r(p) be the first derivative of p + 1/20*p**4 - 3 + 3/10*p**3 + 3/5*p**2. Let m(g) be the first derivative of r(g). Factor m(x).
3*(x + 1)*(x + 2)/5
Suppose 2*t - 8 = -2*t. Determine h so that -2*h**2 + 2*h**2 + 8 + 2*h**5 - 10*h**4 - 16*h + 14*h**3 + t*h**2 = 0.
-1, 1, 2
Let l(x) be the first derivative of 2/55*x**5 + 0*x**2 + 0*x + 2/33*x**3 - 1/11*x**4 + 1. Factor l(h).
2*h**2*(h - 1)**2/11
Let l(s) be the second derivative of s**7/28 + s**6/30 - s**5/10 - s**4/12 + s**3/12 + 4*s. What is i in l(i) = 0?
-1, 0, 1/3, 1
Factor 0*g - 3/7 + 6/7*g**2 + 0*g**3 - 3/7*g**4.
-3*(g - 1)**2*(g + 1)**2/7
Let w(s) = s**3 + 6*s**2 + 5*s - 1. Let p be w(-4). Suppose -o + n = -3, 5*o - 4*n - p = -3*n. Find l, given that -8*l**3 - 3*l + o*l + 9*l**3 = 0.
-1, 0, 1
Factor 2/3*y**2 + 4 - 14/3*y.
2*(y - 6)*(y - 1)/3
Suppose 9 - 24 = -3*j - 3*w, w - 29 = -5*j. Let s be (6/117)/(j/36). Factor -2/13*o**2 + 6/13*o - s.
-2*(o - 2)*(o - 1)/13
Let a be ((-4)/14)/(17/(476/(-24))). Factor 0 + 0*x + a*x**2.
x**2/3
Factor 1/3*p**2 + 0 + 1/3*p.
p*(p + 1)/3
Factor 10*i**3 - 1 - 4*i**2 - 2 + 3.
2*i**2*(5*i - 2)
Suppose 2 = 3*g - z, 0 = g - 4*z + 2*z + 6. Suppose 16*l**2 + 0*l**3 - 20*l**3 - 4 + 6*l + g*l**2 = 0. Calculate l.
-1/2, 2/5, 1
Let l(d) be the first derivative of 2*d**3/15 + 6*d**2/5 + 18*d/5 + 5. Factor l(b).
2*(b + 3)**2/5
Let j(r) be the first derivative of r**3 - 15*r**2/8 + 3*r/4 - 2. Determine y, given that j(y) = 0.
1/4, 1
Let y(a) be the first derivative of 4*a**3/3 + 4*a**2 - 12*a - 10. Factor y(d).
4*(d - 1)*(d + 3)
Suppose -15*h + 11*h = 0. Let o(p) be the second derivative of p + 1/3*p**4 + 0 + 0*p**2 + 3/10*p**5 + h*p**3 + 1/15*p**6. Let o(s) = 0. What is s?
-2, -1, 0
Let k(c) be the second derivative of -1/120*c**6 + 0*c**2 - 2*c + 1/48*c**4 - 3/80*c**5 + 1/12*c**3 + 0 + 1/168*c**7. Factor k(x).
x*(x - 2)*(x - 1)*(x + 1)**2/4
Suppose 4*d = -2*n + 18, -3*n + 7*n - 4*d = 24. Let l = n + -5. Factor -5*j**2 + j**2 + j**3 + 3*j**l.
j**2*(j - 1)
Let m(z) be the second derivative of 2*z**6/45 - z**5/12 + z**4/36 - z. Factor m(r).
r**2*(r - 1)*(4*r - 1)/3
Factor 2*g - g + 9*g**2 - 7*g + g**3 - 4*g**3.
-3*g*(g - 2)*(g - 1)
Let s(k) be the second derivative of 1/5*k**3 - 1/30*k**4 - k + 0*k**2 + 0. Factor s(w).
-2*w*(w - 3)/5
Let d be 5/3 - (-2)/6. Let l(h) = -47*h**2 + 26*h**2 - 4*h**3 - 5*h - 1 + 22*h**2. Let b(j) = -j. Let i(w) = d*l(w) - 18*b(w). Factor i(a).
-2*(a - 1)*(a + 1)*(4*a - 1)
Suppose -2*o = -8 + 4. Factor -g**3 - g**3 + 0*g**o + 2*g**2.
-2*g**2*(g - 1)
Let t(u) be the second derivative of -u**6/840 - u**5/56 - u**4/14 - 2*u**3/3 - 4*u. Let k(j) be the second derivative of t(j). Determine q so that k(q) = 0.
-4, -1
Let w(m) be the second derivative of -m**4/12 + m**2/2 + 3*m. Solve w(c) = 0.
-1, 1
Let z(y) be the third derivative of -y**8/3696 - y**7/1155 - y**6/1320 + 42*y**2. Suppose z(q) = 0. What is q?
-1, 0
Let j(f) = f**3 + f**2 + 2. Let o be j(0). Let l(c) = -c**2 + 6*c + 9. Let w be l(7). Find x, given that x**w - 9*x + 7*x + x**o = 0.
0, 1
Let p = 671/4 - 167. Let v(k) be the first derivative of -p*k**4 + 4 - 1/3*k**3 + 4/5*k**5 + 0*k**2 + 0*k. Determine g so that v(g) = 0.
-1/4, 0, 1
Let g = 17 + -13. Let d(v) be the second derivative of -2*v + 0*v**3 + 1/6*v**g + 1/5*v**5 + 0 + 0*v**2. Let d(f) = 0. What is f?
-1/2, 0
Suppose -10 = 4*l + 2*r, -3*l - 14 = 3*r + 1. Factor 2/7*m**4 - 2/7*m**3 + l*m + 0 + 4/7*m**5 + 0*m**2.
2*m**3*(m + 1)*(2*m - 1)/7
Let p = -1/47 - -2117/94. Let u = -22 + p. Factor -u*k**2 + 0 + 0*k.
-k**2/2
Suppose w - 27 = 4*z + 4*w, 2*z + 4*w = -26. Let s = 6 + z. Factor -3*h**s - 4*h**4 + 5*h**2 + 5*h**5 - h**5 - h - h**4.
h*(h - 1)**2*(h + 1)*(4*h - 1)
Let b(v) be the second derivative of -2*v**7/7 + 4*v**6/15 + v**5/5 + 31*v. Solve b(r) = 0 for r.
-1/3, 0, 1
Suppose -3*j**4 - 16*j**3 + 6*j**4 + 6*j + 15*j**2 + 28*j**3 = 0. Calculate j.
-2, -1, 0
Suppose 9*z = 5*z + 12. Let w(a) = -2*a - 9. Let f be w(-6). Suppose z - 2*v**2 + 2*v**3 - f = 0. Calculate v.
0, 1
Factor 8 + 2*p**2 - 20*p + 3*p**2 + 24 - 12.
5*(p - 2)**2
Let b(d) be the second derivative of 0*d**3 + 1/60*d**4 + 0*d**2 + 0 - 1/100*d**5 - 3*d. Factor b(r).
-r**2*(r - 1)/5
Suppose -2/7*q**2 - 4/7 - 6/7*q = 0. Calculate q.
-2, -1
Suppose -2*j + 8 = 4. What is n in 6 - 12*n - j*n**3 - n**4 - 10 - 13*n**2 - 4*n**3 = 0?
-2, -1
Factor 10*j + 0*j - 4*j - 3*j**2.
-3*j*(j - 2)
Let j be (-12)/(-4) + -2 + 4. Let g be 4/14*7/j. Solve 0*b + 0 + 2/5*b**2 + g*b**3 = 0 for b.
-1, 0
Suppose 0 = 14*p - 13*p. Let t(d) be the second derivative of -1/55*d**5 + 1/55*d**6 - 1/66*d**4 + 0*d**2 + 0 + p*d**3 - 4*d. Factor t(h).
2*h**2*(h - 1)*(3*h + 1)/11
Let n(j) be the second derivative of -j**7/756 - j**6/540 - j**4/12 + 2*j. Let w(x) be the third derivative of n(x). Factor w(h).
-2*h*(5*h + 2)/3
Let o be (-1)/(0 - (-2 + 6)). Let r(f) be the first derivative of -1/6*f**3 - 1/10*f**5 - 3 + 0*f**2 - o*f**4 + 0*f. Find y such that r(y) = 0.
-1, 0
Let y = -1 - 20. Let c be y/(-9)*3/2. Solve 9/2*n**2 + 1/2*n**4 + 5/2*n**3 + 1 + c*n = 0 for n.
-2, -1
Let x(p) be the first derivative of -p**4/6 - 4*p**3/9 + p**2/3 + 4*p/3 - 6. Factor x(j).
-2*(j - 1)*(j + 1)*(j + 2)/3
Let g = 71 - 71. Determine m, given that g + m**3 + 1/2*m**2 - 1/2*m**4 - m = 0.
-1, 0, 1, 2
Let v(n) = -3*n + 1. Let p be v(1). Let b(m) = -m**3 - 3*m**2 - 3*m - 2. Let r be b(p). Solve -14*q**3 + 6*q**2 + 14*q + 4 - 10*q**4 + r + 0 = 0 for q.
-1, -2/5, 1
Let -1/5*k**5 + 0*k + 0 - 3/5*k**3 - 3/5*k**4 - 1/5*k**2 = 0. Calculate k.
-1, 0
Let n(v) be the third derivative of v**7/735 + v**6/84 + 3*v**5/70 + v**4/12 + 2*v**3/21 + 2*v**2. Determine h, given that n(h) = 0.
-2, -1
Suppose 3*u = -12, -2*j = u - 1 - 7. Let y = j - 3. Factor -2*h**3 - 3*h**2 - 2*h**4 - h + y*h + 5*h**2.
-2*h*(h - 1)*(h + 1)**2
Suppose 29*o = 33*o - 20. Let l(v) be the first derivative of -2/21*v**3 + 3 + 0*v + 0*v**2 - 2/35*v**o + 1/7*v**4. Factor l(t).
-2*t**2*(t - 1)**2/7
Suppose 2*p = 5*p + 6. Let r be -1 + p/((-2)/3). Factor 2/3 + 4/3*b + 2/3*b**r.
2*(b + 1)**2/3
Let h(x) be the second derivative of -x**4/28 + x**3/7 - 3*x**2/14 - 5*x. Determine u, given that h(u) = 0.
1
Let q(z) be the second derivative of z**6/180 - z**5/15 + z**4/3 - z**3/2 + 3*z. Let d(k) be the second derivative of q(k). Factor d(l).
2*(l - 2)**2
Suppose -5*u + 7*u - 40*u**2 - 40*u**3 - 4*u**5 - 4 - 22*u - 20*u**4 = 0. What is u?
-1
Factor 2/13*u**2 + 8/13*u + 8/13.
2*(u + 2)**2/13
Solve -5*q - 19*q + 6*q - 81 - q**2 = 0 for q.
-9
Let f(t) be the third derivative of t**8/168 + t**7/105 - t**6/12 - t**5/6 + t**4/3 + 4*t**3/3 + 25*t**2. Let f(k) = 0. What is k?
-2, -1, 1, 2
Let k(b) be the first derivative of -b**7/735 - b**6/420 + b**5/210 + b**4/84 + 3*b**2/2 - 4. Let f(z) be the second derivative of k(z). Solve f(j) = 0.
-1, 0, 1
Let b(p) = -p**2 + 5*p + 2. Let a be b(5). Let x be ((-1)/3)/((-3)/9). Find m, given that x + m - 2 - m**a - 3*m = 0.
-1
Factor 0*w + 16/3*w**3 - 8/3*w**2 + 0 - 10/3*w**4 + 2/3*w**5.
2*w**2*(w - 2)**2*(w - 1)/3
Let b(d) be the first derivative of d**5/80 - d**4/16 + d**3/12 + d + 2. Let w(c) be the first derivative of b(c). Find p, given that w(p) = 0.
0, 1, 2
Let t(l) = l**3 - 6*l**2 + 9*l - 1. Let q be t(4). Let r = -1 + 1. Solve 0 + r*n - 3/2*n**5 - 3/2*n**4 + 0*n**q + 0*n**2 = 0.
-1, 0
Let f be ((-2)/3)/(30/(-135)). Let o be 0 + f - (-2)/(-2). Find n, given that -1/3 - 1/3*n**o + 2/3*n = 0.
1
Factor 72/5 + 2/5*b**2 - 24/5*b.
2*(b - 6)**2/5
Factor 10/3*h**2 + 0 - 5/3*h**3 - 5/3*h.
-5*h*(h - 1)**2/3
Let o be 15/25 + 8/(-15). Let j(n) be the second derivative of o*n**6 + 0*n**3 + 0 + 1/10*n**5 + 0*n**4 - 2*n + 0*n**2. Suppose j(i) = 0. Calculate i.
-1, 0
Let g be (3/2)/(9/12). Suppose x + 49 = 3*c + 18, c - 7 = -3*x. Find q such that 0*q**2 + c*q + 8 - 2*q + g*q**2 = 0.
-2
Let j be -2*(3 + (-20)/4). Solve -1/2*u**j + 0*u + 2*u**3 - 2*u**5 + 1/2*u**2 + 0 = 0 for u.
-1, -1/4, 0, 1
Let -4/3 - 7/3*i**4 - 19/3*i**3 - 1/3*i**5 - 16/3*i - 25/3*i**2 = 0. Calculate i.
-2, -1
Let p(o) be the second derivative of 0 + 1/4*o**2 + 3/16*o**4 + 7/24*o**3 + 1/120*o**6 + 1/16*o**5 + 3*o. Factor p(k).
(k + 1)**3*(k + 2)/4
Let v(x) be the second derivative of -x**6/30 + x**5/10 - x**3/3 + x**2/2 - 8*x. Let v(a) = 0. What is a?
-1, 1
Suppose -3*j = -3*u + 3, 0 = 