.
0, 1
Let n = 618/5 + 16. Let o = 140 - n. Suppose o*p**2 + 0*p + 0 - 2/5*p**4 + 0*p**3 = 0. Calculate p.
-1, 0, 1
Let u be 2/(-10)*-4 - 0. Suppose -7*s + 9*s = 0. Suppose 6/5*l**3 + s*l + u*l**2 + 0 = 0. What is l?
-2/3, 0
Let l be ((-68)/(-102))/((-1)/(-6)). Let f(o) be the second derivative of 1/54*o**l - 1/27*o**3 + 0 - 3*o + 0*o**2. Factor f(t).
2*t*(t - 1)/9
Let z(n) be the second derivative of 7/6*n**3 + 0 - 1/2*n**4 - 1/5*n**5 - 1/14*n**7 + 3*n + 4/15*n**6 - n**2. Determine c, given that z(c) = 0.
-1, 2/3, 1
Let w(l) = l**2 - 14*l - 11. Let r be w(15). Let z(g) be the first derivative of 1/6*g**2 - 1/9*g**3 + 2 + 0*g - 1/12*g**r + 1/15*g**5. Factor z(c).
c*(c - 1)**2*(c + 1)/3
Suppose -120*f = -114*f. Factor f + 0*j**2 - 2/3*j + 2/3*j**3.
2*j*(j - 1)*(j + 1)/3
Let t = -26 + 29. What is k in 2/3*k**5 + 0 + 0*k**t + 4/3*k**4 - 2/3*k - 4/3*k**2 = 0?
-1, 0, 1
Suppose -m + 4*z - 5 = 0, 0*z = m + z - 5. Let l(h) be the third derivative of 0 + 0*h + 1/120*h**5 + 3*h**2 + 1/48*h**4 - 1/6*h**m. Factor l(d).
(d - 1)*(d + 2)/2
Let p(h) = -81*h**2 - 1119*h - 6879. Let j(o) = 5*o**2 + 70*o + 430. Let a(i) = -33*j(i) - 2*p(i). Factor a(c).
-3*(c + 12)**2
Let v(x) be the first derivative of -3*x**4/26 - 4*x**3/39 + 27. Solve v(d) = 0 for d.
-2/3, 0
Factor -20 + 20 + 2*h**2 + 2*h.
2*h*(h + 1)
Let j(k) be the first derivative of -3*k - 1 + 21/4*k**3 - 3/16*k**4 + 3/2*k**2 - 87/20*k**5 - 15/8*k**6. Find d, given that j(d) = 0.
-1, 2/5, 2/3
Let m = -1034 - -7241/7. What is i in 3/7*i**2 - m*i + 0 = 0?
0, 1
Let z = 14 + -10. Let 3*j**2 - j**4 + 19 - 19 + 6*j - 6*j**3 - 2*j**z = 0. What is j?
-2, -1, 0, 1
Let m be (-4)/(-20) + 89/5. Let c be (-4)/m + (-20)/(-9). Factor 4 - 2 - 7*x**c + 5*x**2.
-2*(x - 1)*(x + 1)
Let k(r) be the first derivative of r**8/224 - 3*r**7/140 + 3*r**6/80 - r**5/40 - r**2 - 1. Let s(c) be the second derivative of k(c). Factor s(i).
3*i**2*(i - 1)**3/2
Let n(l) be the second derivative of -l**7/12 - l**6/12 + l**5/20 + 5*l. Factor n(o).
-o**3*(o + 1)*(7*o - 2)/2
Let v = 2/7564711 - -757805989/226941330. Let g = -1/170 + v. Determine k, given that -2/3*k - 8/3*k**5 + 2*k**2 + 0 - 2*k**4 + g*k**3 = 0.
-1, 0, 1/4, 1
Let f(l) be the first derivative of 3 - 1/9*l**3 + 1/3*l**4 + 1/3*l - 2/3*l**2. Factor f(r).
(r - 1)*(r + 1)*(4*r - 1)/3
Suppose -5*v + y - 3 = 0, -2*y + 6 = -0. Factor 1/2*d**2 - 1/4*d**3 + v - 1/4*d.
-d*(d - 1)**2/4
Let c(s) be the second derivative of s**7/210 - 2*s**6/75 + 3*s**5/50 - s**4/15 + s**3/30 + 16*s. Factor c(j).
j*(j - 1)**4/5
Suppose -3*l**4 + 5*l**5 + 1 + 4*l**4 - 2*l**2 - 4*l**3 + 2*l**3 + l - 4*l**5 = 0. Calculate l.
-1, 1
Let q(v) be the third derivative of 1/210*v**7 - 1/6*v**3 + 1/60*v**6 - 1/12*v**4 + 0 + 0*v**5 + 0*v + 6*v**2. Factor q(s).
(s - 1)*(s + 1)**3
Factor -3*j - j + 2*j**3 + 2*j**3.
4*j*(j - 1)*(j + 1)
Suppose 4 = -3*u + 1. Let w be (1 - 1)/(u + -1). Solve -1/2*z - 7/2*z**3 + w + 3/2*z**4 + 5/2*z**2 = 0.
0, 1/3, 1
Let u(q) be the first derivative of q**7/315 + q**6/90 - q**4/18 - q**3/9 + 2*q**2 - 1. Let z(x) be the second derivative of u(x). Factor z(r).
2*(r - 1)*(r + 1)**3/3
Let g be (-4)/16 - 172/(-240). Let p = g - 2/15. Solve 0*x**2 - 2/3*x + 1/3*x**4 - p + 2/3*x**3 = 0 for x.
-1, 1
Let o(w) = -3*w**4 + 3*w**3 + 5*w**2 - 15*w + 6. Let n(f) = -f**2. Let j(i) = -4*n(i) + o(i). Determine x so that j(x) = 0.
-2, 1
Let k(g) be the third derivative of -g**5/420 + g**4/56 - g**3/21 + 17*g**2. Factor k(o).
-(o - 2)*(o - 1)/7
Let p(c) = 3*c**3 - c**2 + 1. Let x be p(-1). Let k = 0 - x. Factor -2/5*a**k + 0 + 0*a**2 + 0*a - 2/5*a**4.
-2*a**3*(a + 1)/5
Let t(s) be the second derivative of s**6/240 + s**5/480 + s**3/2 + s. Let x(c) be the second derivative of t(c). Determine y, given that x(y) = 0.
-1/6, 0
Let c(d) be the third derivative of d**7/945 - d**6/60 + 29*d**5/270 - 13*d**4/36 + 2*d**3/3 - 7*d**2. Find z, given that c(z) = 0.
1, 2, 3
Let y(z) be the third derivative of -z**7/180 - z**6/180 - z**4/8 - 2*z**2. Let g(i) be the second derivative of y(i). Suppose g(c) = 0. What is c?
-2/7, 0
Let k(s) be the third derivative of s**5/180 - s**4/72 + 6*s**2. Let k(f) = 0. Calculate f.
0, 1
Let l be (6/(-8))/(5/(-4)). Let b be (3/10)/(19/114). What is n in l*n**3 + 0 - b*n**2 + 6/5*n = 0?
0, 1, 2
Let f(l) = 15*l**2 + 104*l + 81. Let r(v) = 3*v**2 + 21*v + 16. Let x(m) = -4*f(m) + 22*r(m). What is k in x(k) = 0?
-7, -2/3
Let j(n) = n**2 - 18*n + 4 + 0*n**2 + 15*n. Let t be j(2). Determine l so that 0 + 0*l + l**5 - l**3 - 2/3*l**t + 2/3*l**4 = 0.
-1, -2/3, 0, 1
Suppose 0 = 4*k - 5*k. Suppose 2*z + 8 = 6*z. Determine v, given that -2*v**z + k*v + v**2 - v = 0.
-1, 0
Let v(q) be the second derivative of -2*q**6/15 - 3*q**5/5 - q**4 - 2*q**3/3 - 7*q. Find x, given that v(x) = 0.
-1, 0
Suppose -3*a + 1 + 2 = -3*t, 3*a - 5*t = -7. Solve j - j + j**5 + 4*j**4 + a*j**3 + j + 4*j**2 = 0 for j.
-1, 0
Let c(x) be the third derivative of -1/5*x**3 + 0*x - 1/200*x**6 - 3/100*x**5 + 0 + 1/350*x**7 + 1/8*x**4 + 6*x**2. Let c(n) = 0. Calculate n.
-2, 1
Factor -53*t**2 - t**3 - t**4 + 101*t**2 - 46*t**2.
-t**2*(t - 1)*(t + 2)
Let y(j) be the second derivative of j**6/10 - 3*j**5/10 + j**3 - 3*j**2/2 + 7*j. Solve y(a) = 0.
-1, 1
Let u(z) be the first derivative of -z**8/6720 + z**7/3360 + 5*z**3/3 - 3. Let m(k) be the third derivative of u(k). Factor m(g).
-g**3*(g - 1)/4
Let p = 394/5 - 78. Let -p*s**3 + 0 + 2*s**4 + 0*s**2 + 0*s = 0. What is s?
0, 2/5
Let d = 393/47 - 17411/188. Let l = d - -85. Determine j so that -1/4*j**4 + j + 1 - l*j**2 - j**3 = 0.
-2, -1, 1
Let k(c) be the third derivative of -c**6/12 + 7*c**5/30 + c**4/12 - c**3 - 3*c**2. Factor k(l).
-2*(l - 1)**2*(5*l + 3)
Determine i, given that i**2 - 1 - 1/2*i**3 + 1/2*i = 0.
-1, 1, 2
Let o = -69 + 72. Find i, given that -2/5*i**2 - 13/5*i**4 + 0 + 4/5*i**5 + 11/5*i**o + 0*i = 0.
0, 1/4, 1, 2
Let l(u) = u**3 - 4*u**2 - u + 2. Let b(s) = 2*s**3 - 9*s**2 - 3*s + 5. Let v(f) = f - 2. Let h be v(-3). Let w(x) = h*l(x) + 2*b(x). Factor w(r).
-r*(r - 1)**2
Let s(l) be the second derivative of l**4/60 + l**3/30 - l**2/5 + 2*l - 44. What is i in s(i) = 0?
-2, 1
Let f(u) = 7*u**2 - 9*u. Let r(h) = 4*h**2 - 5*h. Let d(j) = 3*f(j) - 5*r(j). Factor d(a).
a*(a - 2)
Determine z, given that -18/7*z**2 + 12/7*z - 30/7*z**3 + 0 = 0.
-1, 0, 2/5
Let g(y) = y**2 - 3*y. Suppose 7*b - 16 = 3*b. Let r be g(b). Let 1/2*d**3 + 0*d**2 - 1/4*d**5 + 0*d**r + 0 - 1/4*d = 0. Calculate d.
-1, 0, 1
Solve 1/3*p**4 + 2/3*p**5 - 2*p**3 + 0 - 7/3*p**2 - 2/3*p = 0 for p.
-1, -1/2, 0, 2
Let r(u) be the third derivative of -u**6/60 + u**5/15 + u**4/12 - 2*u**3/3 - 24*u**2. Factor r(d).
-2*(d - 2)*(d - 1)*(d + 1)
Let y = -6393/4564 - 22/163. Let c = y - -16/7. Suppose c*u - 1/2 + 1/2*u**2 = 0. Calculate u.
-2, 1/2
Let m be (2 - 3) + 6/3. Let w be (m/((-2)/(-4)))/3. Factor 2/3*f**2 + 0 + w*f.
2*f*(f + 1)/3
Let v be ((-6)/12)/1*(-2)/5. Factor -v*a**3 - 3/5*a**2 - 1/5 - 3/5*a.
-(a + 1)**3/5
Let k(s) be the first derivative of 1/6*s**3 + 2*s - s**2 - 1. Factor k(v).
(v - 2)**2/2
Let r = -22 - -7. Let n = r - -15. Factor -4/9*x**3 + n - 2/3*x**4 + 0*x + 2/9*x**2.
-2*x**2*(x + 1)*(3*x - 1)/9
Suppose 4*r - 5*t = -3, -r + 18 - 6 = 3*t. Solve 0 + r*s**3 + 2*s**2 + 1/2*s + 1/2*s**5 + 2*s**4 = 0 for s.
-1, 0
Suppose -3*f - 6 - 10 = -4*y, 3*y - 4*f - 12 = 0. Factor -y*k - k + 4*k - 2*k**2.
-k*(2*k + 1)
Let f(x) be the second derivative of -x**7/42 + x**6/10 - 3*x**5/20 + x**4/12 + 3*x. Suppose f(n) = 0. What is n?
0, 1
Let j(r) = -4*r + 2. Let a be j(3). Let z be 5/5 + 8/a. Factor 0 - z*f**4 - 3/5*f**2 - 3/5*f**3 - 1/5*f.
-f*(f + 1)**3/5
Let g(n) be the first derivative of 0*n + 1/3*n**3 + 3 + 1/2*n**2. Factor g(s).
s*(s + 1)
Let g(t) be the third derivative of -t**6/120 - t**5/15 - t**4/6 - 6*t**2. Solve g(s) = 0.
-2, 0
Let u(l) be the third derivative of -l**8/2016 + l**7/210 - l**6/60 + l**5/36 - l**4/48 + 2*l**2. Factor u(i).
-i*(i - 3)*(i - 1)**3/6
Let p(b) be the second derivative of 1/2*b**3 + 3*b + 0 + 1/80*b**5 + b**2 + 1/8*b**4. Suppose p(c) = 0. What is c?
-2
Let c be 1 + -2 - (-2 + -1). Suppose 3*s + 4*t + 0*t + 2 = 0, s - 2*t - 6 = 0. Factor 4*h**3 - 5*h**5 - h**3 + 3*h**4 + s*h**5 - 2*h**2 - h**c.
-3*h**2*(h - 1)**2*(h + 1)
Let x(b) be the first derivative of -b**5/10 + b**4/6 + 