p**7/252 - p**6/30 + p**5/15 + 5*p**4/12 - 8*p. Let g(k) be the third derivative of h(k). Factor g(a).
2*(a - 2)*(5*a - 2)
Let h(v) = v**2 - v - 2. Let m be h(0). Let j be -1 + ((-10)/m - 2). Factor 8/3 + 2/3*c**j - 8/3*c.
2*(c - 2)**2/3
Let l(f) be the second derivative of 0 + 2*f + 0*f**2 + 0*f**4 + 0*f**5 - 1/30*f**6 + 0*f**3 + 1/42*f**7. Suppose l(t) = 0. What is t?
0, 1
Let a = -11 + 23/2. Let v(z) be the first derivative of -a*z**4 - 3/2*z**2 - 3/2*z**3 - 2 - 1/2*z. Factor v(d).
-(d + 1)**2*(4*d + 1)/2
Suppose -2*j - 109 = -5*n, -4*n + 29 = -5*j - 65. Let x be 4*3/(n*2). Let -x*r**2 - 2/7*r**3 + 2/7*r + 2/7 = 0. Calculate r.
-1, 1
Solve -w**2 - 3*w**4 + w + 5*w**3 - 3*w + w = 0.
-1/3, 0, 1
Let l be (-2 + (-5 - -7))/(-1). Suppose 0*k + 2/3*k**5 + 0*k**4 + l*k**2 - 2/3*k**3 + 0 = 0. What is k?
-1, 0, 1
Let f(g) = -g**3 + 7*g**2 + 8*g. Let r be f(8). Factor -2/9*d**3 + 4/9*d**2 + r - 2/9*d.
-2*d*(d - 1)**2/9
Let z(n) be the first derivative of -n**5/5 + 9*n**4/16 - n**3/2 + n**2/8 - 1. Determine a, given that z(a) = 0.
0, 1/4, 1
Factor 0 - 2/19*t**2 + 0*t.
-2*t**2/19
Let g = -109 + 547/5. Factor -g*s**2 + 0 + 0*s + 2/5*s**3.
2*s**2*(s - 1)/5
Let n be (-2 + -1 - -1)*1/(-6). Determine p, given that p**2 - 2/3 - n*p = 0.
-2/3, 1
Let n(r) be the second derivative of r**4/6 - r**2 + 2*r. Find i such that n(i) = 0.
-1, 1
Find k, given that -1/2*k + 3/4*k**5 - 1/4*k**4 + 0 + 9/4*k**2 - 9/4*k**3 = 0.
-2, 0, 1/3, 1
Let o(q) be the second derivative of 2*q**6/75 + 3*q**5/25 + 2*q**4/15 + 3*q. Find p, given that o(p) = 0.
-2, -1, 0
Let r = -18 + 9. Let u be (-3)/2*12/r. Factor -2/5*m**u + 0*m + 2/5.
-2*(m - 1)*(m + 1)/5
Let l = -4 - -7. Let f be l*(-3 + 33/9). Factor -f*h + 9*h + 2*h**2 - 3*h - 2*h**3.
-2*h*(h - 2)*(h + 1)
Let o(n) be the first derivative of -35*n**3/3 - 75*n**2 - 40*n + 29. Factor o(r).
-5*(r + 4)*(7*r + 2)
Find p such that -2/9*p**4 + 0*p - 2/9*p**2 + 4/9*p**3 + 0 = 0.
0, 1
Let z(h) be the second derivative of h**6/45 - h**5/5 + 2*h**4/3 - 8*h**3/9 + 54*h. Suppose z(k) = 0. What is k?
0, 2
Let h = -177 - -1241/7. Factor -h*j**2 - 8/7*j - 6/7.
-2*(j + 1)*(j + 3)/7
Let r(h) be the second derivative of 0*h**3 - 1/160*h**6 + 0 + 1/120*h**5 - h**2 + 2*h + 0*h**4. Let t(v) be the first derivative of r(v). Factor t(b).
-b**2*(3*b - 2)/4
Factor -4/3*x**5 + 0*x**4 + 4*x**3 + 0*x + 0 + 8/3*x**2.
-4*x**2*(x - 2)*(x + 1)**2/3
Find g, given that 15*g**2 - 19*g**2 + 19*g**3 + g**3 = 0.
0, 1/5
Factor 4*m**3 + 592*m + 4*m**2 - 592*m.
4*m**2*(m + 1)
Let k(g) = 29*g**3 + 8*g**2 - 3*g**2 - 6*g + 7 - 26*g**3 - 7*g. Let c(s) = 6*s**3 + 11*s**2 - 25*s + 13. Let u(x) = -2*c(x) + 5*k(x). Solve u(f) = 0.
-3, 1
Let o be 10/135*-3*(-6)/80. Let z(p) be the third derivative of -2*p**2 + 0 - 1/6*p**4 + o*p**5 + 2/3*p**3 + 0*p. Let z(b) = 0. What is b?
2
Find f, given that 2/3*f**4 - 7/3*f**3 + 0 - 2/3*f**2 + 7/3*f**5 + 0*f = 0.
-1, -2/7, 0, 1
Let y(h) be the first derivative of h**8/840 - h**7/540 - h**6/810 + h**3 + 5. Let b(n) be the third derivative of y(n). Factor b(z).
2*z**2*(z - 1)*(9*z + 2)/9
Suppose -4*j - b + 4 = -5*b, -23 = -5*j - b. Suppose 2*x**5 + 2*x**3 - 5*x**4 + x**4 - 3*x**j + 3*x**4 = 0. What is x?
0, 1
Let c(f) = -2*f - 2. Let y be c(-3). Suppose -8 = -3*j + 4, -y*d + 4 = -2*j. Factor 4*h**2 + 0*h**2 - h**d + 3*h**3.
2*h**2*(h + 2)
Let c(o) be the third derivative of 0*o**3 + 0 + 1/120*o**6 + 0*o - 1/60*o**5 + 1/210*o**7 + 4*o**2 - 1/336*o**8 + 0*o**4. Suppose c(k) = 0. Calculate k.
-1, 0, 1
Let d be (-33)/(-12) + (-1)/(-4). Factor -p**4 + 0*p**4 + 0*p**3 - 2*p**d.
-p**3*(p + 2)
Let a(x) be the second derivative of -35*x**6/36 + 11*x**5/4 + 53*x**4/72 - 2*x**3/3 - x**2/3 + 11*x. Suppose a(m) = 0. Calculate m.
-1/5, 2/7, 2
Suppose -5*r - 4*q + 24 = 0, -q = -r + 3*q. Suppose -14 = -4*p - r*w + 10, 2 = -3*p + 2*w. Let -2*a**3 + p*a**2 - 1 - 3 + 4 = 0. Calculate a.
0, 1
Let l be (-2)/(-3*(-4)/(-30)). Let b = l - 3. Factor -6*z + 8 - 4 + 0 + 2*z**b.
2*(z - 2)*(z - 1)
Let o(m) be the first derivative of -2*m**3/39 + 2*m/13 - 32. Factor o(r).
-2*(r - 1)*(r + 1)/13
Let m = 350/267 + 2/89. Solve -26/3*t**2 - 40/3*t**3 + 0 - 6*t**4 - m*t = 0 for t.
-1, -2/9, 0
Suppose 2*n + 4*i + 2 = 0, -2*n - i = 2*i. Let z(x) be the first derivative of -3/4*x**2 - 1 - 1/2*x - 1/2*x**n - 1/8*x**4. Solve z(v) = 0.
-1
Let n(p) = p**2 + p. Let q(j) = -8*j**2 - 9*j. Let d(v) = 28*n(v) + 4*q(v). Let d(o) = 0. What is o?
-2, 0
Let z(t) be the third derivative of 2*t**2 + 0*t + 0 + 5/12*t**4 + 1/60*t**6 - 2/3*t**3 - 2/15*t**5. Factor z(f).
2*(f - 2)*(f - 1)**2
Let b(k) be the third derivative of -k**10/12096 + k**9/4320 - k**8/6720 - k**4/6 - 7*k**2. Let t(s) be the second derivative of b(s). Factor t(r).
-r**3*(r - 1)*(5*r - 2)/2
Let y = -138 - -693/5. Let 1/5*w**2 + y - 4/5*w = 0. What is w?
1, 3
Let g(r) = -r**3. Let k(q) = -q**4 - 9*q**3 - 35*q**2 - 25*q. Let y(a) = -6*g(a) - 3*k(a). Find o such that y(o) = 0.
-5, -1, 0
Let h(k) be the first derivative of 1/6*k**3 + 0*k - 4 + 1/30*k**5 + 1/8*k**4 + 1/12*k**2. What is f in h(f) = 0?
-1, 0
Suppose 28 = 3*p - p - 4*g, 0 = 3*p + 2*g - 2. Suppose -2 = c - p. Factor -t**2 + 4*t**c - 6*t**2 + 6 + 3*t.
-3*(t - 2)*(t + 1)
Let a(q) be the second derivative of 0 - 1/90*q**5 + 0*q**2 - 1/54*q**4 - 3*q + 0*q**3. Factor a(h).
-2*h**2*(h + 1)/9
Factor -2/9*w - 4/9*w**2 + 0 - 2/9*w**3.
-2*w*(w + 1)**2/9
Let a(n) = n**2 + 7*n + 3. Let y be a(-7). Let i(f) be the third derivative of -2*f**2 + 1/150*f**5 + 0*f + 0 - 1/15*f**y + 0*f**4. What is t in i(t) = 0?
-1, 1
Let s(w) be the first derivative of w**6/360 - w**5/180 + 2*w**2 - 4. Let j(u) be the second derivative of s(u). Suppose j(f) = 0. What is f?
0, 1
Factor 1/3*b - 1/3*b**2 + 2/3.
-(b - 2)*(b + 1)/3
Let x(a) be the third derivative of 0*a + 0 - 5*a**2 - 1/60*a**5 - 1/360*a**6 + 0*a**4 + 2/9*a**3. Let x(b) = 0. Calculate b.
-2, 1
Suppose 4/9 + 10/9*u + 2/9*u**3 + 8/9*u**2 = 0. Calculate u.
-2, -1
Let b(r) = -10*r**4 + 56*r**3 - 68*r**2 + 12*r + 4. Let n(f) = 31*f**4 - 169*f**3 + 205*f**2 - 37*f - 11. Let m(u) = -11*b(u) - 4*n(u). Solve m(x) = 0 for x.
0, 2/7, 2
Let k(q) be the second derivative of q**7/2520 + q**6/540 + q**5/360 + 5*q**3/6 - 5*q. Let n(a) be the second derivative of k(a). Factor n(j).
j*(j + 1)**2/3
Let c(l) be the third derivative of -l**10/75600 + l**9/30240 - l**5/30 - 4*l**2. Let n(h) be the third derivative of c(h). Factor n(b).
-2*b**3*(b - 1)
Let a(j) = 1 - 2*j**2 - 15*j + 2 + 5 - 2*j**2. Let p(i) = -2*i**2 - 8*i + 4. Let k(o) = 6*a(o) - 11*p(o). Suppose k(f) = 0. What is f?
-2, 1
Let z(n) = n**3 - 6*n**2 - 8*n + 9. Let t be z(7). Let d(a) be the second derivative of 1/42*a**4 - 2/21*a**3 - a + 0 + 1/7*a**t. Factor d(m).
2*(m - 1)**2/7
Factor -2/9*q**5 - 10/9*q**4 - 2*q**3 + 0 - 4/9*q - 14/9*q**2.
-2*q*(q + 1)**3*(q + 2)/9
Let i(s) be the second derivative of s**4/12 + 5*s**3/6 - 3*s**2 - 51*s. Let i(j) = 0. Calculate j.
-6, 1
Solve 4/3*x**2 + 4/3 - 10/3*x = 0.
1/2, 2
Suppose 0 = -3*f + 2 + 10. Let c(z) be the first derivative of z**f + 2/5*z**5 - 2*z**2 - 2*z + 0*z**3 - 1. What is n in c(n) = 0?
-1, 1
Suppose -2*v = -7*v + 5*i - 30, -v + 3*i = 6. Let k be 6/(-2)*4/v. Let c + 0 + 1/2*c**k - c**3 - 1/2*c**4 = 0. What is c?
-2, -1, 0, 1
Let v(r) be the first derivative of -r**4/3 + 4*r**3/3 + 3*r - 2. Let d(j) be the first derivative of v(j). Factor d(y).
-4*y*(y - 2)
Let w(v) = -v**2 - v - 4. Let m(l) = -3*l**2 - 2*l - 11. Let b(n) = 4*m(n) - 11*w(n). Find s such that b(s) = 0.
0, 3
Find r such that 2/3*r - 2/3*r**2 + 8 = 0.
-3, 4
Let d(s) = -105*s**3 + 105*s**2 + 260*s - 300. Let n(r) = 8*r**3 - 8*r**2 - 20*r + 23. Let z(x) = 3*d(x) + 40*n(x). Factor z(k).
5*(k - 2)*(k - 1)*(k + 2)
What is k in -3/4*k**3 + 0*k**2 + 3/2 + 9/4*k = 0?
-1, 2
Let a = 374 + -371. Solve 3/2*t - 21/4*t**2 - 21/2*t**5 - 9/2*t**a + 0 + 75/4*t**4 = 0 for t.
-1/2, 0, 2/7, 1
Let k be (-16)/(1/(-2)*4). Factor 3*c**2 + 3*c + c**5 - 4*c**5 - 2*c**4 + k*c**4 - 9*c**2.
-3*c*(c - 1)**3*(c + 1)
Let o(g) = g**3 + 1. Let a(d) = -10 + 2*d + 2*d**3 - 3*d**2 - 2*d**2 + 9. Let c(i) = a(i) + o(i). Determine z so that c(z) = 0.
0, 2/3, 1
Let y(g) be the second derivative of -g**5/10 + g**4/3 - g**3 + 2*g**2 + 6*g. Let x(n) = n**3 - n**2. Let k(f) = 4*x(f) + y(f). What is p in k(p) = 0?
-2, 1
Factor