, 1
Let s(y) be the first derivative of -2*y**5/5 - y**4 + 2*y**3 + 4*y**2 - 8*y - 6. Determine i so that s(i) = 0.
-2, 1
Suppose 19 + 6 = -5*f, -2*z = -4*f + 20. Let l be (z/(-25))/((-2)/(-10)). Suppose 2*v + 0*v**l - v**3 - v + v**2 - v**4 = 0. What is v?
-1, 0, 1
Let l = 3 - 2. Let i(k) be the first derivative of 2/3*k**3 - 1/2*k**4 + l + k**2 - 2/5*k**5 + 0*k. Factor i(v).
-2*v*(v - 1)*(v + 1)**2
Let j = 1392 + -250559/180. Let g(y) be the third derivative of 0*y + 0 + j*y**5 + 0*y**3 - 1/72*y**4 + y**2. Find r such that g(r) = 0.
0, 1
Suppose 5*o + 2*n - 7 = 0, -9 = -4*o + 3*n + 15. Let r(y) be the first derivative of -3 + 5*y**2 - 4*y + 14/3*y**o. Factor r(c).
2*(c + 1)*(7*c - 2)
Let 1/6*n**4 + 0*n**2 + 0 + 0*n + 1/6*n**3 = 0. Calculate n.
-1, 0
Let y = 3 + -3. Suppose y*f - 2 + 2 + f**2 + f = 0. Calculate f.
-1, 0
Factor 16*a**3 + 69*a**4 - 21*a**4 - 36*a**4 + 4*a**2 - 24*a**4 - 18*a + 8 + 2*a**5.
2*(a - 4)*(a - 1)**3*(a + 1)
Factor -1/9*f**4 + 1/9*f**2 + 2/9*f**3 - 2/9*f + 0.
-f*(f - 2)*(f - 1)*(f + 1)/9
Let a(j) = -7*j**4 + 13*j**5 + 6 + 7*j - 6*j**3 + 0*j**4 - 6. Let i(l) = -4*l**5 + 2*l**4 + 2*l**3 - 2*l. Let b(v) = 2*a(v) + 7*i(v). Factor b(h).
-2*h**3*(h - 1)*(h + 1)
Let a = 55/8 - 51/8. Let o be ((-3)/2)/(6/(-8)). Find i, given that -1/2*i**o - a + i = 0.
1
Let k(l) be the second derivative of -2*l**7/105 - l**6/30 - l**5/40 - l**4/2 - 5*l. Let w(v) be the third derivative of k(v). What is i in w(i) = 0?
-1/4
Let d = 5 - 3. Let a(f) be the third derivative of 1/30*f**5 - 1/12*f**4 - f**d + 0*f + 0*f**3 + 0. Factor a(l).
2*l*(l - 1)
Let p(a) be the third derivative of -2*a**2 + 1/140*a**7 + 0*a**6 + 0*a - 1/448*a**8 + 0 - 1/40*a**5 + 0*a**3 + 1/32*a**4. What is b in p(b) = 0?
-1, 0, 1
Factor 5*w**2 - 5 - 1/2*w**3 + 1/2*w.
-(w - 10)*(w - 1)*(w + 1)/2
What is b in 8*b**3 - b**4 + 12 - 2*b**2 - 2*b**2 + 6 + 3*b**4 - 24*b = 0?
-3, 1
Suppose -5*s - 5 = -0*s. Let d = s - -3. Factor -u**4 - u**2 - 3*u**3 + 3*u**3 + d*u**3.
-u**2*(u - 1)**2
Let p(u) = -3*u - 4. Let k be p(-3). Factor 2*b**2 + 4*b**2 - k*b**2.
b**2
Determine p so that -1/6*p**3 + 1/6*p - 1/6 + 1/6*p**2 = 0.
-1, 1
Let x(h) be the first derivative of h**6/660 - h**4/132 - h**2 - 2. Let p(n) be the second derivative of x(n). Find b such that p(b) = 0.
-1, 0, 1
Let y(x) be the first derivative of 1/20*x**5 - 1 - 3/2*x**2 + 0*x - 1/8*x**4 + 1/6*x**3 - 1/120*x**6. Let t(r) be the second derivative of y(r). Factor t(f).
-(f - 1)**3
Let j = 73/252 - 5/28. Let t(q) be the first derivative of -2 - 2/3*q - j*q**3 + 1/2*q**2. Factor t(r).
-(r - 2)*(r - 1)/3
Suppose 4*m = -4*v + 3*m + 34, -3*v + 16 = -4*m. Let u be (3*2)/((-2)/(-1)). Suppose 14*i**u + 0*i - 2*i - 3*i**2 - v*i**4 - i**2 = 0. What is i?
-1/4, 0, 1
Let o(r) be the first derivative of -r**3/3 + 3*r**2/2 - 2*r + 20. Factor o(k).
-(k - 2)*(k - 1)
Factor -2/5*l + 1/5*l**2 - 8/5.
(l - 4)*(l + 2)/5
Solve 2*w - w**3 - 10*w + 6*w**2 + 2 - 2*w**2 + 3*w = 0 for w.
1, 2
Suppose 3*c - 3 = -h - 0, -2 = 2*c + 2*h. Let -n**3 + 0 + 2*n**3 + 3*n - c*n**3 + 2 = 0. What is n?
-1, 2
Let f(z) = 13*z**3 + z**2 - 2*z + 1. Let h be f(1). Suppose 2*a + 4*s = 0, 5*a + 2*s - h - 3 = 0. Factor 1/2*u**3 - 1/4*u**a + 0*u**2 - 1/2*u + 1/4.
-(u - 1)**3*(u + 1)/4
Let g(p) be the third derivative of p**7/1260 - p**6/360 - p**5/30 + 7*p**4/24 + 8*p**2. Let x(v) be the second derivative of g(v). What is k in x(k) = 0?
-1, 2
Suppose -9*h = -h - 40. Let q(m) be the first derivative of -2 - 6*m**2 - 4*m - 5/3*m**3 + 9/5*m**h + 3*m**4. Determine y, given that q(y) = 0.
-1, -2/3, 1
Let b(v) be the first derivative of 2*v**3/69 + 3*v**2/23 - 8*v/23 + 10. Determine z, given that b(z) = 0.
-4, 1
Let h(q) = 4*q**2 + 12*q + 11. Let b(p) = 1. Let m(y) = 3*b(y) - h(y). Suppose m(k) = 0. Calculate k.
-2, -1
Let c(v) = 3*v**2 - 19*v. Let s(n) = n. Let i(q) = c(q) + s(q). Factor i(y).
3*y*(y - 6)
Let l = 226 - 1129/5. Factor -1/5*u + 1/5 - l*u**2 + 1/5*u**3.
(u - 1)**2*(u + 1)/5
Let r(u) be the second derivative of -u**6/90 + u**4/12 + u**3/9 - 17*u. Let r(l) = 0. Calculate l.
-1, 0, 2
Factor 722*i**4 - 17*i**3 - 720*i**4 + 42*i**2 - 36*i + i**3.
2*i*(i - 3)**2*(i - 2)
Let u(s) = 4*s + 4. Let y(j) = j**2 - 4*j - 3. Let v(w) = -3*u(w) - 4*y(w). Factor v(k).
-4*k*(k - 1)
Let i(l) = -l + 6. Let a be i(-5). Factor -6 - 2*j**3 + 6*j - 1 + a.
-2*(j - 2)*(j + 1)**2
Let g(f) be the first derivative of -1/9*f**3 + 0*f + 1/15*f**5 + 1/6*f**2 + 5 - 1/12*f**4. Factor g(n).
n*(n - 1)**2*(n + 1)/3
Let n(q) = -q - 16. Let g be n(-21). Factor 8/7*m + 162/7*m**g - 396/7*m**4 + 314/7*m**3 + 0 - 88/7*m**2.
2*m*(m - 1)**2*(9*m - 2)**2/7
Let t = -104 - -1354/13. Factor t*k - 2/13*k**2 - 2/13*k**3 + 2/13.
-2*(k - 1)*(k + 1)**2/13
Let 2*u - 8/5 - 2/5*u**2 = 0. Calculate u.
1, 4
Let d(k) be the third derivative of k**5/180 - k**4/24 + k**3/9 - 6*k**2. Factor d(f).
(f - 2)*(f - 1)/3
Let c(n) be the first derivative of -n**5/25 + n**4/5 - 2*n**3/15 - 2*n**2/5 + 3*n/5 - 55. Determine p, given that c(p) = 0.
-1, 1, 3
Let y(x) = x**2 + 4*x - 8. Let t be y(-6). Suppose 5*h + t*k = 4, 3*h = 2*h + 2*k + 12. Solve 2*a**3 - 10/7*a**h - 2*a + 4/7 + 6/7*a**2 = 0.
-1, 2/5, 1
Let o(i) be the third derivative of -i**7/15120 + i**6/1080 - i**5/180 - 5*i**4/24 - 2*i**2. Let q(n) be the second derivative of o(n). Factor q(c).
-(c - 2)**2/6
Solve -3/2*l**3 - 3*l**2 + 1/2*l**4 + 14*l - 12 = 0.
-3, 2
Let f(v) be the second derivative of -3*v - 1/15*v**3 + 0 + 1/30*v**4 + 0*v**2. Suppose f(d) = 0. Calculate d.
0, 1
Let g(q) be the first derivative of q**8/84 - q**6/15 + q**4/6 - 5*q**2/2 - 3. Let l(a) be the second derivative of g(a). Factor l(v).
4*v*(v - 1)**2*(v + 1)**2
Suppose 4*w - 3 = 2*s + 7, 0 = -w - s + 7. Let k be (-742)/(-693) + w/(-22). Determine c, given that -8/9 + k*c - 2/9*c**2 = 0.
2
Let a(q) be the third derivative of q**7/945 - q**5/270 + 4*q**2. Factor a(m).
2*m**2*(m - 1)*(m + 1)/9
Let y(h) = 2*h**2 - 6*h + 7. Let i be y(2). Let s(k) be the third derivative of 0*k + 0 - 1/60*k**5 - 1/24*k**4 + 1/3*k**i + 3*k**2. Let s(u) = 0. What is u?
-2, 1
Factor 25*y**3 - 14 - 17 - 60*y + 11 - 15*y**2.
5*(y - 2)*(y + 1)*(5*y + 2)
Suppose 4 = -g - 2. Let b(u) = -u**2 - 4*u + 12. Let i be b(g). Factor 2/9*a**4 + i + 0*a + 4/9*a**3 + 2/9*a**2.
2*a**2*(a + 1)**2/9
Let s be (-1 - -3 - 1) + -3. Let u be 3 + (-1)/(s + 3). Factor 0 - 2/3*z + 2/3*z**u.
2*z*(z - 1)/3
Let x(t) = -96*t**2 - 8*t + 88. Let w(r) = r**2 - 1. Let p(c) = 528*w(c) + 6*x(c). Let m(s) = 3*s**2 + 3*s. Let v(b) = -33*m(b) - 2*p(b). Factor v(d).
-3*d*(d + 1)
Let o(h) be the third derivative of h**8/6048 - 2*h**7/2835 + h**6/3240 + h**5/270 - h**4/8 + 4*h**2. Let p(q) be the second derivative of o(q). Solve p(g) = 0.
-2/5, 1
Let n be -1 + -1 - (-44)/11. Factor 3*x + 1/3*x**3 + 0 - 2*x**n.
x*(x - 3)**2/3
Let o(i) be the first derivative of 2*i**2 - 2/3*i**3 + 3 + 0*i. Determine c so that o(c) = 0.
0, 2
Factor 3 - y**3 + 5*y**3 + 8*y**2 - 12*y - 3.
4*y*(y - 1)*(y + 3)
Factor 0*z**3 + 4*z**3 + 125*z - 625 + z**3 - 75*z**2 + 250*z.
5*(z - 5)**3
Suppose 1 = 2*r - r. Let d(m) = -m**2. Let f(p) = -4 - p + 4. Let q(k) = r*f(k) + d(k). Solve q(s) = 0 for s.
-1, 0
Let i(q) = -q**3 - q**2 + q - 1. Let t(v) = 11*v**3 - 27*v**2 + 9*v + 1. Let f(k) = 3*i(k) - t(k). Factor f(x).
-2*(x - 1)**2*(7*x + 2)
Let s(v) = v**4 + 3*v**3 + 5*v**2 + 3*v + 2. Suppose 0 = -2*i + 4 - 8. Let h(d) = -d**2 - d - 1. Let g(u) = i*h(u) - s(u). Factor g(a).
-a*(a + 1)**3
Let d(x) be the first derivative of x**7/84 - x**6/60 - 2*x + 2. Let u(o) be the first derivative of d(o). Factor u(w).
w**4*(w - 1)/2
Suppose 0*c + 3/4*c**3 - 3/4*c**5 - 3/2*c**2 + 3/2*c**4 + 0 = 0. What is c?
-1, 0, 1, 2
Let g(f) = 15*f - 2*f**2 - 34 - f**2 + 4 + 0*f**2. Let t(m) = 3*m**2 - 16*m + 29. Let j = -1 - -4. Let u(l) = j*t(l) + 2*g(l). Find c such that u(c) = 0.
3
Let q = 2243/9 - 249. Factor 2/3*j**3 + 2/9*j + 2/3*j**2 + 0 + q*j**4.
2*j*(j + 1)**3/9
Factor -35*g**5 - 25*g**2 + 4*g**3 + 7*g + 85*g**4 + 13*g - 29*g**3 - 20*g**3.
-5*g*(g - 1)**3*(7*g + 4)
Find i, given that 1/4*i - 1/8*i**2 + 0 = 0.
0, 2
Let k(u) be the third derivative of -u**9/60480 - u**5/20 + 3*u**2. Let l(t) be the third derivative of k(t). Factor l(o).
-o**3
Let r(g) be the first derivative of -g**6/180 - g**5/30 - 2*g**3/3 + 2. Let