the third derivative of g**5/10 + g**4/3 - 4*g**3/3 - 34*g**2. Determine l so that a(l) = 0.
-2, 2/3
Suppose -4*p - r = -26, 5 + 1 = 3*r. Let b(a) be the first derivative of 6*a**3 - 2*a**2 + 7/3*a**p + 0*a - 5/2*a**4 - 18/5*a**5 + 1. Let b(d) = 0. Calculate d.
-1, 0, 2/7, 1
Let j(k) = 2*k**2 - 9*k - 5. Let y be j(5). Determine t so that y + 20/3*t**3 + 6*t**5 - 11*t**4 + 0*t - 4/3*t**2 = 0.
0, 1/2, 2/3
Suppose k + 8 = 5*f, 3*f = 2*f + k. Suppose 0 = 2*i + f*i - 8. Factor 2*v**3 + 2*v**2 - 2*v + 2 - 2*v**i - 2*v**2.
2*(v - 1)**2*(v + 1)
Let p(m) be the first derivative of 0*m**2 + 0*m**3 + 0*m + 3 + 1/2*m**4. Factor p(b).
2*b**3
Let l(m) be the second derivative of -m**7/105 - m**6/75 + m**5/50 + m**4/30 + 27*m. Determine g so that l(g) = 0.
-1, 0, 1
Let t be (-10)/(-50)*1/(-1)*-2. Let c(v) be the first derivative of -2/15*v**3 - 3 + t*v + 0*v**2. Suppose c(o) = 0. What is o?
-1, 1
Factor 0*i + 2/5*i**2 + 4/5*i**4 + 0 - 1/5*i**5 - i**3.
-i**2*(i - 2)*(i - 1)**2/5
Let d(u) be the third derivative of u**7/315 - u**6/180 - u**5/30 + u**4/36 + 2*u**3/9 + 25*u**2. Factor d(w).
2*(w - 2)*(w - 1)*(w + 1)**2/3
Let h(l) = l**4 - l**3 - 1. Let u(b) = b**5 - 4*b**4 + 6*b**3 - 2*b**2 - b + 6. Suppose -2*q - 7 - 5 = 0. Let k(z) = q*h(z) - u(z). What is y in k(y) = 0?
-1, 0, 1
Let s(o) = -6*o**3 + 2*o**2 + 4*o. Let x(t) = -5*t**3 + t**2 + 3*t. Suppose -2*i - 6 = -0. Let f(z) = i*s(z) + 4*x(z). What is y in f(y) = 0?
-1, 0
Let y(j) be the first derivative of j**7/1050 + j**6/300 + j**5/300 + 2*j**2 + 1. Let a(n) be the second derivative of y(n). Factor a(m).
m**2*(m + 1)**2/5
Factor -6*j + 6*j**3 + 0 - 6/5*j**4 + 6/5*j**2.
-6*j*(j - 5)*(j - 1)*(j + 1)/5
Let b be (-3)/4*(-12)/36. Factor -1/4 + 1/4*c**2 - 1/4*c**3 + b*c.
-(c - 1)**2*(c + 1)/4
Let r = -69 - -484/7. Find i such that -2/7*i + 0 - r*i**2 = 0.
-2, 0
Let k(t) = -6*t - 1. Let s be k(-1). Suppose -s*y + 2*y = 0. Factor 0*c**2 + 0*c - 1/2*c**3 + y.
-c**3/2
Let g = -2 + 5. Factor -4*w**2 + 3*w**3 - w**g + w + w.
2*w*(w - 1)**2
Let y(x) be the second derivative of 1/6*x**4 - 3*x**2 + 0 + 2*x - 2/3*x**3. Factor y(v).
2*(v - 3)*(v + 1)
Let j(z) be the first derivative of -z**7/15 - 3*z**6/20 - z**5/15 - z**2/2 + 4. Let t(g) be the second derivative of j(g). Factor t(r).
-2*r**2*(r + 1)*(7*r + 2)
Suppose 8*l - 76 = 4*l. Factor 14*i**3 - l*i**2 - 16*i**4 - 5*i**2 + 22*i**3 + 4*i.
-4*i*(i - 1)**2*(4*i - 1)
Let p(u) be the third derivative of u**7/42 - u**5/4 - 5*u**4/12 + 2*u**2. Find t, given that p(t) = 0.
-1, 0, 2
Let l = -1 + 9. Factor -3*m**5 + l*m**5 + 4*m**2 - m**5 + 12*m**4 + 9*m**3 + 3*m**3.
4*m**2*(m + 1)**3
Let g(c) be the second derivative of c**4/6 - 4*c**3/3 + 48*c. Find f such that g(f) = 0.
0, 4
Let o(t) be the second derivative of t**10/120960 - t**8/8960 + t**7/5040 + t**4/12 + 4*t. Let i(q) be the third derivative of o(q). Solve i(h) = 0.
-2, 0, 