 p(o) be the first derivative of n(o). What is h in p(h) = 0?
0, 1
Let a(o) be the second derivative of 0 - 3/4*o**4 + 0*o**2 - 3/4*o**5 - 1/10*o**6 + 9/2*o**3 - 6*o. Determine y so that a(y) = 0.
-3, 0, 1
Factor 8/11 - 2/11*i**3 + 12/11*i**2 - 18/11*i.
-2*(i - 4)*(i - 1)**2/11
Let q(f) be the third derivative of f**10/75600 + f**9/15120 - f**7/1260 - f**6/360 - f**5/6 + 5*f**2. Let u(t) be the third derivative of q(t). Factor u(i).
2*(i - 1)*(i + 1)**3
Suppose 5*r + 0*r - 10 = 0. Factor x**3 + 6*x**r - 6*x**2 - x.
x*(x - 1)*(x + 1)
Let j(q) be the first derivative of 0*q + 1/2*q**6 + q**3 - 3/5*q**5 + 3 + 0*q**2 - 3/4*q**4. What is p in j(p) = 0?
-1, 0, 1
Let k(b) = -b**2 - 13*b + 3. Let w be k(-10). Let y(p) = 24*p**2 + 15*p - 9. Let a(o) = 3*o**2 + 2*o - 1. Let c(n) = w*a(n) - 4*y(n). Factor c(r).
3*(r + 1)**2
Let x be (12/(-14))/((-6)/28). Let t(h) be the first derivative of 0*h + 1/4*h**2 + 0*h**5 + 1/12*h**6 + 0*h**3 - 1/4*h**x + 3. Factor t(q).
q*(q - 1)**2*(q + 1)**2/2
Let q(r) = -7*r**3 + 4*r**2 + 5*r + 6. Let l(t) = 15*t**3 + t**2 + 0*t**3 - 12 - 9*t - 10*t**2. Let v(g) = 4*l(g) + 9*q(g). Factor v(b).
-3*(b - 2)*(b + 1)**2
Let n(u) be the first derivative of u**4/4 + u**3/3 - u**2/2 - 2*u + 3. Let d be n(2). Factor -1 + 15*a + d*a**2 - 36*a**2 - 1.
-(4*a - 1)*(7*a - 2)
Let s = -15 + -15. Let z be (s/(-75))/(2/10). Factor 0 - 2/5*x**3 + 1/5*x - 1/5*x**z.
-x*(x + 1)*(2*x - 1)/5
Suppose v = 3*v + 4. Let y = -2 - v. Factor y*l**3 - 2*l**3 + 0*l**4 + 2*l**4.
2*l**3*(l - 1)
Let j(x) = -5*x**4 - 12*x**3 + 55*x**2 + 58*x - 178. Let h(v) = -v**3 - v + 1. Let d(t) = -2*h(t) + j(t). Factor d(z).
-5*(z - 2)**2*(z + 3)**2
Let t(w) be the second derivative of w**5/70 - 4*w**4/21 + 16*w**3/21 - 6*w. Factor t(d).
2*d*(d - 4)**2/7
Let v = -651 + 5861/9. Suppose v*p**3 - 4/9*p**2 + 0*p + 0 = 0. What is p?
0, 2
Let i(v) = v**2 - 2*v - 7. Let p be i(0). Let d = p + 9. Determine c, given that -1/2*c**4 - 4 - 9*c**d - 10*c - 7/2*c**3 = 0.
-2, -1
Let v(d) = d**4 + 5*d**3 + 3*d**2 - 5*d + 1. Let n(f) = -f**3 - f**2 + f. Let z(h) = -5*n(h) - v(h). Factor z(o).
-(o - 1)**2*(o + 1)**2
Let d(h) = h**2 - h. Let y(b) = -2*b**2 + 2*b. Let u(j) = -5*d(j) - 2*y(j). Factor u(p).
-p*(p - 1)
Let k(g) be the second derivative of -g**4/20 - 4*g**3/5 + 20*g. Factor k(w).
-3*w*(w + 8)/5
Factor 0*u**4 + 100*u - 4*u**4 + 78*u**3 - 140*u**2 - 34*u**3.
-4*u*(u - 5)**2*(u - 1)
Let k = 3 - -2. Suppose 4*u - k*u = -4. Factor -2*d**4 + 5*d**2 - 3*d**2 + 5*d - u*d**3 - d.
-2*d*(d - 1)*(d + 1)*(d + 2)
Let l(a) be the first derivative of a**4/10 - 2*a**3/15 - a**2/5 + 2*a/5 + 3. Factor l(n).
2*(n - 1)**2*(n + 1)/5
Let z(a) be the second derivative of -a**8/448 - a**7/840 + a**6/160 + a**5/240 - a**2 + a. Let r(f) be the first derivative of z(f). Solve r(i) = 0 for i.
-1, -1/3, 0, 1
Let g(l) be the first derivative of -l**6/18 + l**5/15 + 7. Factor g(p).
-p**4*(p - 1)/3
Let m be 3/(((-18)/(-15))/2). Let p be (1 + -2 + 1)*(-3)/(-3). Factor p + 1/3*q**m + 0*q**2 + 0*q**4 - 2/3*q**3 + 1/3*q.
q*(q - 1)**2*(q + 1)**2/3
Suppose -2*w = 0, -n + 5*w = -2*n + 4. Factor 6/7*a**3 - 2/7*a**n + 2/7*a + 0 - 6/7*a**2.
-2*a*(a - 1)**3/7
Suppose -7*m + 35 = 7. Let y(n) be the second derivative of 1/4*n**m + 0*n**2 - 1/3*n**3 + 2*n + 0 + 3/5*n**5 + 7/30*n**6. Solve y(h) = 0 for h.
-1, 0, 2/7
Let n be 33/6 + -3 - 2. Let f(u) be the first derivative of 2/3*u**3 + 1 - 2/5*u**5 + n*u**4 + 0*u - u**2. Factor f(g).
-2*g*(g - 1)**2*(g + 1)
Let d(j) = j**3 + 7*j**2 + 7*j + 4. Let v be d(-6). Let q be (4 + (-4 - v))/1. Solve -z**2 - 4*z - 6*z - 3*z**q - 10*z**2 - 2 - 6*z**3 = 0.
-1, -1/3
Let f = -16 - -18. What is l in 2/13*l**3 + 12/13*l**f + 0 + 18/13*l = 0?
-3, 0
Let a(y) be the third derivative of -y**5/30 - y**4/12 - 10*y**2. Factor a(l).
-2*l*(l + 1)
Find s such that 1 - 3*s**4 + s**2 + s - 7*s**3 + 3*s**3 + 3*s + s**2 = 0.
-1, -1/3, 1
Suppose 2*s - 5*g = -11, -2*s = 2*s - g - 23. Factor 3*o**4 - o**4 - o**3 - s*o**4 + 2*o**5 + 4*o**4.
o**3*(o - 1)*(2*o + 1)
Let m(h) be the second derivative of -h**8/5880 + h**7/1470 - h**6/1260 + h**3/6 - h. Let t(j) be the second derivative of m(j). Factor t(a).
-2*a**2*(a - 1)**2/7
Let f = 10 - 7. Let s = -3 + 4. Factor a**3 - s - 2*a**2 - 2*a**3 + 0*a**3 + f + a.
-(a - 1)*(a + 1)*(a + 2)
Suppose -80*k + 78*k = -4. Factor 0 + 0*y - 2/3*y**k - 2/3*y**3.
-2*y**2*(y + 1)/3
Factor 2*h**2 + 21*h - 20*h - h**2 - 2.
(h - 1)*(h + 2)
Let j(i) be the third derivative of -i**6/360 + i**5/15 - 2*i**4/3 + 32*i**3/9 + 21*i**2. Let j(m) = 0. What is m?
4
Let l(i) be the first derivative of -i**8/420 - i**7/105 - i**6/90 + 5*i**3/3 - 3. Let p(f) be the third derivative of l(f). Suppose p(r) = 0. What is r?
-1, 0
Find q, given that -2/7*q**4 + 2/7*q**3 + 6/7*q + 10/7*q**2 + 0 = 0.
-1, 0, 3
Let n = -3 + 61/20. Let p(g) be the second derivative of 1/30*g**6 - n*g**5 + 0*g**2 + 3*g + 0 + 0*g**4 + 0*g**3. Suppose p(l) = 0. Calculate l.
0, 1
Let n(t) be the first derivative of t**5/5 - t**4/2 + t**2 - t + 34. Factor n(l).
(l - 1)**3*(l + 1)
Let c = 7 - 5. Let u(p) = 7*p**3 - 23*p**2 - 4*p**3 + 15*p + 5*p**c. Let s(d) = -d**2 + d. Let n(l) = 18*s(l) - u(l). Find t, given that n(t) = 0.
-1, 0, 1
Let g(p) be the second derivative of -p**4/4 + p**3/6 + p**2 - p. Factor g(d).
-(d - 1)*(3*d + 2)
Let r(j) be the second derivative of j**4/48 - j**3/12 + j**2/8 + 5*j. Factor r(l).
(l - 1)**2/4
Let s(i) be the second derivative of 0 + 5/4*i**3 + 1/2*i**4 + 5*i + 3/40*i**5 + 3/2*i**2. Find x such that s(x) = 0.
-2, -1
Let p = 61 - 59. Let a(v) be the second derivative of 1/14*v**7 + 0*v**p + 2*v + 0 + 1/6*v**4 - 1/20*v**5 - 2/15*v**6 + 0*v**3. Solve a(f) = 0 for f.
-2/3, 0, 1
Let s(p) = 6*p**2 - 3*p + 6. Let i(t) = -7*t**2 + 2*t - 7. Suppose 3*o + 2*c - 19 = 0, -2*c = 2*o - 5*c + 9. Let r(d) = o*i(d) + 4*s(d). Factor r(n).
3*(n - 1)**2
Let f(c) = c + 3. Let d be f(5). Suppose -d = -3*y + 7. Let -4*u**5 + y*u**3 + 4*u**4 - 3*u**3 + 6*u**5 = 0. What is u?
-1, 0
Let g(f) be the third derivative of -2*f**7/245 - f**6/42 - 2*f**5/105 - 12*f**2. Factor g(y).
-4*y**2*(y + 1)*(3*y + 2)/7
Find i such that -55*i + 3*i**4 + 12 + 40*i**3 - 24*i**2 + 23*i + 9*i**4 - 8*i**3 = 0.
-3, -1, 1/3, 1
Let n(t) be the first derivative of 1/27*t**6 - 2/9*t**4 + 1/3*t**2 - 4/27*t**3 + 4/9*t + 8 + 0*t**5. Factor n(h).
2*(h - 2)*(h - 1)*(h + 1)**3/9
Let n(u) be the second derivative of u**5/30 - u**4/6 - u**3/9 + u**2 + 4*u. Factor n(r).
2*(r - 3)*(r - 1)*(r + 1)/3
Let c(k) be the second derivative of -1/135*k**6 + 4*k + 0*k**2 + 0 + 0*k**3 + 1/45*k**5 + 0*k**4. Factor c(a).
-2*a**3*(a - 2)/9
Let h(p) be the first derivative of 5*p**3/3 - 5*p**2/2 - 13. Factor h(i).
5*i*(i - 1)
Let p be (-1)/(-5)*-6*1/(-6). Factor -1/5 - 3/5*d**2 + 3/5*d + p*d**3.
(d - 1)**3/5
Let b(p) be the first derivative of p**6/9 + 2*p**5/15 - p**4/2 - 2*p**3/9 + 2*p**2/3 - 6. Solve b(m) = 0 for m.
-2, -1, 0, 1
Let j(n) be the third derivative of -n**5/6 - 17*n**4/24 - n**3/2 - 4*n**2. Let z(r) = -29*r**2 - 50*r - 8. Let x(c) = -17*j(c) + 6*z(c). Factor x(i).
-(i + 3)*(4*i - 1)
Let v(h) be the second derivative of 1/63*h**7 + 0*h**2 + 3*h + 0*h**3 + 1/45*h**6 + 0*h**5 + 0*h**4 + 0. Find w such that v(w) = 0.
-1, 0
Solve -182/11*u**3 + 0 - 6/11*u**4 - 450/11*u - 1410/11*u**2 = 0 for u.
-15, -1/3, 0
Let a be 104/330*3 - 588/1078. Factor a*l + 4/5*l**2 + 2/5*l**3 + 0.
2*l*(l + 1)**2/5
Let x(d) be the second derivative of -d**6/150 - d**5/50 + d**4/60 + d**3/15 + 12*d. Suppose x(k) = 0. Calculate k.
-2, -1, 0, 1
Let r = 14 - 3. Let f = -11 + r. Determine h, given that -1/2*h**5 - 1/2*h**4 + 1/2*h**3 + 1/2*h**2 + 0*h + f = 0.
-1, 0, 1
Let j(h) be the first derivative of 2*h + 1/50*h**5 - 1/15*h**3 - 2 + 1/30*h**4 - 1/5*h**2. Let w(b) be the first derivative of j(b). Factor w(z).
2*(z - 1)*(z + 1)**2/5
Factor -2 - 16*s + 65*s**2 + 2 - 69*s**2.
-4*s*(s + 4)
Let l be 3/(-12) - 9/(-4). Factor -3*u**4 - 6*u + l*u**4 + 9*u**2 - 2*u**4.
-3*u*(u - 1)**2*(u + 2)
Suppose 4*p + 2 + 66 = 0. Suppose 6 = -0*c - c. Let h(k) = -4*k**2 - 5*k - 1. Let r(u) = 11*u**2 + 14*u + 3. Let o(x) = c*r(x) + p*h(x). What is a in o(a) = 0?
-1, 1/2
Let y(v) be the first derivative of 2/3*v**3 - v**2 + 0*v - 3. Determine g so that y(g) = 0.
0, 1
Suppose -1/8*c**3 - 125/8 - 15/8*c**2 - 75