, 1
Find l, given that -1/2 + 5/4*l + 7/4*l**2 = 0.
-1, 2/7
Let h(f) be the second derivative of 5*f**7/42 + f**6/3 - 5*f**4/6 - 5*f**3/6 + 8*f. Solve h(m) = 0.
-1, 0, 1
Let -1/3*h**2 - 4/3*h + 0 = 0. Calculate h.
-4, 0
Let v(t) = -t**4 + t**2. Let r(y) = 2*y**5 - 18*y**4 + 12*y**3 + 2*y**2 + 2*y. Let h(i) = r(i) - 10*v(i). Factor h(d).
2*d*(d - 1)**4
Let c be 64/126 + (-2)/7. Let a(q) be the first derivative of -2/3*q + 2 + c*q**3 + 0*q**2. Suppose a(i) = 0. What is i?
-1, 1
Let n(s) be the second derivative of s**6/60 - s**5/75 + 3*s**2 + 3*s. Let k(o) be the first derivative of n(o). Let k(i) = 0. What is i?
0, 2/5
Let x(r) = -10*r**2 + 30*r + 7. Let o(f) = -11*f**2 + 29*f + 6. Let u(y) = 3*o(y) - 4*x(y). Solve u(z) = 0.
-2/7, 5
Let f be 1*0*(-1)/(-3). Let w = 55/2 + -27. Factor 1/2*o**3 - o**2 + w*o + f.
o*(o - 1)**2/2
Let z(w) be the second derivative of w**7/210 - w**6/30 + w**5/10 - w**4/6 + w**3/6 + 5*w**2/2 + w. Let k(v) be the first derivative of z(v). Factor k(s).
(s - 1)**4
Let g(h) = -12*h**2 - 12*h + 10. Suppose -8 = -s + 2. Let j(p) = p**2 + p - 1. Let z(b) = s*j(b) + g(b). Suppose z(a) = 0. What is a?
-1, 0
Let u(k) = -k**4 + k**2. Let o(m) = -3*m**5 + 21*m**4 - 3*m**3 - 15*m**2. Let y(w) = o(w) + 15*u(w). Let y(l) = 0. Calculate l.
0, 1
Let t(f) be the first derivative of f**3/3 + 7*f - 3. Let m be t(0). Find k such that -1 + 3*k + m*k**2 - 3*k**2 - 6*k = 0.
-1/4, 1
Let d = 8 + -4. Suppose -d*p + p = 0. Let -6/5*s**3 - 2*s**2 - 4/5*s + p = 0. What is s?
-1, -2/3, 0
Let k(o) be the second derivative of -o**5/60 - o**4/12 + 2*o**2/3 + 33*o. Factor k(l).
-(l - 1)*(l + 2)**2/3
Let r be 391/1265 - 3/(-33). Solve -r*t + 0 - 2/5*t**2 = 0 for t.
-1, 0
Let i(s) be the third derivative of s**8/168 + s**7/105 - 5*s**2. Determine v so that i(v) = 0.
-1, 0
Let f(p) be the second derivative of 1/6*p**4 + 0 - 4*p - 1/15*p**6 + 1/10*p**5 - 1/3*p**3 + 0*p**2. Determine v so that f(v) = 0.
-1, 0, 1
Let b(d) be the third derivative of d**5/12 - 55*d**4/12 + 605*d**3/6 + 5*d**2. Let b(l) = 0. What is l?
11
Let j(l) be the first derivative of 2*l**4/9 - 34*l**3/27 + 20*l**2/9 - 8*l/9 - 48. Solve j(a) = 0.
1/4, 2
Suppose -3 = -6*b + 3*b - 3*k, 4 = 4*b - k. Let l be ((-1)/2 - -1)*b. Factor -1/2*d**2 + 1/2 + l*d**3 - 1/2*d.
(d - 1)**2*(d + 1)/2
Suppose 2*v = -2*j + 10, 5 = 4*j - j + v. Factor 4*h**3 + j*h**3 - h**5 - 2*h**4 - 5*h**3.
-h**3*(h + 1)**2
Let j(y) = y + 2. Let n(s) = s**2 + 4*s + 2. Let b be n(-4). Let r be j(b). Factor -11*i + 7*i + 4 - 3*i**2 + 0*i**r + i**4 + 2*i**3.
(i - 1)**2*(i + 2)**2
Suppose 0 = 4*q + 2*t, 5*q + 4*t = -0*t. Solve -2/3*p**2 + q - 2/3*p = 0.
-1, 0
Let l be -3*((-33)/9 + 4). Let g be 3*-2*l - 3. Determine b so that 2/7*b**g + 4/7*b**2 + 0 + 2/7*b = 0.
-1, 0
Let 2/5 - 4/5*d + 2/5*d**2 = 0. What is d?
1
Suppose -3*p - 2 = -11. Suppose -3*j**3 + 2*j + 4*j**p + 3*j**2 - 5*j + 2*j**3 - 3 = 0. Calculate j.
-1, 1
Let i be -1*(-15)/(-24) - 0. Let l = i - -23/24. What is d in 0 - l*d - 1/3*d**3 - 2/3*d**2 = 0?
-1, 0
Let h(b) = 2*b**2 - 4*b + 2. Let l be h(2). Let m(n) be the second derivative of -1/6*n**4 + 1/2*n**2 + 0*n**3 + 0 + l*n + 0*n**5 + 1/30*n**6. Factor m(u).
(u - 1)**2*(u + 1)**2
Let w = 154/115 + 6/23. Factor -1/5*t**3 - 6/5*t**2 - w - 12/5*t.
-(t + 2)**3/5
Let p(w) be the third derivative of -w**7/105 + w**6/60 + w**5/10 - 5*w**4/12 + 2*w**3/3 + w**2 + 4*w. Factor p(y).
-2*(y - 1)**3*(y + 2)
Let m = 97 - 95. Let u(x) be the first derivative of -3 - 1/6*x**4 + 2/3*x**3 + 2/3*x - x**m. Factor u(o).
-2*(o - 1)**3/3
Suppose -19*q + 24*q - 25 = 0. Let d(w) be the third derivative of 1/210*w**q + w**2 + 0 - 1/28*w**4 + 0*w + 2/21*w**3. Factor d(a).
2*(a - 2)*(a - 1)/7
Suppose -2 - 2*d - 1/2*d**2 = 0. What is d?
-2
Let c(z) be the third derivative of 0 + 0*z - 1/120*z**6 - 1/24*z**4 + 0*z**3 + 1/30*z**5 + 3*z**2. Factor c(h).
-h*(h - 1)**2
Let o(z) be the third derivative of 0*z + 0*z**4 + 1/60*z**6 + 0*z**3 + 0 - 7*z**2 - 1/105*z**7 - 1/90*z**5 + 1/504*z**8. Factor o(p).
2*p**2*(p - 1)**3/3
Let t(d) = d**2 - 2*d + 4. Let f(b) = 3*b**2 - 7 - b**2 - b - 4*b**2 + 4*b. Let a = 12 + -8. Let l(o) = a*f(o) + 7*t(o). Determine w, given that l(w) = 0.
-2, 0
Let t(n) be the second derivative of 8*n**7/21 + 8*n**6/15 - 11*n**5/5 - 20*n**4/3 - 22*n**3/3 - 4*n**2 + 16*n. Let t(w) = 0. Calculate w.
-1, -1/2, 2
Let s(x) = 5*x**3 - x**2 + 3*x - 1. Let f be s(1). Let m be ((-34)/f)/((-18)/27). Find b such that 5/2*b**4 + 4*b + 23/3*b**3 + 2/3 + m*b**2 = 0.
-1, -2/3, -2/5
Let z(n) be the first derivative of 4*n**5/5 + 7*n**4 + 68*n**3/3 + 34*n**2 + 24*n - 13. Suppose z(r) = 0. What is r?
-3, -2, -1
Let g(v) be the second derivative of 3*v**5/80 - v**4/8 - v**3/8 + 3*v**2/4 - 3*v. Factor g(t).
3*(t - 2)*(t - 1)*(t + 1)/4
Let j(m) = -8*m**2 + 5*m - 3. Let d(c) = 7*c**2 - 5*c + 2. Let w(h) = -3*d(h) - 2*j(h). Determine p so that w(p) = 0.
0, 1
Let y(p) be the second derivative of -p**9/6048 + p**8/2240 - p**6/1440 + p**3/2 + p. Let f(n) be the second derivative of y(n). Solve f(l) = 0.
-1/2, 0, 1
Let u(p) be the first derivative of -p**5/30 + p**4/12 + 2*p**3/9 - p**2/6 - p/2 + 12. Let u(l) = 0. Calculate l.
-1, 1, 3
Solve 2*y**4 + 4/11*y**5 + 0*y - 10/11*y**2 + 8/11*y**3 + 0 = 0.
-5, -1, 0, 1/2
Let j(x) be the second derivative of x**4/24 - x**3/4 - 5*x. What is l in j(l) = 0?
0, 3
Let u(h) = h**3 - 8*h**2 - 13*h + 38. Let b be u(9). Let c = -37/2 + 19. Factor 0*s - 1/2*s**b - c*s**3 + 0.
-s**2*(s + 1)/2
Factor 0*l**2 - 8/9*l**4 - 2/3*l**3 - 2/9*l**5 + 0*l + 0.
-2*l**3*(l + 1)*(l + 3)/9
Factor 2/5*m**2 - 4/15*m**3 + 8/15*m - 8/15 - 2/15*m**4.
-2*(m - 1)**2*(m + 2)**2/15
Factor -4*s**3 - 17*s + 25*s + 6*s**3 + 12*s**2 + 2*s**3.
4*s*(s + 1)*(s + 2)
Let s(q) be the third derivative of 0 + 1/90*q**5 - 1/1008*q**8 - q**2 + 0*q + 1/72*q**4 - 1/315*q**7 + 0*q**3 + 0*q**6. Find p such that s(p) = 0.
-1, 0, 1
Let i(n) = 6*n**2 - n**5 - 4*n**3 - 3*n**4 - n**5 - 5*n - 7*n**4 - 5. Let m(j) = -j**5 - j**4 - j**3 + j**2 - j - 1. Let o(q) = i(q) - 5*m(q). Factor o(w).
w**2*(w - 1)**2*(3*w + 1)
Determine v so that -6/7*v**2 + 9/7*v**3 - 3/7*v + 0 = 0.
-1/3, 0, 1
Factor -15/4*t**3 + 3*t + 0 - 6*t**2.
-3*t*(t + 2)*(5*t - 2)/4
Let t be 55/22 + (-2)/4. Factor 0*d + 0 - 2/3*d**2 - t*d**4 - 2/3*d**5 - 2*d**3.
-2*d**2*(d + 1)**3/3
Factor 3*d**2 + 3/2*d**4 + 0*d + 0 - 9/2*d**3.
3*d**2*(d - 2)*(d - 1)/2
Let s be ((-4)/(-6))/(4/6). Suppose 0 = 3*f - s - 8. Suppose -6*v**3 + f*v**3 + 4*v**3 - v = 0. Calculate v.
-1, 0, 1
Let a = -81 - -406/5. Let s(b) be the third derivative of 0 - a*b**3 + 1/100*b**5 - 3*b**2 + 0*b + 1/40*b**4. Factor s(d).
3*(d - 1)*(d + 2)/5
Let h be (-2)/9 - 80/(-36). Factor -k + k**2 - k + 4 - h*k.
(k - 2)**2
Suppose 62*x - 68*x = -24. Find h, given that 3/4*h**3 + 5/4*h**2 + 0 - 1/4*h**5 - 1/4*h**x + 1/2*h = 0.
-1, 0, 2
Let f = 11/84 + -1/12. Let y(x) be the second derivative of -2*x - 1/105*x**6 + 0 + 0*x**5 - 1/7*x**2 + 0*x**3 + f*x**4. Let y(u) = 0. Calculate u.
-1, 1
Factor -q**5 - q**5 + 0*q**5 + 3*q - 6*q**3 + 5*q**5 - 3*q**4 + 6*q**2 - 3.
3*(q - 1)**3*(q + 1)**2
Let j be 2*(0 + (-9)/(-2)). Solve 3*h - 30*h**3 + j - 6*h**2 + h**2 + 31*h**3 = 0 for h.
-1, 3
Let 4/7*p**2 - 4/7*p**4 + 0*p**3 - 2/7*p + 2/7*p**5 + 0 = 0. Calculate p.
-1, 0, 1
Solve -3*a**3 - 174 - 5*a**3 + 12*a**2 + 170 = 0 for a.
-1/2, 1
Factor 0 - 3/7*m + 1/7*m**2.
m*(m - 3)/7
Let v be 0 + (2 - 4) - -8. Let a be ((-4)/v)/((-16)/6). Factor 0*m**4 + 0 + 0*m**2 - a*m**5 + 1/4*m**3 + 0*m.
-m**3*(m - 1)*(m + 1)/4
Let d(n) be the first derivative of -1 + 1/3*n**2 + 0*n + 2/9*n**3. Let d(k) = 0. Calculate k.
-1, 0
Let s be (2 - 0/(-2)) + (-322)/184. Find n such that -s*n**3 + 1 - 1/4*n**2 + n = 0.
-2, -1, 2
Suppose 4 = 2*h - s, 2*h = -0*h - 4*s + 4. Let y be h/(-10) - 216/(-30). Factor -y*a + a - 1 + 2*a**2 + 9 - 2*a.
2*(a - 2)**2
Let a(v) be the second derivative of -5*v**7/36 - 13*v**6/18 - 17*v**5/12 - 10*v**4/9 + 5*v**3/36 + 5*v**2/6 + 3*v. Factor a(u).
-5*(u + 1)**4*(7*u - 2)/6
Let o(h) = -3*h**2. Let c(t) = -4*t**2. Let y be -3*(-2)/(-4 - -2). Let s(m) = y*o(m) + 2*c(m). What is a in s(a) = 0?
0
Suppose -a - 38 = -v + 4*a, 112 = 2*v - a. Let z = v - 231/4. Factor 1/4*y**2 + 0*y + z*y**3 + 0.
y**2*(y + 1)/4
Let q(s) be the first derivative of -s - 1/10*s**5 - 1 - 8*s**2