7*o**2 - 7*o - 6. Let l be g(-6). Let p(k) be the second derivative of -1/90*k**5 + k + 1/27*k**3 + 0*k**2 + l*k**4 + 0. Factor p(m).
-2*m*(m - 1)*(m + 1)/9
Let -23 + 18*l**2 + 23 - 4*l**3 - 16*l - 2*l**2 = 0. Calculate l.
0, 2
Let r = -6 + 2. Let y be r/(-35)*(-5)/(-2). Let 0*z - 6/7*z**2 - 4/7*z**3 + y = 0. Calculate z.
-1, 1/2
Let k(s) be the first derivative of -4*s**5/15 + 2*s**4/3 - 4*s**2/3 + 4*s/3 + 36. Let k(r) = 0. What is r?
-1, 1
Let h(i) be the third derivative of -i**5/390 + i**4/26 - 3*i**3/13 + 4*i**2. Find a, given that h(a) = 0.
3
Let h be 1 - 2 - (-2 - -1). Let m(j) be the third derivative of 1/40*j**6 + 0*j + j**2 + 0*j**4 + 0*j**3 + 1/40*j**5 + h + 1/140*j**7. What is b in m(b) = 0?
-1, 0
Let t(z) = 2*z**2 + 8*z + 18. Let o(j) = -4 + 4 - 1. Suppose -w + 22 = 2*y + 7, 55 = 5*y - w. Let s(p) = y*o(p) + t(p). Determine x, given that s(x) = 0.
-2
Let p = 23 - 20. Let 2*f**3 - p*f**4 - 6*f + 2*f**2 + f**2 + 0*f**3 + 4*f**3 = 0. What is f?
-1, 0, 1, 2
Let q be 6/3*(-41)/(-2). Let d = q - 163/4. Factor 1/2*k**4 + 1/4*k**5 + 0 - 1/2*k**2 - d*k + 0*k**3.
k*(k - 1)*(k + 1)**3/4
Let r(x) be the first derivative of x**4/12 + x**3 + 5*x**2/2 - 25*x/3 - 28. Factor r(a).
(a - 1)*(a + 5)**2/3
Suppose -3*v - 8 = -0*d + 4*d, -2*v = d - 3. Suppose 0 = -5*a, -5*a - 17 - 8 = -5*t. Find x, given that 14/3*x**v - 2*x**t - 32/9*x**3 + 0*x + 8/9*x**2 + 0 = 0.
0, 2/3, 1
Suppose 592 = 2*u + 586. Factor -1/2 - 2*l**u - 9/2*l**2 - 3*l.
-(l + 1)**2*(4*l + 1)/2
Factor 15/2*i**3 + 3 + 3/2*i**4 + 21/2*i + 27/2*i**2.
3*(i + 1)**3*(i + 2)/2
Let l(c) be the third derivative of 0 + 1/48*c**6 + 5/96*c**4 + 1/24*c**5 + 0*c + 1/1344*c**8 + 1/168*c**7 + 2*c**2 + 1/24*c**3. What is p in l(p) = 0?
-1
Let x(n) = n**2 + 3*n - 4. Let p be x(-5). Factor 33*d**2 + p*d + 0*d**4 + 53*d**4 - 2*d**4 + 63*d**3 + 15*d**5 + 0*d.
3*d*(d + 1)**3*(5*d + 2)
Let g = 4 + -8. Let n = 7 + g. Solve -q**n - 4/3 - 13/3*q**2 - 16/3*q = 0 for q.
-2, -1/3
Let k(b) be the second derivative of -b**6/720 + b**5/240 - b**3/6 + 3*b. Let a(n) be the second derivative of k(n). Factor a(u).
-u*(u - 1)/2
Let w(j) = 3*j**2 - j. Let m be w(0). Find y, given that 2/9*y**4 + 0*y + m - 2/9*y**2 + 2/9*y**3 - 2/9*y**5 = 0.
-1, 0, 1
Let d(x) be the second derivative of x**4/84 + 4*x**3/21 + 8*x**2/7 + 6*x. Factor d(b).
(b + 4)**2/7
Let w(k) be the third derivative of 5*k**2 - 1/780*k**6 + 0 + 1/390*k**5 + 0*k**4 + 0*k + 0*k**3. Suppose w(d) = 0. Calculate d.
0, 1
Let v = -7/5 - -73/45. Determine p, given that -v*p**2 - 2/9 - 4/9*p = 0.
-1
Let q(x) = 17*x**2 - x**3 - 5*x**3 - 7*x**2. Let a(w) = -7*w**3 + 11*w**2 + w. Let h(n) = -4*a(n) + 5*q(n). Factor h(k).
-2*k*(k - 2)*(k - 1)
Let v be (-86)/(-12) - 2/(-8)*-20. Suppose -v*g**4 + 8/3*g**2 - 1/2*g**3 + 2/3*g - 2/3*g**5 + 0 = 0. What is g?
-2, -1/4, 0, 1
Factor 7*k**3 - 23*k**3 - 3*k**4 - 4*k**2 + 7*k**2 + 10*k**3 + 6*k.
-3*k*(k - 1)*(k + 1)*(k + 2)
Let p be 2 - (-3 - (3 - 4)). Suppose p*q + 6 + 6 = 0, -4*g + 15 = -q. Let -4/3 + 2*d**2 + 2*d - 4/3*d**g = 0. Calculate d.
-1, 1/2, 2
Let p(r) be the third derivative of -r**8/336 + r**7/70 - r**6/120 - r**5/20 + r**4/12 - 6*r**2. Determine d, given that p(d) = 0.
-1, 0, 1, 2
Let m(i) be the third derivative of i**6/360 + i**5/45 + 5*i**4/72 + i**3/9 + 3*i**2. Determine w, given that m(w) = 0.
-2, -1
Let z(c) be the third derivative of -c**5/135 + 2*c**3/27 - 15*c**2. Factor z(v).
-4*(v - 1)*(v + 1)/9
Let f(r) = 2*r - 2. Let k be f(3). Let c = k + 1. Solve -2*q**c + 4*q**4 - 3*q**2 + q**5 - 3*q**3 + 4*q**2 + 4*q - 5*q**2 = 0.
-1, 0, 1, 2
Factor -3*t - 3*t**2 - 6 + 8*t**2 - 2*t**2.
3*(t - 2)*(t + 1)
Let i(d) = d**2 + 2*d - 5. Let b be i(-4). Suppose -b - 2*g**2 + 2 + 3 = 0. Calculate g.
-1, 1
Let h(b) be the first derivative of -b**4/14 + b**2/7 + 14. Suppose h(y) = 0. What is y?
-1, 0, 1
Let z = -232 + 929/4. Find a such that -1/4 - z*a**3 + 1/4*a + 1/4*a**2 = 0.
-1, 1
Suppose -1/2*y - 1/2*y**4 - 3/2*y**3 - 3/2*y**2 + 0 = 0. What is y?
-1, 0
Let f(o) be the third derivative of -3*o**7/350 + o**6/10 - 13*o**5/75 - 4*o**4/3 - 32*o**3/15 - 2*o**2 - 15*o. Find g such that f(g) = 0.
-2/3, 4
Let y(q) be the second derivative of 1/30*q**5 - q**2 - q + 1/6*q**4 + 1/3*q**3 + 0. Let d(c) be the first derivative of y(c). Factor d(b).
2*(b + 1)**2
Let y be 2/(-4)*7/(-210). Let j(m) be the second derivative of 1/15*m**3 - 1/50*m**6 + 0*m**2 + y*m**4 + 0 + m - 1/25*m**5. Suppose j(k) = 0. What is k?
-1, 0, 2/3
Let s = 14/115 - 1/46. Let g(x) be the second derivative of 4*x**3 + 0 + x + x**4 + 8*x**2 + s*x**5. Factor g(p).
2*(p + 2)**3
Let y = 3 + -5. Let d be y + 2*3 + -1. Let 3 - 2*g - 3*g**4 + 7*g**d + 3*g**2 - 3 - 5*g**5 = 0. What is g?
-1, 0, 2/5, 1
Let p(s) = 16*s**3 - s**2 - 5*s - 10. Let k(v) = -3*v**3 + v + 2. Let b(o) = 22*k(o) + 4*p(o). Factor b(w).
-2*(w - 1)*(w + 1)*(w + 2)
Let x = 3 + -5. Let t be 1/x*12/(-18). Suppose 1/3*j**3 + 0 - t*j**2 + 0*j = 0. What is j?
0, 1
Let b(m) = m**3 - m - 1. Let v(k) = 34*k**3 - 33*k**2 - 4*k + 5. Let r(g) = 2*b(g) + v(g). Factor r(a).
3*(a - 1)*(3*a + 1)*(4*a - 1)
Let d(x) be the second derivative of x**5/70 + x**4/14 + 4*x. Factor d(i).
2*i**2*(i + 3)/7
Suppose 4*c = 10*c + 36. Let a be (3/(c/4))/(-8). Suppose -a*z - 1/2 + 1/4*z**2 = 0. Calculate z.
-1, 2
Let p(c) be the second derivative of c**4/12 + 5*c**3/6 - 2*c**2 - 6*c. Let i be p(-6). Suppose -i*k**3 + 0 - 2/3*k**4 - 2/3*k - 2*k**2 = 0. Calculate k.
-1, 0
Let l = -16 - -12. Let c(y) = 2*y - 3*y + 0*y - 3 - y**2. Let h(u) = u**2 + u + 2. Let m(k) = l*c(k) - 6*h(k). Factor m(s).
-2*s*(s + 1)
Let v = 359/11628 + -1/323. Let q(p) be the third derivative of 1/90*p**5 + 0*p**3 + 0*p - v*p**4 + 0 - 2*p**2. Determine g, given that q(g) = 0.
0, 1
Let l(v) be the third derivative of v**8/10080 + v**7/3780 - v**4/12 + 6*v**2. Let g(x) be the second derivative of l(x). Solve g(j) = 0 for j.
-1, 0
Factor 3/7*x**4 - 1/7*x**3 - 11/7*x**2 - 12/7*x + 1/7*x**5 - 4/7.
(x - 2)*(x + 1)**3*(x + 2)/7
Let h(d) = -2*d**4 - 10*d**3 + 2*d - 2. Let w(g) = g**4 + 9*g**3 - 3*g + 3. Let l(f) = -3*h(f) - 2*w(f). Factor l(p).
4*p**3*(p + 3)
Let y(b) = b**3 - 7*b**2 + 6*b + 4. Let p(r) = 2*r**3 - 3*r**2 + 2. Let g be p(2). Let c be y(g). Factor -3*x**2 + 2*x**3 - x**3 - c*x**3.
-3*x**2*(x + 1)
Let b(w) = w**3 - w**2 - w + 1. Let z(f) = 9*f**3 - 9*f**2 - 5*f + 5. Let t(i) = 5*b(i) - z(i). Factor t(s).
-4*s**2*(s - 1)
Suppose -5*r - 19 = -94. Let b be 0 + (r/(-9) - -2). Factor 1/3*m**2 - 2/3*m + b.
(m - 1)**2/3
Suppose -55 = -3*b - 2*d, 0 = b - 4*d - 1 + 6. Factor -12*y - b*y**2 + 10*y**2 + 12 + 8*y**2.
3*(y - 2)**2
Let i = -17 + 24. Let u = i - 5. Let -2*q - 2*q**2 - 2*q**3 - 2*q + 8*q**u = 0. What is q?
0, 1, 2
Let k = 6/41 + 122/287. Factor -2/7 + k*a**2 - 2/7*a.
2*(a - 1)*(2*a + 1)/7
Let n = -9 - -13. Suppose 4*o - n = o + g, g - 5 = 0. Suppose 0*f**2 + 0 - 1/3*f**o + 1/3*f = 0. What is f?
-1, 0, 1
Let v(t) be the first derivative of -t**6/15 - 4*t**5/25 - 11. Suppose v(l) = 0. What is l?
-2, 0
Let l(v) be the second derivative of 3*v**7/14 - v**6/5 - 2*v**5/5 + v**4/2 - v**3/6 - 16*v. What is o in l(o) = 0?
-1, 0, 1/3, 1
Suppose 3*v + 5*r - 73 = 0, 0*r - 11 = -v + r. Suppose -v = -5*n + n. Determine s so that s**n + s**2 - s**2 - s**5 = 0.
0, 1
Let g(u) be the first derivative of 2 - 1/4*u**2 + 3/8*u**3 + u - 7/48*u**4. Let f(n) be the first derivative of g(n). Find o such that f(o) = 0.
2/7, 1
Let f be (-36)/(-45)*(-15)/(-6). Factor 6/7*t**f - 15/7*t**3 + 0 + 0*t + 6/7*t**4.
3*t**2*(t - 2)*(2*t - 1)/7
Let v be (9 - 6)/(3/2). What is n in n**3 + 5*n**3 - 2*n**4 - 3*n**3 + n**5 + 5*n**4 + n**v = 0?
-1, 0
Factor -2*p + 0*p**2 + 2*p**2 + 0*p**2.
2*p*(p - 1)
Let r(k) = 3*k + 9. Let y(b) = b + 2. Let x(l) = -2*r(l) + 9*y(l). Let c be x(1). Factor 2 - 7 + 5*h**2 + c - 3*h**2.
2*(h - 1)*(h + 1)
Factor 3*r**2 + r**2 - r**2 - r**2 - 4 - 2*r.
2*(r - 2)*(r + 1)
Let j(h) = -2*h**4 - 5*h**3 + 3*h**2 + 4*h - 8. Let d = 4 - 0. Let f(m) = -m**2 + 7*m - m**d - 7*m. Let u(p) = -3*f(p) + j(p). Determine v, given that u(v) = 0.
-1, 2
Let c(u) be the first derivative of -u**9/378 + u**8/168 - u**7/420 + 4*u**3/3 - 3. Let p(d) be the third derivative of c(d). Factor p(k).
-2*k**3*(k - 1)*(4*k - 1)
Let k(r) be the first derivative of -1/3*r**3 - 3 + 0*r**2 + 0*r**4 + 1/5