
(m - 1)**3*(m + 2)/4
Let x = -15 - -15. Let n(y) be the second derivative of 0*y**2 + 1/50*y**5 + x*y**3 + 0*y**4 - y + 0 - 1/25*y**6. Factor n(t).
-2*t**3*(3*t - 1)/5
Let z(r) be the third derivative of -25*r**8/1512 - 2*r**7/27 - 23*r**6/180 - 14*r**5/135 - r**4/27 + r**2. Determine x so that z(x) = 0.
-1, -2/5, 0
Let h(r) be the second derivative of r**6/45 - 2*r**5/15 - r**4/18 + 4*r**3/9 - 7*r. Factor h(n).
2*n*(n - 4)*(n - 1)*(n + 1)/3
Let o(a) be the first derivative of 2*a**3/3 + 2*a**2/3 - 2*a/3 + 10. Factor o(r).
2*(r + 1)*(3*r - 1)/3
Let f = -634/65 - -132/13. Factor -f*y + 1/5 + 1/5*y**2.
(y - 1)**2/5
Let o(i) be the first derivative of -1 + i + 1/3*i**3 + i**2 - 1/6*i**4 - 1/10*i**5. Let l(x) be the first derivative of o(x). Suppose l(p) = 0. What is p?
-1, 1
Let p(k) = -2*k. Suppose 0 = 4*a - 9*a. Let r be p(a). What is q in 0 + 0*q**2 + 3/5*q**4 + 3/5*q**5 + 0*q + r*q**3 = 0?
-1, 0
Suppose -4/7*q**2 + 8/7*q**4 - 2/7*q**3 + 6/7*q**5 + 0 + 0*q = 0. Calculate q.
-1, 0, 2/3
Let l(k) be the first derivative of -2*k**3/39 + 10*k**2/13 - 18*k/13 - 41. Determine n, given that l(n) = 0.
1, 9
Suppose 8*q + 1 = 17. Let g(s) be the first derivative of -2/45*s**5 - 1/18*s**4 + 0*s**3 + 1 + 0*s + 0*s**q. Determine b, given that g(b) = 0.
-1, 0
Let z(l) be the second derivative of -l**4/18 + 4*l**3/9 - 14*l. Find p, given that z(p) = 0.
0, 4
Let n(w) be the first derivative of -w**3/3 + w + 22. Factor n(h).
-(h - 1)*(h + 1)
Let q be 0/8 - -1*(-1)/(-4). Factor -1/4*u**3 + 0 + q*u - 3/4*u**2 + 3/4*u**4.
u*(u - 1)*(u + 1)*(3*u - 1)/4
Suppose o + 0 - 10 = 0. Let s(g) = 8*g**5 - 6*g**3 + 10*g**2 - 2*g - 10. Let u(i) = -i**5 + i**3 - i**2 + 1. Let v(r) = o*u(r) + s(r). Solve v(x) = 0 for x.
-1, 0, 1
Let l be (2 + -11)*1/3. Let u be l*(-4)/((-24)/(-5)). Let -u*i**3 + 0*i + i**2 + 0 = 0. Calculate i.
0, 2/5
Let f = -9359/60 + 156. Let x(w) be the second derivative of f*w**4 + 0*w**2 + 3*w + 1/30*w**3 + 0. Find m such that x(m) = 0.
-1, 0
Let o(j) be the third derivative of 0 - 5*j**2 - j**3 + 3/8*j**4 + 1/4*j**5 + 0*j. Let o(y) = 0. What is y?
-1, 2/5
Suppose 2*s - s - 7 = 0. Let v = s + -3. Factor -2*y - 2*y**2 - 2*y**2 + 2 + v*y.
-2*(y - 1)*(2*y + 1)
Suppose 104*a**2 + 30*a - 52*a**2 - 49*a**2 = 0. Calculate a.
-10, 0
Factor -2/11*t - 6/11*t**2 + 0 - 2/11*t**4 - 6/11*t**3.
-2*t*(t + 1)**3/11
Let s(w) be the second derivative of -49*w**4/66 + 28*w**3/33 - 4*w**2/11 - 7*w. Let s(c) = 0. Calculate c.
2/7
Find a such that a**2 + 0*a**2 - 2*a**3 + 7*a**3 - 4*a**3 = 0.
-1, 0
Solve -1/5*t**3 - 4/5 + 1/5*t**2 + 4/5*t = 0.
-2, 1, 2
Let l(d) = 42*d**2 - 3*d - 2. Let b be l(-2). Let p = 1208/7 - b. What is k in -p - 2/7*k + 2/7*k**2 = 0?
-1, 2
Suppose -74 = -4*k + 2*k. Factor -81*p + 10*p**2 - 3*p**3 - 82 + 8 - k*p**2 - 7.
-3*(p + 3)**3
Factor 3/2*f - 1/2*f**2 - 1.
-(f - 2)*(f - 1)/2
Suppose p + 1 + 6 = 5*l, -p = -l - 1. Factor 0*o + 2*o**p + 0 - 4/5*o**2.
2*o**2*(5*o - 2)/5
Let n be (0 + 4/(-400))/((-4)/5). Let p(g) be the second derivative of 3*g + 1/24*g**4 + 0*g**2 + n*g**5 + 0 + 1/24*g**3. Suppose p(u) = 0. Calculate u.
-1, 0
Let w be (3 - (2 - 3)) + -1. Let a(m) be the first derivative of 0*m**2 - 1/18*m**4 + 0*m - 2/27*m**w - 2. Solve a(s) = 0 for s.
-1, 0
Solve 9*z**3 - 2*z**2 + 4*z**2 + 6*z**2 - 11*z**3 = 0.
0, 4
Let p(s) = -7*s**2 + 9*s + 1. Let f(x) = -28*x**2 + 36*x + 5. Let v(u) = -6*f(u) + 26*p(u). Factor v(z).
-2*(z - 1)*(7*z - 2)
Let f(g) be the first derivative of -7/2*g**4 + 1 + 4/3*g**3 + 7*g**2 - 4*g. Factor f(s).
-2*(s - 1)*(s + 1)*(7*s - 2)
Let n(i) be the third derivative of i**6/1980 - i**5/660 - i**3/3 + i**2. Let p(w) be the first derivative of n(w). Factor p(f).
2*f*(f - 1)/11
Let v(p) be the second derivative of -p**6/30 - 3*p**5/20 - p**4/12 + p**3/2 + p**2 + p - 21. Factor v(l).
-(l - 1)*(l + 1)**2*(l + 2)
Let t(b) be the third derivative of b**7/315 + b**6/180 - b**5/30 - 5*b**4/36 - 2*b**3/9 - 12*b**2. Factor t(p).
2*(p - 2)*(p + 1)**3/3
Let q(a) be the first derivative of 5*a**4/4 + 25*a**3/3 + 15*a**2/2 - 45*a - 14. Factor q(c).
5*(c - 1)*(c + 3)**2
Let p(k) = 3*k + 8. Let d(u) = u + 3. Let v(i) = -11*d(i) + 4*p(i). Let w be v(4). Factor 2*b**2 + 10/3*b - 2/3*b**4 + 4/3 - 2/3*b**w.
-2*(b - 2)*(b + 1)**3/3
Let b be 9/(-3) + (-4 - 105). Let u be (-4)/14 + (-116)/b. Suppose -3/4*q + 0 + 0*q**2 + u*q**3 = 0. Calculate q.
-1, 0, 1
Let r(p) = 6*p + 3. Let o be r(3). Let z be (o/9 - 3)*-6. Factor v**3 + 3*v**2 + v**z - 2*v**2 - 5*v**3 + 2*v**3.
v**2*(v - 1)**2
Determine f so that 0 + 2/9*f**2 - 34/9*f = 0.
0, 17
Suppose 3*f + 13 = 4. Let a(h) = h + 3. Let s be a(f). Factor 0*u + s + 1/4*u**2.
u**2/4
Let m(f) be the second derivative of 2*f**7/315 - f**6/180 - 3*f**2/2 - 2*f. Let v(g) be the first derivative of m(g). Determine d, given that v(d) = 0.
0, 1/2
Let g = 7 - 3. Factor 2*o**3 + 4*o**2 - 1 + 1 + g*o - o**3.
o*(o + 2)**2
Let l(a) be the third derivative of 5*a**8/336 + a**7/14 - a**6/24 - a**5/4 + 8*a**2. Determine k, given that l(k) = 0.
-3, -1, 0, 1
Let g = -12 - -15. What is j in 20*j**2 - 10 - 25*j**3 + g - 4*j + 7 = 0?
0, 2/5
Determine d so that 3/2*d - 1/2*d**2 + 0 = 0.
0, 3
Suppose -5*q + 28 = 2*v, 3*v + q = -4*q + 32. Let t(z) = -3*z**2 + 2*z + 1. Let d = -3 + 0. Let n(p) = -2*p**2 + p + 1. Let k(i) = d*t(i) + v*n(i). Factor k(h).
(h - 1)**2
Let q(b) = 7*b**3 + 5*b**2 + b. Let a(n) be the first derivative of -7*n**4/2 - 10*n**3/3 - n**2/2 - 3. Let s(y) = -3*a(y) - 5*q(y). What is w in s(w) = 0?
-1, 0, 2/7
Suppose 3/7*a**3 - 1/7*a**2 + 2/7 - 3/7*a - 1/7*a**4 = 0. What is a?
-1, 1, 2
Let t(f) be the first derivative of -f**3/5 - f**2/2 - 2*f/5 - 5. Find q, given that t(q) = 0.
-1, -2/3
Let z = 161 + -1769/11. Find c, given that -4/11*c - 14/11*c**2 + 0 - z*c**3 + 6/11*c**5 + 14/11*c**4 = 0.
-2, -1, -1/3, 0, 1
Let d(j) = 2*j**2 - 6*j + 2. Let z(p) = p**4 + p**2 - 5*p + 2. Let a(o) = 3*d(o) - 4*z(o). Let n(y) = y**4 + y**2 - y. Let r(c) = -a(c) - 2*n(c). Factor r(g).
2*(g - 1)**2*(g + 1)**2
Let j(f) be the first derivative of -1/3*f**3 + 1/8*f**4 + 0*f + 1/10*f**5 + 0*f**2 - 4. Factor j(m).
m**2*(m - 1)*(m + 2)/2
Let g(p) be the second derivative of 7/2*p**3 + 7*p + 9*p**2 + 0 - 3/4*p**4. Factor g(c).
-3*(c - 3)*(3*c + 2)
Factor 10/7*a + 2/7*a**2 - 12/7.
2*(a - 1)*(a + 6)/7
Let y(o) = o + 9. Let i be ((-2)/6)/((-3)/(-63)). Let c be y(i). What is z in 0 + 1/4*z**3 + 0*z**c + 0*z = 0?
0
Factor 1/2 - 1/4*s**2 + 1/4*s.
-(s - 2)*(s + 1)/4
Let r = -12 + 14. What is z in 6*z**3 - r*z**3 - z**4 + 3*z**4 + 2*z**2 = 0?
-1, 0
Let b = -2 + 3. Let d be (b - (3 + 1))/(-1). Solve 53*f + 8 + 70*f**2 + 39*f**d - 9*f - 14*f**3 = 0.
-2, -2/5
Let j(i) be the third derivative of -i**6/200 + i**5/50 + i**4/40 - i**3/5 - 4*i**2. Let j(f) = 0. What is f?
-1, 1, 2
What is i in -2*i + 6*i**2 - 15*i**2 - 6*i**3 + 2*i**4 + 15*i**2 = 0?
0, 1
Let y(f) be the second derivative of -f**4/30 - 2*f**3/15 + 3*f**2/5 + f. Factor y(q).
-2*(q - 1)*(q + 3)/5
Let p(j) be the second derivative of j**7/840 + j**6/180 - j**5/120 - j**4/12 - j**3/2 - j. Let b(u) be the second derivative of p(u). Factor b(w).
(w - 1)*(w + 1)*(w + 2)
Factor 2/3*c + 0 + 10*c**3 + 8/3*c**5 + 26/3*c**4 + 14/3*c**2.
2*c*(c + 1)**3*(4*c + 1)/3
Let j(y) be the first derivative of y**4/20 - 3*y**2/10 - 2*y/5 - 1. Factor j(s).
(s - 2)*(s + 1)**2/5
Let x(w) be the first derivative of -w**4/38 - 2*w**3/19 - 3*w**2/19 - 2*w/19 + 4. Solve x(g) = 0.
-1
Let x be 0 - ((2 - 2) + 3). Let d be 15/(-6)*x/30. Factor -1/4 + d*r**2 + 0*r.
(r - 1)*(r + 1)/4
Let o be 3 + -2 + -2 + 1. Suppose o = 3*i + f - 3*f - 17, f + 26 = 5*i. Suppose -8*v**4 + i*v**3 + 9*v**2 + 9*v**4 + 8*v - v + 2 = 0. What is v?
-2, -1
Let j be (-168)/(-16)*(-2)/(-3). Suppose t + j = 3*b, 4*b - 2*t = 5 + 5. Determine i so that -2/5*i**4 + 0 + 0*i**b + 0*i**3 + 0*i = 0.
0
Determine h, given that 17*h**2 - h**2 - 4*h**4 - 7*h**3 + 2*h**5 + h**3 + 0*h**3 - 8*h = 0.
-2, 0, 1, 2
Let v(q) be the second derivative of -q**7/126 + q**6/18 - 2*q**5/15 + q**4/9 + 11*q. Suppose v(b) = 0. What is b?
0, 1, 2
Let w be -4*3/6 - (-480)/168. Determine l, given that w*l**3 + 24/7*l - 22/7*l**2 - 8/7 = 0.
2/3, 1, 2
Let o(b) = 6*b - 4. Let s be o(4). Let v = s - 17. Factor 2/5*g**5 + 0*g**2 + 0*g + 0*g**v + 2/5*g**4 + 0.
2*g**4*(g + 1)/5
Let t(r) be th