-k**7/2520 - k**6/1080 + k**5/360 + k**4/72 - k**3/6 + 3*k**2. Let m(s) be the first derivative of b(s). Factor m(o).
-(o - 1)*(o + 1)**2/3
Let y = -10 + 19. Let n be (-4)/(3/1 - y). What is v in -1/3 - 1/3*v**2 - n*v = 0?
-1
Let m(n) be the second derivative of 0 - 1/4*n**2 + 1/6*n**4 + 3*n - 1/4*n**3. Factor m(u).
(u - 1)*(4*u + 1)/2
Let k = -1/4 - -1/2. Let a(b) be the first derivative of 1/6*b**3 - 1/4*b**2 + k*b**4 + 1 + 0*b. Factor a(n).
n*(n + 1)*(2*n - 1)/2
Let f(j) be the second derivative of 2*j**6/15 - j**5/5 - j**4 + 2*j**3/3 + 4*j**2 - 3*j. Suppose f(z) = 0. What is z?
-1, 1, 2
Let l be (-2)/(-3 + -1)*2. Let q be (8 - 8)*l/(-3). What is a in 11/5*a**2 - 7/5*a**3 - 4*a**4 - 2/5*a + q = 0?
-1, 0, 1/4, 2/5
Let f be -3 + 234/135 + 10/6. Factor -f*p + 4/5 - 2/5*p**2.
-2*(p - 1)*(p + 2)/5
Let v(t) be the second derivative of t**6/360 - t**5/20 + 3*t**4/8 - 5*t**3/6 + 2*t. Let k(r) be the second derivative of v(r). Factor k(g).
(g - 3)**2
Let u(v) be the third derivative of -v**5/24 + v**4/32 + 17*v**2. Factor u(x).
-x*(10*x - 3)/4
Let r(t) = -t**3 + 4*t**2 + 5*t - 4. Let m(w) = w**2 + 2*w - 1. Let k(b) = -6*m(b) + 3*r(b). Factor k(i).
-3*(i - 2)*(i - 1)*(i + 1)
Let r(g) be the third derivative of -g**5/90 + g**4/36 - 6*g**2. Factor r(o).
-2*o*(o - 1)/3
Factor -2*x**2 + 7*x + 0*x - 3*x + 0 - 2.
-2*(x - 1)**2
Let b be 87/6 - (-2 + -1). Let a = b + -16. Factor -1/4*m - 1/4*m**5 - m**2 - a*m**3 - m**4 + 0.
-m*(m + 1)**4/4
Let p(o) be the second derivative of -o**5/40 - o**4/8 + 2*o**2 - 3*o. Let n(y) be the first derivative of p(y). Find w, given that n(w) = 0.
-2, 0
Let j(c) = -c**3 + 9*c**2 - 12*c + 11. Let t be j(8). Let g be ((-111)/t - 2) + -3. Factor 8/7*s**2 - g + 6/7*s.
2*(s + 1)*(4*s - 1)/7
Let t(p) be the first derivative of 2*p**5/35 + p**4/7 + 2*p**3/21 + 16. Let t(d) = 0. What is d?
-1, 0
Suppose 0*u = 3*u + x - 37, -23 = -2*u - x. Suppose -r - z + u = 4*r, 0 = 2*r + 3*z - 3. Factor 1/5 - 1/5*l - 1/5*l**5 + 2/5*l**r + 1/5*l**4 - 2/5*l**2.
-(l - 1)**3*(l + 1)**2/5
Let n(q) be the first derivative of q**4/4 + 7*q**3/3 + 11*q**2/2 + 5*q - 28. Factor n(s).
(s + 1)**2*(s + 5)
Let t(j) = -j - 11. Let k be t(-10). Let o be (1 - k/(-3))*1. Factor 2*y**2 - o*y**3 + 2/3 - 2*y.
-2*(y - 1)**3/3
Suppose 11*a - 2*a = 27. Factor 2/5*b**a + 0 + 2/5*b + 4/5*b**2.
2*b*(b + 1)**2/5
Suppose g - 2*o = -g + 14, 3*g - 18 = 2*o. Suppose g*k = k. Factor -r**3 + 2*r**3 - 2*r**2 + k*r**2 - 2*r**3.
-r**2*(r + 2)
Suppose -6/7*d**2 - 4/7 + 10/7*d = 0. Calculate d.
2/3, 1
Let h(t) be the second derivative of t**5/20 + t**4/4 + t**3/3 - 14*t. Solve h(l) = 0 for l.
-2, -1, 0
Let c(s) be the first derivative of s**6/132 + s**5/30 + 7*s**4/132 + s**3/33 + s**2 + 4. Let h(z) be the second derivative of c(z). Factor h(w).
2*(w + 1)**2*(5*w + 1)/11
Let n(w) = w**2 - w + 3. Let j(m) = -m**3 + 9*m**2 + 3. Let f be j(9). Let l(x) = -2*x**2 + 2*x - 5. Let o(d) = f*l(d) + 5*n(d). Find b, given that o(b) = 0.
0, 1
Let m(k) be the first derivative of -k**3/9 + 2*k**2/3 - 4*k/3 - 1. Suppose m(z) = 0. Calculate z.
2
Suppose -5*k = 15, 3*j - 6 - 3 = k. Let l be 3 - (3 - (-9)/(-3)). Factor x**4 - x**j + l*x - 3*x.
x**2*(x - 1)*(x + 1)
Factor z**3 + 2*z**2 - 3*z + 3*z + z - 4*z.
z*(z - 1)*(z + 3)
Let g(b) = b**3 + 12*b**2 + b + 16. Let q be g(-12). Factor -6*v**2 + 5*v**3 + 5*v**3 - q*v**3 - 2*v**4 + 2*v.
-2*v*(v - 1)**3
Let p(o) be the first derivative of o**4/14 - 2*o**3/21 + 19. Let p(z) = 0. What is z?
0, 1
Let h(k) be the third derivative of k**7/630 + k**6/72 + 2*k**5/45 + k**4/18 - 51*k**2. What is q in h(q) = 0?
-2, -1, 0
Let l(v) be the first derivative of 2*v**5/55 - 3*v**4/11 + 26*v**3/33 - 12*v**2/11 + 8*v/11 + 16. Factor l(a).
2*(a - 2)**2*(a - 1)**2/11
Let u be 1*(-3)/12*-1. Factor 0 + 1/4*x - u*x**2.
-x*(x - 1)/4
Let i = -42 + 169/4. Let 1/4*h**4 + 0 + 0*h - i*h**2 - 1/4*h**5 + 1/4*h**3 = 0. What is h?
-1, 0, 1
Let j(f) = -f + 8. Let m be j(6). Let w = 3/65 + 97/715. Factor -2/11*o**5 + 0*o**3 - 4/11*o**m + 4/11*o**4 + 0 + w*o.
-2*o*(o - 1)**3*(o + 1)/11
Let m = -7 + 10. Suppose 0 = 3*x + m*o - 9, 2*x = 6*x - 4*o - 12. Factor -b**5 - b**3 - b**4 - 4*b**4 + 0*b**4 + x*b**4.
-b**3*(b + 1)**2
Let d(c) = c**2 - 11*c + 6. Let b be d(11). Let h be (1/(9/b))/2. Determine y so that -1/3*y**3 + 0 - h*y + 2/3*y**2 = 0.
0, 1
Find j, given that -10/11*j - 4/11*j**2 - 2/11 + 28/11*j**3 - 18/11*j**5 + 6/11*j**4 = 0.
-1, -1/3, 1
Let b(h) = -h**2 + 9*h. Let y be b(9). Let a be (-4 + 9)*(-6)/(-10). Factor -1/2*m**2 + 1/2*m**4 + y + 0*m + 0*m**a.
m**2*(m - 1)*(m + 1)/2
Let n(z) be the second derivative of -z**5/10 + z**4/6 - z. Solve n(l) = 0 for l.
0, 1
Let w(g) = 2*g**3 + 2*g**2 - 2*g**2 - g**3. Let m(b) = -21*b**3 + 27*b**2 - 36*b + 12. Let d(h) = m(h) + 15*w(h). Factor d(n).
-3*(n - 2)**2*(2*n - 1)
Let a be 10/(-24) - 14/(-21). Suppose -1/4*b**2 + 0 - a*b = 0. Calculate b.
-1, 0
Let j(y) be the first derivative of 1/12*y**2 + 2 - 1/30*y**5 - 1/24*y**4 + 1/18*y**3 + 0*y. Let j(w) = 0. What is w?
-1, 0, 1
Let 2/5*d - 1/2 + 1/10*d**2 = 0. What is d?
-5, 1
Suppose -r - 2*r + 15 = 0. Suppose 4 = 4*x - 4. Factor b**r + 0*b**4 + 2*b**x - b - 3*b**4 + b**4.
b*(b - 1)**3*(b + 1)
Let x(h) be the second derivative of -1/2*h**2 + 0*h**3 - 1/6*h**4 + 0 + 1/6*h**5 + h. Let p(f) be the first derivative of x(f). Factor p(q).
2*q*(5*q - 2)
Factor 32*c**2 - 6 - 9*c**2 + 22*c**2 - 27*c - 12*c.
3*(c - 1)*(15*c + 2)
Suppose b - 27 = -22. Suppose b*f + 3 = 23. Determine q, given that 1/2*q + 0 + 0*q**3 - q**f - 1/2*q**5 + q**2 = 0.
-1, 0, 1
Let k = 29 + -23. Let s(p) be the third derivative of 0 - 2*p**2 + 2/105*p**k - 1/21*p**3 + 0*p + 1/245*p**7 + 1/35*p**5 + 0*p**4. Find c such that s(c) = 0.
-1, 1/3
Let d(g) = -g**2 - 10*g + 11. Let o be d(-10). Factor -3*a**3 - 4*a + 3*a**2 - a**2 + o*a + 2.
-(a - 2)*(a + 1)*(3*a + 1)
Factor -3/2*c**2 - 1/2 - 2*c.
-(c + 1)*(3*c + 1)/2
Let k be 1 + (-3 - -4) + 15. Factor -70*i**2 - 2 + 18*i**3 + 34*i + k*i**3 - 12*i + 15*i**3.
2*(i - 1)*(5*i - 1)**2
Suppose -p + 3*p = 16. Let o = p - 2. Solve -16*k**5 + 5*k - 2*k**4 + 2*k**2 + 18*k**5 - o*k**3 - k = 0 for k.
-1, 0, 1, 2
Suppose -3*z + 15 = 5*x - 22, 2*x = 5*z - 10. Let w(m) be the first derivative of 4/5*m - z + 2/15*m**3 - 3/5*m**2. Factor w(h).
2*(h - 2)*(h - 1)/5
Let p(l) be the third derivative of 0 - 1/70*l**7 + 1/8*l**6 - l**3 + 7/8*l**4 + 0*l + 5*l**2 - 9/20*l**5. Factor p(a).
-3*(a - 2)*(a - 1)**3
Let u(t) be the second derivative of -t**4/3 + 4*t**3/3 - 7*t. Find n, given that u(n) = 0.
0, 2
Let d(y) = 2*y**2 + y + 1. Let o be d(5). Suppose -o*r - 50*r**3 + 3 - 2*r**5 + 16*r**4 + 54*r**2 + 13 + 22*r**2 = 0. Calculate r.
1, 2
Suppose 2*o**2 + 1090*o - 1105*o + 3*o**2 = 0. What is o?
0, 3
Let m(x) be the first derivative of -3/2*x**2 + 1/4*x**4 - 2*x + 0*x**3 - 1. Suppose m(y) = 0. Calculate y.
-1, 2
Suppose -3*w - 5*t - 2 = -4*w, -2*w + 4*t = -4. Factor 9/5*l + 3/5*l**w + 0.
3*l*(l + 3)/5
Factor j**4 + 25*j - 13*j - 14*j - 2*j**2 + 2*j**3 + j**4.
2*j*(j - 1)*(j + 1)**2
Suppose 4 = h + 1. Suppose p - h = 1. Factor -9*b**2 + 0*b**5 + 4*b**p - 2*b + 5*b**2 + 2*b**5.
2*b*(b - 1)*(b + 1)**3
Suppose 0*v - 2*v - k + 3 = 0, -4*v = 3*k - 5. Factor s**v + 72*s**4 - 73*s**4 + 0*s**2.
-s**2*(s - 1)*(s + 1)
Let s(a) = -a**3 + 2*a**2 + a - 2. Let g be s(2). Factor 2/5*t**3 + g + 6/5*t**2 + 4/5*t.
2*t*(t + 1)*(t + 2)/5
Let o be (-40)/(-16)*32/40. Suppose -8/7*w + 8/7*w**o + 0 - 2/7*w**3 = 0. Calculate w.
0, 2
Suppose -37*b**4 + 50*b**4 + 15*b**3 - 10*b**2 + 12*b**4 = 0. Calculate b.
-1, 0, 2/5
Factor -2*k**3 + 3*k**3 - 4*k**3 - 6*k - 9*k**2.
-3*k*(k + 1)*(k + 2)
Let i(s) be the first derivative of -s**3 - 3*s**2/2 + 6*s - 2. Factor i(x).
-3*(x - 1)*(x + 2)
Let m be ((15/25)/(-3))/(4/(-16)). Factor 0*c - 2/5*c**3 + 2/5*c**4 + 0 - m*c**2.
2*c**2*(c - 2)*(c + 1)/5
Let b(h) be the third derivative of 0*h + 0*h**3 + 1/480*h**6 + 0*h**4 - 1/240*h**5 + 0 - 2*h**2. Factor b(n).
n**2*(n - 1)/4
Let w(d) be the first derivative of -3*d**2 - 4 + 0*d - 3*d**3 - 3/4*d**4. Suppose w(l) = 0. What is l?
-2, -1, 0
Let z(g) = -3*g**3 + 15*g**2 - 5*g - 31. Let f(p) = 6*p**3 - 30*p**2 + 11*p + 61. Let o(r) = -4*f(r) - 7*z(r). Find j, given that o(j) = 0.
-1, 3
Let y be (-1 - -2)*3/1. Let c be -1 + (-36)/(-8) - y. Factor -c*u + 0 - 1