ivative of -1/8*y**4 + 0*y**2 - 1/5*y**5 - 1 - 1/12*y**6 + 0*y + 0*y**3. Factor x(h).
-h**3*(h + 1)**2/2
Let i be (1/(-4))/((-3)/132). Suppose -5*m = 4*l - 2*m, -2*m - i = -l. Factor -2/3*u**l + 0 - 1/3*u**2 - 1/3*u**4 + 0*u.
-u**2*(u + 1)**2/3
Let r = -20 + 23. Find t such that 0*t + 0 + 1/4*t**r - 1/4*t**2 = 0.
0, 1
Let i = 40 + -37. Let v(q) be the second derivative of -q**2 + 0 - 1/6*q**4 - 2/3*q**3 - i*q. Find x, given that v(x) = 0.
-1
Let o be (6/35)/((-6)/(-10)). What is p in -10/7*p - 8/7*p**2 - 4/7 - o*p**3 = 0?
-2, -1
Let a(k) be the third derivative of k**6/24 - 11*k**5/6 - 12*k**2. Factor a(c).
5*c**2*(c - 22)
Let k(h) = -h**2 - 5*h - 6. Let s be k(-2). Let n(w) be the second derivative of 0*w**4 - w + 0*w**3 + s*w**2 + 0 - 1/80*w**5. Factor n(t).
-t**3/4
Let q(w) be the second derivative of 0 + 1/2*w**3 + 0*w**2 - 3/20*w**5 + 0*w**4 + 2*w. Determine z, given that q(z) = 0.
-1, 0, 1
Let w(c) be the first derivative of -3*c**5/25 - 2*c**4/5 + 2*c**3/5 + 4*c**2/5 - 3*c/5 - 10. Solve w(z) = 0.
-3, -1, 1/3, 1
Let p be 0/(-1) - (-3 - 2). Let q = p - 3. Factor 0 - 2/5*k**q + 0*k.
-2*k**2/5
Factor 5*t**3 + 8*t**2 - 5*t**2 - 2*t**3.
3*t**2*(t + 1)
Let j(o) be the first derivative of 3159/10*o**5 - 28/3*o**3 - 2 - 1701/4*o**6 - 8*o - 36*o**2 + 270*o**4. Solve j(v) = 0.
-2/9, 2/7, 1
Let g(z) be the second derivative of z**2 + 1/240*z**6 - 1/12*z**3 - 1/40*z**5 + 1/16*z**4 + 0 - z. Let c(v) be the first derivative of g(v). Factor c(a).
(a - 1)**3/2
Let o(y) be the second derivative of -y**7/630 + y**5/90 - y**3/18 + 2*y**2 + 3*y. Let t(n) be the first derivative of o(n). Factor t(x).
-(x - 1)**2*(x + 1)**2/3
Let v(q) = q**2 + 2*q + 9. Let y be v(7). Let k be 16/y*(3 + -1). Find j, given that -k*j**2 + 0 + 2/9*j + 2/9*j**3 = 0.
0, 1
Let c(p) be the second derivative of -4*p - 1/10*p**5 + 1/25*p**6 + 1/15*p**4 + 0*p**3 + 0*p**2 + 0. Factor c(m).
2*m**2*(m - 1)*(3*m - 2)/5
Factor 1/4*m**5 + m**4 + 1/4*m + m**2 + 0 + 3/2*m**3.
m*(m + 1)**4/4
Determine l so that 840*l**3 + 756*l**4 + 46*l**2 + 500 + 1248*l**3 + 108*l**5 + 1900*l + 2794*l**2 = 0.
-5/3, -1
Let g(r) = -r + 11. Let m be g(9). Factor x**m + x**3 - 2*x**3 + 0*x**3.
-x**2*(x - 1)
Let l(r) be the first derivative of 12*r**5/5 + 13*r**4 + 44*r**3/3 - 10*r**2 - 24*r + 5. Determine w, given that l(w) = 0.
-3, -1, 2/3
Let k(c) be the first derivative of 7 + 1/24*c**6 + 1/8*c**2 - 1/5*c**5 + 0*c + 3/8*c**4 - 1/3*c**3. Factor k(a).
a*(a - 1)**4/4
Let d(b) be the first derivative of -2*b**3/3 + 3*b**2 + 13. Factor d(x).
-2*x*(x - 3)
Let x(n) = -n**3 + 17*n**2 + 3*n - 49. Let v be x(17). Factor -5/2*j**v + j + 0 + 5/2*j**4 - j**3.
j*(j - 1)*(j + 1)*(5*j - 2)/2
Let b(f) be the third derivative of -f**7/1470 + f**6/420 - f**4/84 + f**3/42 - 2*f**2. Factor b(s).
-(s - 1)**3*(s + 1)/7
Let t(i) be the second derivative of i**6/150 - 9*i**5/100 - 11*i**4/60 + 3*i**3/10 + i**2 - 35*i. Factor t(h).
(h - 10)*(h - 1)*(h + 1)**2/5
Let f(t) be the first derivative of t**6/60 - t**4/12 - 3*t**2/2 - 2. Let a(k) be the second derivative of f(k). Factor a(r).
2*r*(r - 1)*(r + 1)
Factor 32*j**2 + 4*j**5 + 24*j**4 - 6*j**5 + 4*j**5 - 48*j**3 - 6*j**5.
-4*j**2*(j - 2)**3
Let f(x) be the second derivative of -2/45*x**5 + 5/27*x**3 - 1/189*x**7 + 2*x + 4/135*x**6 - 1/27*x**4 - 2/9*x**2 + 0. Determine o, given that f(o) = 0.
-1, 1, 2
Let p(b) = 17*b**3 + 45*b**2 + 13*b + 3. Let z(r) = -205*r**3 - 540*r**2 - 155*r - 35. Let g(l) = -35*p(l) - 3*z(l). Determine m, given that g(m) = 0.
-2, -1/4, 0
Let i be 42/20 + (-24)/16. What is u in 0 + 6/5*u**2 + 3/5*u**3 + i*u = 0?
-1, 0
Let m(b) = b**3 - b**2 - 3*b + 1. Let n be m(2). Let x = 6 + n. Factor 0 + 1/4*o**3 + 0*o**4 - 1/4*o**x + 0*o**2 + 0*o.
-o**3*(o - 1)*(o + 1)/4
Suppose 3*i - 4*i + 6 = 0. Let d = i + -1. Factor 3*h**3 - d*h**2 + 6*h**4 - h**4 - h**4 - 3*h + 1.
(h - 1)*(h + 1)**2*(4*h - 1)
Let p(g) be the first derivative of 1/10*g**2 - 2/15*g**3 + 0*g + 0*g**4 + 2/25*g**5 - 1/30*g**6 + 2. Factor p(q).
-q*(q - 1)**3*(q + 1)/5
Let i(n) = 2*n**2 + 11*n + 13. Let c(a) = -a**2 - 5*a - 6. Let o(l) = -13*c(l) - 6*i(l). Suppose o(y) = 0. Calculate y.
0, 1
Factor -2/5*y + 2/5 - 2/5*y**2 + 2/5*y**3.
2*(y - 1)**2*(y + 1)/5
Let u(t) = t**3 - t**2 - 2*t + 3. Let q be u(2). Factor -4 + 9*f**2 + 2*f + f**2 + 7*f**q - 3*f**3.
2*(f + 1)*(f + 2)*(2*f - 1)
Let j = -2 + 7. Suppose -j*g = -35 + 10. Solve 1/3*y**g + 0 + 0*y**2 + 0*y**4 + 0*y + 0*y**3 = 0 for y.
0
Suppose 4*l - 11 = 5. Let o(f) be the first derivative of 0*f + 4/35*f**5 + 0*f**2 - 4/21*f**3 - 3 - 1/14*f**l + 1/21*f**6. Suppose o(w) = 0. What is w?
-2, -1, 0, 1
Factor -72*j**3 - j**2 + 73*j**3 + 3*j**2.
j**2*(j + 2)
Let b(p) = 4*p**2 - 15*p - 2. Let k be ((-30)/(-5))/((-2)/1). Let q(t) = t. Let d(h) = k*b(h) - 24*q(h). Factor d(y).
-3*(y - 2)*(4*y + 1)
Let w(s) be the first derivative of -2*s**5/15 - 2*s**4/3 - 8*s**3/9 + 45. Factor w(c).
-2*c**2*(c + 2)**2/3
Solve 2*r - 8*r**3 + 12*r**3 - 1 - 6*r**3 + 0*r**4 + r**4 = 0.
-1, 1
Let j(l) be the third derivative of -l**7/210 + l**6/30 - l**5/10 + l**4/6 - l**3/6 - 21*l**2. Determine o so that j(o) = 0.
1
Let t = 7 - 5. Let f(s) = 7*s**t + 2*s + s + 3*s. Let v(x) = -13*x**2 - 11*x. Let w(g) = -7*f(g) - 4*v(g). Factor w(n).
n*(3*n + 2)
Let u be 56/48*3/14. Let z(a) be the first derivative of 1/8*a**4 - u*a**2 + 1/6*a**3 - 1 - 1/2*a. Solve z(g) = 0 for g.
-1, 1
Factor -2/3*t + 1/3*t**2 - 1.
(t - 3)*(t + 1)/3
Let t(q) = q**2 + 6*q - 5. Let p be t(-7). Factor -2/11*s**3 + 2/11*s + 0 - 2/11*s**p + 2/11*s**4.
2*s*(s - 1)**2*(s + 1)/11
Let b(p) be the third derivative of p**7/35 + 3*p**6/40 + p**5/20 - 20*p**2. Factor b(a).
3*a**2*(a + 1)*(2*a + 1)
Let t(v) be the second derivative of v**6/300 - v**5/150 - v**4/60 + v**3/15 - 3*v**2/2 + v. Let r(c) be the first derivative of t(c). Factor r(o).
2*(o - 1)**2*(o + 1)/5
Let l(f) = 4*f**2 - 6*f + 2. Let m(r) = -4*r**2 + 5*r - 1. Let q(c) = -5*l(c) - 6*m(c). Determine v, given that q(v) = 0.
-1, 1
Let n(m) be the third derivative of -m**8/504 + m**6/90 - m**4/36 + 25*m**2. Factor n(g).
-2*g*(g - 1)**2*(g + 1)**2/3
Let k = 2343 + -11662/5. Let r = -9 + k. Suppose -r*y**4 + 12/5*y**3 + 2/5*y**5 + 0 - 8/5*y**2 + 2/5*y = 0. Calculate y.
0, 1
Let v(h) be the third derivative of -h**7/945 - h**6/180 - h**5/135 - 4*h**2. Determine c, given that v(c) = 0.
-2, -1, 0
Suppose -10 = -4*i + 2*s, -3*s + 0*s = -3. Let a(v) be the first derivative of -2 - 1/5*v**2 + 2/5*v + 1/10*v**4 - 2/15*v**i. Let a(t) = 0. Calculate t.
-1, 1
Let d(t) be the first derivative of -3/8*t**2 - 1/12*t**3 + 1/2*t + 8 - 1/20*t**5 + 3/16*t**4. Let d(i) = 0. What is i?
-1, 1, 2
Factor 0 - 1/4*w**4 + 1/4*w**2 + 1/2*w - 1/2*w**3.
-w*(w - 1)*(w + 1)*(w + 2)/4
Let u = -12 - -14. Factor -2*n**3 + n**3 - n**4 + u*n**3 + n**3.
-n**3*(n - 2)
Let 14*b - 7*b**2 + 6*b + 5*b**2 + 7*b**2 = 0. Calculate b.
-4, 0
Let p(a) be the first derivative of 2*a**3/27 + a**2/3 + 4*a/9 - 2. Determine o, given that p(o) = 0.
-2, -1
Let u(s) be the third derivative of -s**6/40 - s**5/5 - 5*s**4/8 - s**3 - 10*s**2. Determine v, given that u(v) = 0.
-2, -1
Let h(i) be the second derivative of -2*i**7/273 - i**6/195 + 3*i**5/65 + 7*i**4/78 + 2*i**3/39 - 5*i. Suppose h(j) = 0. Calculate j.
-1, -1/2, 0, 2
Factor -4/3*y**4 + 0*y**3 + 2/3*y**5 - 2/3*y + 4/3*y**2 + 0.
2*y*(y - 1)**3*(y + 1)/3
Let y(f) = -f**2 - 11*f - 8. Let m be y(-10). Suppose 4*u = 2*c - c + 26, 0 = -u - 2*c + m. Solve -3*p**4 + u*p - 33 + 9*p**5 - 15*p**3 + 3*p**2 + 33 = 0 for p.
-1, -2/3, 0, 1
Let 18/5*u**3 - 24/5*u**2 - 6/5*u**5 + 4/5*u**4 + 8/5*u + 0 = 0. What is u?
-2, 0, 2/3, 1
Let g be 52/24 + (-15)/18. Find r, given that -g + 2*r + 10/3*r**2 = 0.
-1, 2/5
Suppose 0 = 3*x + x. Suppose 4*f + 5*t + 8 + 5 = 0, x = 5*t + 25. Find m such that -6*m**3 + 3*m**2 - m**3 + 4*m**f - m + m**4 = 0.
0, 1
Let r(f) be the first derivative of -4*f**3/3 + 6*f**2 + 16*f - 2. What is z in r(z) = 0?
-1, 4
Suppose -j + 5 = 2. Let a(z) be the first derivative of 0*z + 0*z**2 - 1/3*z**j + 2. Solve a(r) = 0 for r.
0
Let u(x) be the first derivative of x**5/30 - x**4/12 + 3*x**2/2 + 4. Let w(b) be the second derivative of u(b). Find m such that w(m) = 0.
0, 1
Let i(p) be the first derivative of -p**7/140 + p**6/36 - p**5/60 - p**4/12 + 2*p**3 + 5. Let r(k) 