
1
Factor 2/3 + 22/9*v - 2/3*v**3 + 10/9*v**2.
-2*(v - 3)*(v + 1)*(3*v + 1)/9
Let q(v) be the second derivative of -v**6/75 - 2*v**5/25 - 2*v**4/15 - 48*v. Let q(o) = 0. What is o?
-2, 0
Suppose 0*c - 4/13*c**4 + 2/13*c**3 + 4/13*c**2 + 0 - 2/13*c**5 = 0. What is c?
-2, -1, 0, 1
Determine v, given that 2/5 + 6/5*v + 4/5*v**2 = 0.
-1, -1/2
Let f(c) = -c**2 + 7*c + 2. Let t be f(7). Let p be (-3 + -1)/(-20)*t. Factor -p - 2/5*a**3 + 2/5*a + 2/5*a**2.
-2*(a - 1)**2*(a + 1)/5
Let u(w) = -3*w**3 + 4*w**2 - w + 2. Let v(l) = -4*l**3 + 3*l + 8*l**3 - 3 - 2*l - 5*l**2. Let n(y) = 3*u(y) + 2*v(y). Factor n(t).
-t*(t - 1)**2
Let x(c) be the second derivative of c**4/4 - c**3/2 + 17*c. Let x(u) = 0. Calculate u.
0, 1
Let z(q) be the first derivative of -q**3/3 + q**2/2 + 2*q + 1. Find h such that z(h) = 0.
-1, 2
Factor -1/3*t**2 + 1/3*t + 2.
-(t - 3)*(t + 2)/3
Let x(u) be the second derivative of -1/6*u**3 - 1/24*u**4 + 0 - u - 1/4*u**2. Factor x(t).
-(t + 1)**2/2
Let x(r) = -r**3 - r**2 + 2*r - 2. Let g = 3 - 2. Let z(m) = m**3 - m + 1. Let j(i) = g*x(i) + 2*z(i). What is d in j(d) = 0?
0, 1
Let i(d) be the first derivative of 0*d - 2 + 1/15*d**3 + 1/10*d**2. Let i(q) = 0. What is q?
-1, 0
Let k(l) be the first derivative of 0*l**3 + 1/10*l**5 - 4 - 1/4*l**4 - 1/2*l + 1/2*l**2. Factor k(w).
(w - 1)**3*(w + 1)/2
Suppose 4*x - 14 = -7*u + 2*u, 4*x - 3*u = 30. Suppose -4*a + x = j - 3*j, j + 3 = -a. Factor -1/3*f**2 + 1/3*f**4 - 1/3*f**5 + 1/3*f**3 + a*f + 0.
-f**2*(f - 1)**2*(f + 1)/3
Let n(w) be the first derivative of -w**4/4 + w**2/2 - 3. What is s in n(s) = 0?
-1, 0, 1
Let l(g) be the first derivative of 3*g**4/4 - g**3 - 3*g**2 + 3. Factor l(q).
3*q*(q - 2)*(q + 1)
Let v(b) = -2*b - 22. Let d be v(-12). Factor 1 + 121/4*q**d + 11*q.
(11*q + 2)**2/4
Let x be (45/(-30))/((-1)/2). Factor -8 - 2*a + 14*a - 5*a**3 - a**x + 2*a**3.
-4*(a - 1)**2*(a + 2)
Let i be 3/3 - 9/11. Solve 4/11 - 2/11*g**2 - i*g = 0.
-2, 1
Let q(y) = -y**3 + 0*y - 1 + y**2 - 2*y**2 + 0*y. Let o(r) = -4*r**3 - 5*r**2 - r - 5. Let f(d) = o(d) - 5*q(d). Solve f(s) = 0.
-1, 0, 1
Solve 2/3*b + 0 - 1/3*b**2 = 0 for b.
0, 2
Let c(l) be the first derivative of -2*l**2 + 1/36*l**4 + 1/180*l**5 + 0*l - 1 + 1/18*l**3. Let s(v) be the second derivative of c(v). Factor s(h).
(h + 1)**2/3
Let p(g) be the third derivative of -g**7/140 + g**6/20 - g**5/8 + g**4/8 + 9*g**2. Suppose p(h) = 0. Calculate h.
0, 1, 2
Let o(b) be the second derivative of b**7/119 + 11*b**6/255 + 7*b**5/85 + b**4/17 - b**3/51 - b**2/17 + 6*b. Factor o(g).
2*(g + 1)**4*(3*g - 1)/17
Factor 1/5 - 1/5*c**2 + 0*c.
-(c - 1)*(c + 1)/5
Let c(a) be the first derivative of -4*a**3/3 + 8*a**2 - 12*a + 21. Factor c(v).
-4*(v - 3)*(v - 1)
Solve -4*u - 1/4*u**4 - 5/4 - 9/2*u**2 - 2*u**3 = 0.
-5, -1
Let q be 1/14 + (-130)/(-91). Factor 3*g**2 + 0 + 3/2*g + q*g**3.
3*g*(g + 1)**2/2
What is g in 4*g**2 - 2*g**2 + 4*g + 3 + 3 - 4 = 0?
-1
Let o(d) = d**4 + d**3 + d**2 + d - 1. Let f(k) = 10*k**4 + 9*k**3 + 11*k**2 + 11*k - 11. Let n(t) = 4*f(t) - 44*o(t). Factor n(r).
-4*r**3*(r + 2)
Suppose y - 2 = m - 3, 2*m = -5*y + 9. Suppose 0*f - m = -f. Let -2*i**2 + i**2 + 0*i**f - i = 0. Calculate i.
-1, 0
Let b be 0 + -4 + 2 + 161/69. Factor -1/3*d**3 + b - 1/3*d**2 + 1/3*d.
-(d - 1)*(d + 1)**2/3
Let o(i) be the second derivative of -i**7/11340 + i**6/1620 - i**5/540 - i**4/4 + 2*i. Let f(h) be the third derivative of o(h). Let f(g) = 0. What is g?
1
Let r(j) be the third derivative of 1/84*j**4 + 0*j**3 + 0 - 1/735*j**7 + 3*j**2 + 0*j + 1/210*j**5 - 1/420*j**6. Factor r(m).
-2*m*(m - 1)*(m + 1)**2/7
Factor 12/5*b**2 + 6/5 - 27/5*b.
3*(b - 2)*(4*b - 1)/5
Suppose 29 = s + 5*g, -4*s = s - 5*g + 5. Let u(v) be the first derivative of 1 + 0*v**2 + 0*v - 2/3*v**3 + 1/2*v**s. Find m such that u(m) = 0.
0, 1
Suppose 0 = 4*z + 2*q - 7*q + 10, 0 = q - 2. Let k(t) be the second derivative of z*t**2 + 0 - 1/6*t**4 + 3*t + 1/15*t**3 + 2/25*t**5. Factor k(m).
2*m*(m - 1)*(4*m - 1)/5
Let l(o) be the third derivative of -o**8/84 - 2*o**7/15 - o**6/2 - 3*o**5/5 - 21*o**2. What is p in l(p) = 0?
-3, -1, 0
Let r = 1/8 - -1/8. Factor 0*m**2 + r*m**3 - 1/4*m + 0.
m*(m - 1)*(m + 1)/4
Let m(y) = 5*y**5 - 12*y**4 + 10*y**3 - y + 1. Let f be (5 + -1)/(10/(-5)). Let s(a) = a**5 - a**4 + a**3 + a**2 + 1. Let k(u) = f*m(u) + 2*s(u). Factor k(b).
-2*b*(b - 1)**3*(4*b + 1)
Let m(r) be the first derivative of r**8/672 + r**7/420 - r**6/120 - r**2 - 5. Let o(h) be the second derivative of m(h). Factor o(y).
y**3*(y - 1)*(y + 2)/2
Suppose -3*n - 9 = -n - 3*t, 5*n = 5*t - 15. Factor n + 2/3*k + 2/3*k**4 - 2/3*k**3 - 2/3*k**2.
2*k*(k - 1)**2*(k + 1)/3
Factor 1/5*q - 1/5*q**2 + 2/5.
-(q - 2)*(q + 1)/5
Let j(g) = -7 + 5*g**2 - 6*g**2 - 3*g**3 - 3*g**2. Let t(a) = a**3 + a**2 + 2. Let i be ((-4)/(-6))/((-1)/(-3)). Let x(z) = i*j(z) + 7*t(z). Factor x(p).
p**2*(p - 1)
Factor -2 - 2 - n**3 + n + 40*n**2 - 36*n**2.
-(n - 4)*(n - 1)*(n + 1)
Let l(s) = -s**3 + 3*s**2 + 3*s - 3. Let w = 24 - 14. Let n = -14 + w. Let h(z) = -z**3 + 4*z**2 + 4*z - 4. Let v(x) = n*h(x) + 6*l(x). Factor v(t).
-2*(t - 1)**2*(t + 1)
Let m(i) be the first derivative of i**3 - 3*i**2/2 + 5. Let m(u) = 0. Calculate u.
0, 1
Let w = -1 - -7. Suppose 5*s + a = 0, -a + 24 = -s - w*a. Let r(z) = -z**2 - 8*z - 2. Let m(o) = -o. Let p(i) = s*r(i) - 5*m(i). What is v in p(v) = 0?
-2, -1
Let n(r) be the second derivative of -1/5*r**5 + 7/12*r**4 - 1/2*r**2 + r + 0 - 1/3*r**3. Factor n(w).
-(w - 1)**2*(4*w + 1)
Let t(r) = r**2. Let g = 3 + -2. Let j = 0 - g. Let c(i) = i - 1. Let u(m) = j*t(m) + 4*c(m). Determine k, given that u(k) = 0.
2
Let y = -5835/91 - -444/7. Let r = 49/52 + y. Find w such that 1/4 + 3/4*w**2 + r*w**3 + 3/4*w = 0.
-1
Let t(m) be the third derivative of -m**8/784 + m**6/140 - m**4/56 - 6*m**2. Find p such that t(p) = 0.
-1, 0, 1
Suppose -g + 3*v = 9, 5*v = 3*g - 2*g + 17. Factor 0 + 1/3*r**g + 5/6*r**2 + 1/3*r.
r*(r + 2)*(2*r + 1)/6
Suppose 0 = 5*d + 2*y + 3*y - 35, -2*d = -5*y. Let p = d - 3. Let 2 + 4*c + 0*c + 0*c**2 + 2*c**p = 0. What is c?
-1
Find r such that 2/3 + 8/9*r + 2/9*r**2 = 0.
-3, -1
Let y(a) be the second derivative of 2*a**7/189 + 8*a**6/135 + a**5/45 - 14*a**4/27 - 40*a**3/27 - 16*a**2/9 - 4*a. Suppose y(q) = 0. Calculate q.
-2, -1, 2
Let y(c) be the third derivative of c**9/37800 - c**8/16800 - c**7/6300 + c**6/1800 + c**4/3 + 11*c**2. Let j(h) be the second derivative of y(h). Factor j(a).
2*a*(a - 1)**2*(a + 1)/5
Let y be (-2)/4*(-3)/162. Let a(t) be the third derivative of 0*t - 1/27*t**3 - 1/540*t**6 + 0 + 1/270*t**5 - 2*t**2 + y*t**4. Solve a(s) = 0 for s.
-1, 1
Let g(b) be the first derivative of 0*b**3 - 5 + 0*b + 2/45*b**5 + 0*b**2 - 1/18*b**4. Factor g(u).
2*u**3*(u - 1)/9
Factor 1/4*a**3 - 1/4 + 1/4*a**2 - 1/4*a.
(a - 1)*(a + 1)**2/4
Suppose 2*b**4 + 81*b + 4*b**2 - 24*b**5 - 81*b + 18*b**3 = 0. What is b?
-2/3, -1/4, 0, 1
Let v(h) = -h**3 - 5*h**2 + 4*h + 2. Let x(u) = -5*u**3 - 21*u**2 + 17*u + 9. Let l(y) = 18*v(y) - 4*x(y). Factor l(k).
2*k*(k - 2)*(k - 1)
Let m(v) be the first derivative of -v**5/30 + v**3/3 + 2*v**2/3 - 2*v + 3. Let a(h) be the first derivative of m(h). Let a(l) = 0. Calculate l.
-1, 2
Solve -4/3*b**3 + 10/3*b**4 + 0 - 10/3*b**2 + 4/3*b = 0.
-1, 0, 2/5, 1
Let k be 2/(1/((-1)/(-10))). Let q be (-7)/(-15) + (-24)/(-180). Solve -d**3 + d - k*d**2 + q*d**4 - 2/5 = 0.
-1, 2/3, 1
Let r(d) be the first derivative of d**6/24 - 3*d**5/20 + d**4/8 + d**3/6 - 3*d**2/8 + d/4 - 14. Suppose r(i) = 0. Calculate i.
-1, 1
Suppose u + u = 2. Factor u - 3*i + 7*i - i + i**2 - i.
(i + 1)**2
Let b(j) be the second derivative of j**4/42 - 2*j**3/21 + j**2/7 - 5*j. Let b(h) = 0. What is h?
1
Solve 1/2*f + 1/4*f**2 - 3/4 = 0.
-3, 1
Factor -2*m + 6 - 2*m**2 + 5*m - m - 2.
-2*(m - 2)*(m + 1)
Let r(u) be the third derivative of -4*u**2 + 0 - 7/48*u**4 + 7/240*u**6 - 1/40*u**5 + 0*u + 1/84*u**7 - 1/6*u**3. Let r(w) = 0. Calculate w.
-1, -2/5, 1
Let q(y) be the first derivative of y**4/18 + 8*y**3/27 + 5*y**2/9 + 4*y/9 + 2. Factor q(w).
2*(w + 1)**2*(w + 2)/9
Let a(x) be the third derivative of x**5/420 + x**4/168 - x**3/21 - 26*x**2. Determine s, given that a(s) = 0.
-2, 1
Let n = -15 - -29. Let o = -5 + n. Factor 3*a + 2*a**4 - o*a**2 - a**3 + 6*a**3 + 4*a**3 - 5*a**4.
-3*a*