.
2*x**3*(x - 1)*(x + 1)
Let y(o) be the third derivative of -o**5/270 - 8*o**2. Determine u so that y(u) = 0.
0
Suppose 9*a = 5*a. Let u(l) be the second derivative of -l**2 + 1/3*l**4 + a + l - 1/3*l**3 + 1/5*l**5 - 1/15*l**6 - 1/21*l**7. What is x in u(x) = 0?
-1, 1
Let g(s) be the first derivative of 1/15*s**6 - 4/5*s**2 + 8/15*s**3 + 3/10*s**4 - 8/25*s**5 + 0*s - 4. Determine b so that g(b) = 0.
-1, 0, 1, 2
Determine t, given that -12*t - 32*t**5 - 20*t**4 - 8*t + 37*t**5 + 20*t**2 + 15*t**3 = 0.
-1, 0, 1, 2
Let k(p) be the second derivative of -p**8/13440 + p**7/5040 + p**4/12 + 3*p. Let b(o) be the third derivative of k(o). Find a such that b(a) = 0.
0, 1
Suppose -s - 4 = -8. Factor w**2 + 0 - w**s + 0*w**3 - 1/2*w**5 + 1/2*w.
-w*(w - 1)*(w + 1)**3/2
Suppose 0 = -3*i - 19*u + 21*u + 8, -3*i + 4 = -4*u. Let m(d) be the second derivative of -1/10*d**5 + 2/9*d**3 - 5*d + 0 + 5/18*d**i + 0*d**2. Factor m(o).
-2*o*(o - 2)*(3*o + 1)/3
Let d(i) be the third derivative of -i**8/6720 + i**7/3360 + i**6/1440 - i**5/480 + 2*i**3/3 + 2*i**2. Let m(x) be the first derivative of d(x). Factor m(k).
-k*(k - 1)**2*(k + 1)/4
Solve p**5 - p**5 + 0*p**3 + 2*p + 2*p**5 - 4*p**3 = 0 for p.
-1, 0, 1
Let s(w) = -6*w**3 + 3*w. Let r = 6 - 4. Let a(n) = -5*n**3 + 2*n. Let m(l) = r*s(l) - 3*a(l). Solve m(g) = 0.
0
Let o(h) be the second derivative of h**5/70 + 5*h**4/42 + 4*h**3/21 + 8*h. What is t in o(t) = 0?
-4, -1, 0
Let n(f) be the third derivative of f**7/735 - f**5/70 - f**4/42 - 35*f**2. Suppose n(t) = 0. Calculate t.
-1, 0, 2
Let y(q) = -11*q**2 + 6*q. Let b(p) = -p**2 + p. Let i(c) = 6*b(c) - y(c). Factor i(a).
5*a**2
Factor 2 - 3 - 1 + 2*b - 2 + 2*b**2.
2*(b - 1)*(b + 2)
What is l in -7/5 + 6/5*l + 1/5*l**2 = 0?
-7, 1
Let x(d) = -d**2 + d + 6. Let k be x(0). Let m(f) = -5*f**3 + f + 1. Let a be m(-1). Factor -k*v**2 - 3*v**3 + 4*v**3 + 1 + a*v**2 - v.
(v - 1)**2*(v + 1)
Let u be (45/60)/((-1)/(-4)). Let k(g) be the second derivative of -3*g - 1/12*g**u + 1/12*g**4 + 0*g**2 + 0 - 1/40*g**5. Factor k(v).
-v*(v - 1)**2/2
Suppose -1 = q - 3*x - 7, -3*x - 6 = 3*q. Suppose 3*s + q*s = 0. Suppose -1/2 + 1/2*i**2 + s*i = 0. Calculate i.
-1, 1
Let l = 1 + 2. Suppose -l*a = -a + 10, 5*g - 20 = 4*a. Find d, given that g*d**3 + 3*d**3 - d**3 + 2*d**4 = 0.
-1, 0
Let d = 409 + -406. Solve 1 + 9/4*g**4 + 15/2*g**d + 37/4*g**2 + 5*g = 0.
-1, -2/3
Let l be (-2 - -1)/(1/(-15)). Let m be l/(-6) + (1 - -2). Find b, given that -1/2*b - b**4 + m*b**3 + 0 + b**2 = 0.
-1, 0, 1/2, 1
Factor 2*j**3 - 4*j**2 - 4*j + j**2 + j**2.
2*j*(j - 2)*(j + 1)
Let i = 7 - 4. Factor 3*l**3 + 4*l - 3*l**i - l**3 - 6*l - 3*l**2.
-l*(l + 1)*(l + 2)
Let r(p) = p**3 - p + 1. Let t(d) = 4*d**3 - 8*d**2 - 3*d - 1. Let q(s) = -4*r(s) - 4*t(s). Factor q(o).
-4*o*(o - 2)*(5*o + 2)
Let t(w) = -8*w**3 + 2*w**2 + 3*w + 8. Let q = 9 + -14. Let v(r) = r**3 - r**2 - 1. Let d(k) = q*v(k) - t(k). Find j such that d(j) = 0.
-1, 1
Let d(u) be the second derivative of -u**7/840 + u**6/60 - u**5/10 + u**4/3 - u**3/3 - 3*u. Let t(z) be the second derivative of d(z). Factor t(w).
-(w - 2)**3
Let b(g) = 20*g + 5 + 4 + 14*g**2 - 1 + 2*g**3. Let l(a) = -2*a**3 - 15*a**2 - 21*a - 8. Suppose 0 = -2*j - 2*j + 16. Let w(t) = j*l(t) + 5*b(t). Factor w(i).
2*(i + 1)*(i + 2)**2
Let v = 7 + -5. Factor 2*s**2 - 3 - s + s + s**v.
3*(s - 1)*(s + 1)
Determine g so that -3/2*g + 3/4*g**2 - 3/4*g**4 + 9/4*g**3 + 0 - 3/4*g**5 = 0.
-2, -1, 0, 1
Let s(h) be the second derivative of -h**7/14 - 3*h**6/10 - 3*h**5/10 + h**4/2 + 3*h**3/2 + 3*h**2/2 - 2*h. Determine t, given that s(t) = 0.
-1, 1
Let p(b) be the second derivative of b**5/4 - 5*b**4/4 + 5*b**3/3 - 8*b. Solve p(a) = 0 for a.
0, 1, 2
Let v(f) = -f**3 + 7*f**2 - 6*f + 8. Let z be v(6). Let a = -4 + z. Find m such that -7*m**3 + 6 + 4*m - 20*m**3 + 15*m**2 - 21*m**a + 23*m = 0.
-1, -2/7, 1
Determine t, given that 3*t**2 - 3/2*t**5 + 0 - 3*t**4 + 0*t**3 + 3/2*t = 0.
-1, 0, 1
Let y be -3 + 3 - (3 + -3). Let m(w) be the second derivative of y + 1/42*w**4 - 2/21*w**3 + w + 1/7*w**2. Factor m(g).
2*(g - 1)**2/7
Let n(i) = 5*i**5 + 2*i**4 - 10*i**3 + 2*i**2 - i. Let p(h) = -h**5 + h**4 + h**3 + h. Let w(o) = -3*n(o) - 3*p(o). Let w(q) = 0. What is q?
-2, 0, 1/4, 1
Let h be (2 - 0 - 2)*(-2)/4. Let f(y) be the second derivative of -1/3*y**3 - 1/3*y**4 - 3*y + y**2 + h. Solve f(q) = 0.
-1, 1/2
Factor -1/4*d**5 + 1/2*d**2 + 1/2*d**3 - 1/4 - 1/4*d - 1/4*d**4.
-(d - 1)**2*(d + 1)**3/4
Let k(h) be the third derivative of -2*h**7/105 - h**6/15 + h**4/3 + 2*h**3/3 - 41*h**2. Factor k(w).
-4*(w - 1)*(w + 1)**3
Let z(n) be the second derivative of -n**5/100 - n**4/60 + n**3/30 + n**2/10 - 11*n. Factor z(j).
-(j - 1)*(j + 1)**2/5
Let o(p) = -8*p**2 + 3*p + 4. Let l(m) = -m**2 + m + 1. Let s(n) = -28*l(n) + 4*o(n). Suppose s(t) = 0. Calculate t.
-3, -1
Suppose 0 = -26*k + 17*k. Factor -1/2*l + 1/2*l**2 + k.
l*(l - 1)/2
Suppose -3*h = 4*d - 11, 0 = 3*h - d - 14 - 2. Let s(w) be the first derivative of 2/5*w**h + 2/15*w**3 + 4/5*w**4 + 3 + 0*w - 2/5*w**2. What is j in s(j) = 0?
-1, 0, 2/5
Let z(k) be the second derivative of k**4/6 + k**3 + 2*k**2 + 8*k. Factor z(q).
2*(q + 1)*(q + 2)
Let f be 2574/252 + (-5)/2. Solve -2/7*h**3 + f - 54/7*h + 18/7*h**2 = 0 for h.
3
Let g(b) be the first derivative of -b**7/147 - 2*b - 5. Let j(n) be the first derivative of g(n). Factor j(i).
-2*i**5/7
Let n(z) be the second derivative of -z**4/18 + 16*z**3/9 - 64*z**2/3 + 60*z. Factor n(s).
-2*(s - 8)**2/3
Let i(r) be the third derivative of -r**8/504 - 4*r**7/105 - 3*r**6/10 - 6*r**5/5 - 9*r**4/4 + 8*r**2. Determine s so that i(s) = 0.
-3, 0
Let b(m) be the first derivative of -m**4/12 - 4*m**3/9 - 5*m**2/6 - 2*m/3 - 7. Suppose b(t) = 0. Calculate t.
-2, -1
Factor -5/3 - 4/3*o + 1/3*o**2.
(o - 5)*(o + 1)/3
Let y be ((-51)/(-459))/(2 - 22/12). Factor 0*s - 8/3*s**2 + 0 + 8/3*s**3 - y*s**4.
-2*s**2*(s - 2)**2/3
Let c(z) be the first derivative of -3*z**5/5 - 9*z**4/4 - z**3 + 9*z**2/2 + 6*z - 11. Factor c(u).
-3*(u - 1)*(u + 1)**2*(u + 2)
Let w(r) be the second derivative of r**5/50 + r**4/15 - 4*r**3/15 - 8*r**2/5 - 7*r. Determine t, given that w(t) = 0.
-2, 2
Suppose 0 = 5*s - 1 - 14. Let x be (-4)/(s + 0 + -5). Factor 7/5*w**x + 0 + w**3 + 2/5*w.
w*(w + 1)*(5*w + 2)/5
Let b be 2/(-3) + 56/21. Determine m so that -1/4*m - 1/4*m**b + 0 = 0.
-1, 0
Factor g**4 + 4*g**2 - 5*g**2 + 2*g**5 + 0*g**3 + g**3 - 3*g**5.
-g**2*(g - 1)**2*(g + 1)
Let c(k) be the second derivative of -k**4/8 - 7*k**3/2 - 39*k**2/4 - 16*k. Factor c(d).
-3*(d + 1)*(d + 13)/2
Suppose 0 - 9/5*c + 12/5*c**4 + 3/5*c**5 - 12/5*c**2 + 6/5*c**3 = 0. What is c?
-3, -1, 0, 1
Let o(a) be the first derivative of -2*a**5/25 + 2*a**4/5 + 4*a**3/15 - 12*a**2/5 - 18*a/5 - 3. Let o(u) = 0. What is u?
-1, 3
Let l(o) be the second derivative of 0*o**3 + 1/90*o**5 - 3/2*o**2 - 1/36*o**4 + 0 - o. Let n(d) be the first derivative of l(d). Factor n(c).
2*c*(c - 1)/3
Let t(c) be the first derivative of -c**7/2520 + c**5/360 - 5*c**3/3 + 5. Let r(y) be the third derivative of t(y). Factor r(p).
-p*(p - 1)*(p + 1)/3
Let s(n) = 3*n + 38. Let v be s(-12). Solve 2/3*c**v + 0 + 2/3*c = 0.
-1, 0
Suppose u + 8 = -3*t - 3*u, -4*u = 2*t + 8. Suppose 5*v + t*v = 15. Factor 0*i**2 - 2*i**4 - 5*i**5 + v*i**5 + 2*i**2 + i + i**5.
-i*(i - 1)*(i + 1)**3
Let 2*t**4 - 17*t**3 - 10*t**2 + 23*t**4 + 2*t**3 = 0. What is t?
-2/5, 0, 1
Suppose 5*q = -0*q + 3*i - 30, -5*q - 25 = -2*i. Let z be 32/18 + q - -3. Factor z + 200/9*c + 1960/9*c**4 + 2030/9*c**3 + 940/9*c**2 + 686/9*c**5.
2*(c + 1)**2*(7*c + 2)**3/9
Let j(t) be the third derivative of -t**5/20 + t**4/30 + 2*t**3/15 + 14*t**2. Factor j(p).
-(3*p - 2)*(5*p + 2)/5
Let h(y) be the third derivative of 0*y - 1/168*y**8 + 0*y**3 + 1/30*y**6 + 3*y**2 + 0*y**7 - 1/12*y**4 + 0*y**5 + 0. Let h(i) = 0. What is i?
-1, 0, 1
Let p(q) = q**2 - 32*q - 225. Let j(t) = 6*t**2 - 161*t - 1125. Let d(b) = 2*j(b) - 11*p(b). What is x in d(x) = 0?
-15
Let b(o) be the third derivative of -o**8/12 - 32*o**7/105 - 2*o**6/15 + 14*o**5/15 + 11*o**4/6 + 4*o**3/3 - 12*o**2. What is x in b(x) = 0?
-1, -2/7, 1
Let w(x) be the second derivative of -x**7/420 - x**6/120 - x**5/120 - 3*x**2/2 - 2*x. Let p(i) be the first derivative of w(i). Factor p(y).
-y**2*(y + 1