t z(b) be the second derivative of j(b). Suppose z(a) = 0. What is a?
-1, 3
Let p be (-2)/7*(48/(-27) - -1). Determine i so that -2/9*i**2 + 2/3*i + 4/9 - 2/3*i**3 - p*i**4 = 0.
-2, -1, 1
Let d(l) be the first derivative of -1/9*l**4 + 1/3*l**2 - 4/27*l**3 - 1/27*l**6 + 3 - 2/9*l + 2/15*l**5. Determine o, given that d(o) = 0.
-1, 1
Factor -8/15*l + 2/15*l**2 + 8/15.
2*(l - 2)**2/15
Let a(k) be the third derivative of k**7/105 - 3*k**6/140 - k**5/42 + 3*k**4/28 - 2*k**3/21 - 7*k**2. Solve a(v) = 0.
-1, 2/7, 1
Let z(b) be the first derivative of -5*b**6/12 + 5*b**5/2 + 5*b**4/8 - 25*b**3/6 + 5. Determine d so that z(d) = 0.
-1, 0, 1, 5
Suppose 5*f - 5 = -0*c - c, 0 = -3*c + 2*f - 2. Factor 0 + 1/2*a**2 + c*a - 1/2*a**3.
-a**2*(a - 1)/2
Suppose 2*i = 4*l + 5*i - 19, -3*l = -2*i - 10. Find c, given that 4*c**5 + 5*c**4 - 2*c**l - 3*c**5 + 2*c**5 = 0.
-1, 0
Suppose -28*q = -188 + 48. Suppose -4/9*j - 38/9*j**4 - 2/9*j**2 + 10/3*j**3 + 0 + 14/9*j**q = 0. What is j?
-2/7, 0, 1
Suppose -k = s + 3*k - 14, 3*s + 3*k - 15 = 0. Let r(q) be the first derivative of 0*q**s + 0*q**4 + 0*q + 1 + 2/5*q**5 - 2/3*q**3. Factor r(b).
2*b**2*(b - 1)*(b + 1)
Let u(w) be the second derivative of 0*w**2 + 2/15*w**6 + 6/5*w**5 - 2/21*w**7 - 4/3*w**4 - 16/3*w**3 + 0 - 10*w. What is z in u(z) = 0?
-2, -1, 0, 2
Let l(g) = 2*g**3 - 2*g**2 - 6*g - 6. Let x(k) = -3*k**3 + 5*k**2 + 12*k + 13. Suppose 2*o - 11 = -3. Let w(i) = o*x(i) + 9*l(i). Factor w(n).
2*(n - 1)*(n + 1)*(3*n + 1)
Solve 1/2*r**3 + 0 + 0*r - 1/2*r**2 = 0 for r.
0, 1
Determine i so that -2/11*i**2 + 12/11 - 2/11*i = 0.
-3, 2
Suppose 3*b = 2*b + 4. What is a in -4*a**4 + b*a**5 + 4*a**4 - 2*a**4 = 0?
0, 1/2
Let x(m) be the first derivative of -6 + 2/21*m**3 - 8/7*m + 0*m**2. Solve x(b) = 0.
-2, 2
Suppose -13 = 4*o - 5*j, 2*o + j + 2*j = -23. Let c be o/((-21)/18) - 1. Factor 4*m**c - m**4 - 4*m**4 - m**4 + 2*m**3.
2*m**3*(m - 1)*(2*m - 1)
Let r = -289 + 289. Suppose 3/2*s**2 - 5/2*s**5 + r + 7/2*s**3 - 3/2*s**4 - s = 0. What is s?
-1, 0, 2/5, 1
Let o(j) = -3*j**2 - 5*j + 3. Suppose 74 - 4 = -5*x. Let w(a) = 8*a**2 + 14*a - 8. Let t(r) = x*o(r) - 5*w(r). Suppose t(b) = 0. What is b?
-1, 1
Let t(a) be the second derivative of a**4/78 + 2*a**3/39 + a**2/13 - 9*a. Factor t(d).
2*(d + 1)**2/13
Let u(n) be the first derivative of 2*n**6/15 - n**4/3 + 4*n - 7. Let y(z) be the first derivative of u(z). Find p, given that y(p) = 0.
-1, 0, 1
Let c(s) be the first derivative of s**9/1512 - s**7/420 - s**3/3 + 3. Let t(x) be the third derivative of c(x). Find b, given that t(b) = 0.
-1, 0, 1
Let r(i) = -i**3 + i + 1. Suppose a + 4 = 5*a. Let k(h) = h**4 - 3*h**3 - 2*h**2 + 3*h + 4. Suppose -4*c - 16 = -4. Let n(q) = a*k(q) + c*r(q). Factor n(v).
(v - 1)**2*(v + 1)**2
Let u = 6 - 3. Factor 13 - 6*n + u*n + 3*n**2 - 13.
3*n*(n - 1)
Suppose -10/21*a + 2/3*a**2 - 4/21 = 0. What is a?
-2/7, 1
Let g(d) be the first derivative of 2/9*d**3 + 0*d**2 - 2/3*d + 3. Let g(h) = 0. Calculate h.
-1, 1
Let u(y) be the first derivative of 3*y**4/4 - 2*y**3 + 3*y**2/2 - 6. Factor u(f).
3*f*(f - 1)**2
Let w be -1 + 11/3 + 22/(-33). Let q(g) be the second derivative of 0 + 0*g**3 + 0*g**w - 3*g + 1/80*g**5 - 1/48*g**4. Find m such that q(m) = 0.
0, 1
Let s(m) = m**3 - 6*m**2 - 1. Let j be s(6). Let l be 4/3*j/(-4). Factor -l*h + 2/3 - 1/3*h**2.
-(h - 1)*(h + 2)/3
Suppose 6 - 2 + 1 - 12*y**3 + 12*y - 9*y**2 + 7 - 3*y**4 = 0. What is y?
-2, -1, 1
Let p(k) be the first derivative of 2 + 1/15*k**5 - 2/9*k**3 - 1/6*k**2 - 1/18*k**6 + 1/6*k**4 + 1/3*k. Factor p(a).
-(a - 1)**3*(a + 1)**2/3
Let c(m) be the first derivative of m**3/12 + m**2/4 - 3. Factor c(v).
v*(v + 2)/4
Let g = -32 - -32. Factor -2/5*l + 0*l**2 + 2/5*l**3 + g.
2*l*(l - 1)*(l + 1)/5
Let t(i) = -4*i**4 + 8*i**2 - 16. Let p(y) be the first derivative of -y**5/5 - 5. Let l(x) = -3*p(x) + t(x). Determine v, given that l(v) = 0.
-2, 2
Suppose -11 = 13*p - 50. Let v(h) be the second derivative of -1/12*h**p + 1/40*h**5 + 1/24*h**4 - h + 0 - 1/4*h**2. Solve v(i) = 0 for i.
-1, 1
Let t(a) = -13*a**2 - 3*a - 17. Let o(p) = 3*p**2 + p + 4. Let r(k) = -9*o(k) - 2*t(k). Factor r(w).
-(w + 1)*(w + 2)
Suppose 4*t - 7 = 9. Factor 6*y + 4 + 3*y**2 - t + 3.
3*(y + 1)**2
Let s(z) = -23*z**4 - 31*z**3 - 3*z**2 + 5*z + 5. Let g(y) = 11*y**4 + 15*y**3 + y**2 - 3*y - 3. Let a = 0 - -3. Let l(k) = a*s(k) + 5*g(k). Factor l(r).
-2*r**2*(r + 1)*(7*r + 2)
Let w be 35/(-5) + 8 + 2/(-5). Factor 1/5*g**2 + 2/5 - w*g.
(g - 2)*(g - 1)/5
Let a be -2*1 + (-4 - -5). Let y = 3 + a. Factor -4/7 + 2/7*f**y + 2/7*f.
2*(f - 1)*(f + 2)/7
Factor -9*f + 10*f**2 - f - 5*f + 46*f**3 - 41*f**3.
5*f*(f - 1)*(f + 3)
Let j(c) be the first derivative of c**4/12 + c**3/9 - c**2/3 - 5. Factor j(b).
b*(b - 1)*(b + 2)/3
Let l be 4/(-7)*(-8)/16. Solve l*y**2 + 4/7 - 6/7*y = 0.
1, 2
Let k(g) = -2*g**3 + 10*g**2 + 6. Let p(c) = -c**3 + 9*c**2 + 5. Let o(x) = -5*k(x) + 6*p(x). Factor o(z).
4*z**2*(z + 1)
Let j = -1/207 - -623/414. Factor -j*h**3 - 3*h**2 - 3/4 - 1/4*h**4 - 5/2*h.
-(h + 1)**3*(h + 3)/4
Let m(l) be the second derivative of -1/9*l**3 + 0*l**2 + 7/36*l**4 + 1/30*l**6 - 2/15*l**5 + 0 + 2*l. Solve m(b) = 0.
0, 2/3, 1
Let a(u) = u**3 + u**2 - u. Let s(c) = -c**4 - 2*c**3 - 3*c**2 + 2*c. Let z(m) = -4*a(m) - s(m). Suppose z(r) = 0. Calculate r.
-1, 0, 1, 2
Solve -8/5*s + 8/5 - 2/5*s**2 + 2/5*s**3 = 0.
-2, 1, 2
Let a be 2/2 - (2 - 1). Let l be 1/(-1) - (a + -3). Solve i + 4*i**2 + l*i - i + 2*i**3 = 0 for i.
-1, 0
Let v(q) = q - 3. Let g be v(6). Determine f so that -3*f**5 - 4*f**2 - 2*f**4 - 2*f**g + 3*f**2 + 5*f**5 + 3*f**2 = 0.
-1, 0, 1
Let b be (243/4)/(35/100). Let g = -173 + b. Solve 10/7*k**2 + 0 + g*k = 0 for k.
-2/5, 0
Let a(z) be the third derivative of -1/504*z**8 + 0*z + 3*z**2 + 0 - 1/2*z**3 - 1/10*z**6 + 1/42*z**7 + 13/90*z**5 + 1/12*z**4. Solve a(i) = 0.
-1/2, 1, 3
Let l(p) = -8*p**4 + 3*p**3 + 2*p**2 - 3*p - 5. Let f(n) = -3*n**4 + n**3 + n**2 - n - 2. Let o(m) = -11*f(m) + 4*l(m). Factor o(g).
(g - 1)**2*(g + 1)*(g + 2)
Suppose 7*f - 11*f = -2*g - 16, -3*g = -2*f + 12. Find k such that -k + 1/4*k**f + 0 - 3/4*k**2 = 0.
-1, 0, 4
Let o be 494/(-210) + 6/21. Let q = 12/5 + o. Factor r**2 + q - r - 1/3*r**3.
-(r - 1)**3/3
Let g be ((-5 - -4) + 0)*0. Suppose g*d - 5 = -d. Factor -3/4*u**2 + 1/4*u**3 + 0 + 3/4*u**4 - 1/2*u + 1/4*u**d.
u*(u - 1)*(u + 1)**2*(u + 2)/4
Let h(s) be the second derivative of -s**5/5 - 19*s**4/3 - 66*s**3 - 162*s**2 - 20*s. Factor h(a).
-4*(a + 1)*(a + 9)**2
Let c(t) = -51*t**4 + 94*t**3 + 19*t**2 - 94*t + 20. Let f(o) = -101*o**4 + 189*o**3 + 39*o**2 - 189*o + 40. Let m(d) = -11*c(d) + 6*f(d). Solve m(l) = 0.
-1, 2/9, 1, 2
Let g be 0 - (3 + 61/2). Let q = g - -343/10. Factor 9*i**3 - 37/5*i**2 + q - 12/5*i.
(i - 1)*(5*i + 2)*(9*i - 2)/5
Let k(a) be the second derivative of 2*a**7/21 + 2*a**6/15 - 2*a**5/5 - 2*a**4/3 + 2*a**3/3 + 2*a**2 - 6*a. What is c in k(c) = 0?
-1, 1
Let f(k) = k**5 - k**4 + k**3 + k**2. Let v(t) = 3*t**5 - 8*t**4 + 15*t**3 - 10*t**2 + 4*t. Let s(h) = -6*f(h) + 3*v(h). Let s(j) = 0. Calculate j.
0, 1, 2
Let s be 56/9 + (-2)/9. Suppose 18 = 4*w + 6. Factor 9*h**4 + 16*h**3 - h**2 + h + s*h**2 - w*h.
h*(h + 1)**2*(9*h - 2)
Let x(j) be the first derivative of -15*j**4 + 7 + 16*j**4 - 2*j**2 - 4. Solve x(m) = 0.
-1, 0, 1
Solve 4*h**2 - 8*h + 12 - h**2 - 3*h**2 - 4*h**2 = 0 for h.
-3, 1
Let u(v) be the first derivative of 3*v**2 - 2*v + 2 - 2*v**3 + 1/2*v**4. Factor u(b).
2*(b - 1)**3
Let a(t) be the first derivative of t**7/4200 - t**6/600 + t**5/200 - t**4/120 + 2*t**3/3 + 1. Let d(m) be the third derivative of a(m). Factor d(z).
(z - 1)**3/5
Let d = -2/35 + 41/105. Determine o so that 0*o**3 + 0*o + d + 1/3*o**4 - 2/3*o**2 = 0.
-1, 1
Suppose 41 = 3*x - x + 3*f, 0 = 5*x + 2*f - 86. Suppose 17*z - 21*z + x = 0. Determine i, given that -6/7*i**2 + 6/7*i**z + 0 + 2/7*i - 2/7*i**3 = 0.
-1, 0, 1/3, 1
Let d(o) = o**3 + 6*o**2 + 4*o - 1. Let a be d(-5). Determine c so that 3/5*c**2 + 1/5*c**a + 0 - 1/5*c - 3/5*c**3 = 0.
0, 1
Let c(f) = f**3 + 2*f**2 - 3*f + 3. Let t be (-3)/4*(2 + 2). Let o be c(t). What is n in -4/11*n**2 - 2/11*n + 0 + 2/11*n**o + 4/11*n**4 = 0?
-1, -1/2, 0, 1
Determine n, given that 3/5*n**4 - 3*n + 3/5*n**3 - 6/5 - 9/5*n**2 = 0.
-1, 2
Suppose -15 = -4*u - 