1*t**3 + 1/7*t**2 + 3. Factor q(n).
2*(n - 1)*(n + 2)/7
Factor 2/13*q**2 + 0*q + 0.
2*q**2/13
Find l, given that -4 - 2/3*l**2 - 10/3*l = 0.
-3, -2
Suppose -2 = -2*o + 4*i, i - 10 = 2*o - 5*o. Suppose -2*f = -f - 6. Determine k so that -4*k**4 + 2 + f*k**3 - 6*k**2 + 8*k**2 - 9*k + o*k = 0.
-1, 1/2, 1
Factor -18/5*z**5 + 0*z**2 + 12/5*z**4 + 0*z + 0 - 2/5*z**3.
-2*z**3*(3*z - 1)**2/5
Let d = 1 - 1. Let l(j) be the first derivative of -16/3*j**6 - 1/2*j**4 + d*j - 4*j**3 + 48/5*j**5 - j**2 - 2. Factor l(h).
-2*h*(h - 1)**2*(4*h + 1)**2
Let h(l) = -4*l - 1 - 2*l + 0*l + 5*l. Let f(n) = -64*n**3 - 64*n**2 - 14*n + 4. Let u(m) = -f(m) - 6*h(m). Find q such that u(q) = 0.
-1/2, -1/4
Let x(y) be the third derivative of y**6/420 - y**5/70 - y**4/84 + y**3/7 - 7*y**2. Solve x(z) = 0.
-1, 1, 3
Let r = -2 - -1. Let h(f) = -f + 1. Let g be h(r). Suppose -k**3 + 0*k**2 - g*k**2 + 3*k**3 + 2*k**4 - 2*k = 0. Calculate k.
-1, 0, 1
Let b(i) = i**2 - 21*i. Let c(s) = -s**2 + 11*s. Let h(v) = 6*b(v) + 11*c(v). Find l, given that h(l) = 0.
-1, 0
Let f(t) = t**5 - 7*t**4 - 4*t**3 + 4*t**2 + 6*t. Let y(w) = w**5 - w**4 + w**3 - w. Let r(q) = -f(q) + 2*y(q). Find l, given that r(l) = 0.
-2, 0, 1
Suppose 5*x = -d + 4 - 41, 0 = -3*d - x - 55. Let b be 27/9 - d/(-7). Factor 0 - 2/7*z + 2/7*z**2 + b*z**3.
2*z*(z + 1)*(2*z - 1)/7
Let z(f) be the first derivative of 5*f**3/21 - 6*f**2/7 + 4*f/7 - 1. Find k, given that z(k) = 0.
2/5, 2
Let w = 1025/2 - 528. Let n = w + 16. Factor -1/2*y**4 - 1/2 - n*y - 1/2*y**5 + y**2 + y**3.
-(y - 1)**2*(y + 1)**3/2
Let n(j) be the first derivative of j**7/168 + j**6/40 + j**5/40 + 5*j - 9. Let m(w) be the first derivative of n(w). What is r in m(r) = 0?
-2, -1, 0
Let s(h) be the second derivative of 7/60*h**6 - 11*h + 0*h**2 + 1/24*h**4 + 0*h**3 - 1/8*h**5 - 1/28*h**7 + 0. Factor s(p).
-p**2*(p - 1)**2*(3*p - 1)/2
Let u(s) = -20*s - 4 + 2*s**2 - 5*s**2 - 1 - 14*s**4 - 12 - 14*s**3. Let j(w) = 5*w**4 + 5*w**3 + w**2 + 7*w + 6. Let n(a) = -17*j(a) - 6*u(a). Factor n(d).
-d*(d - 1)*(d + 1)**2
Let c(d) be the second derivative of d**7/21 - d**5/5 + d**3/3 + 15*d. Factor c(x).
2*x*(x - 1)**2*(x + 1)**2
Let l(y) be the second derivative of y**4/4 - y**3 + 3*y**2/2 - 5*y. Factor l(h).
3*(h - 1)**2
Let g = -9 + 11. What is p in -2*p + g*p**2 - 3*p**2 - 4 + 3 = 0?
-1
Suppose -5*w = -4*s + 6 + 14, -w - 20 = -4*s. Let g(h) be the third derivative of 1/72*h**4 + 1/180*h**5 - 3*h**2 + w*h**3 + 0*h + 0. What is u in g(u) = 0?
-1, 0
Factor -4*p**2 - 16/5 - 32/5*p - 4/5*p**3.
-4*(p + 1)*(p + 2)**2/5
Let y(x) be the first derivative of -5*x**4/8 + 11*x**3/6 - 7*x**2/4 + x/2 - 8. Factor y(j).
-(j - 1)**2*(5*j - 1)/2
Let n(r) be the second derivative of -r**6/480 - r**5/60 - r**4/24 - 3*r**2/2 - 2*r. Let x(v) be the first derivative of n(v). Determine d, given that x(d) = 0.
-2, 0
Let x be 12/4*4/6. Factor -2*a**x + 4 - 2 + 4*a**2 + 4*a.
2*(a + 1)**2
Let h(y) be the first derivative of 5*y**7/42 + 7*y**6/30 + y**5/10 + y - 4. Let n(r) be the first derivative of h(r). Factor n(g).
g**3*(g + 1)*(5*g + 2)
Let l(r) = r**2 - 4*r + 2. Let w be l(3). Let x(z) = 2*z**2. Let j be x(w). Factor 1/3*p**j + 1/3*p - 2/3.
(p - 1)*(p + 2)/3
Let j(q) = q**2 + 9*q + 18. Let y be j(-6). Let -4/3*m**4 + 0*m + y*m**2 + 0*m**3 + 0 + 2*m**5 = 0. Calculate m.
0, 2/3
Let m(n) be the third derivative of -n**8/1680 - n**3/2 - 3*n**2. Let k(o) be the first derivative of m(o). Solve k(x) = 0 for x.
0
Solve 2/3*g + 2*g**3 + 2*g**2 + 0 + 2/3*g**4 = 0.
-1, 0
Let h(m) be the first derivative of -5*m**4/4 - 7*m**3/3 + 2. Let g(f) = -11*f**3 - 15*f**2. Let o(z) = 6*g(z) - 13*h(z). Factor o(q).
-q**2*(q - 1)
Let k(u) be the first derivative of u**8/1344 - u**7/280 + u**6/160 - u**5/240 - 3*u**2/2 - 1. Let v(b) be the second derivative of k(b). What is d in v(d) = 0?
0, 1
Let r = -2/65 - -266/195. Factor r*f - 2/3*f**2 - 2/3.
-2*(f - 1)**2/3
Let o(j) be the first derivative of j**6/480 + j**5/60 + j**4/24 + 3*j**2 - 7. Let k(s) be the second derivative of o(s). Determine r so that k(r) = 0.
-2, 0
Let h = 60847 - 5841251/96. Let o = 1/32 + h. Factor -2/3*q**4 + 2/3*q**2 + 0 - 2/3*q**5 + o*q**3 + 0*q.
-2*q**2*(q - 1)*(q + 1)**2/3
Factor -i - 3*i**4 + i**3 - i + 5*i**2 - 2*i**2 - 26*i**5 + 27*i**5.
i*(i - 2)*(i - 1)**2*(i + 1)
Let u(g) be the second derivative of 0*g**3 + 3/20*g**5 + 0 + g + 0*g**2 + 1/6*g**7 - 1/6*g**4 + 2/5*g**6. Solve u(v) = 0 for v.
-1, 0, 2/7
Let f(g) = -2*g**5 + 7*g**3 + 3*g**2 - 5*g - 3. Let j(s) = s**5 - 6*s**3 - 4*s**2 + 5*s + 4. Let m(y) = 4*f(y) + 3*j(y). Factor m(h).
-5*h*(h - 1)**2*(h + 1)**2
Let l be 7/(385/45) - -1. Factor -2/11 + 10/11*x - 20/11*x**2 - 10/11*x**4 + l*x**3 + 2/11*x**5.
2*(x - 1)**5/11
Solve 5/2*v - 1/4*v**2 - 25/4 = 0.
5
Let d be 22/6 + 6/(-9). Factor -11*i + 4 - 2 - 26*i**d + 4*i**4 + 9*i**4 + i**4 - 3*i**5 + 24*i**2.
-(i - 1)**4*(3*i - 2)
Suppose -12*t**2 + 9*t**2 - 4*t + 19*t - 12 = 0. What is t?
1, 4
Suppose 0*i = -2*i. Let m(x) be the third derivative of 3*x**2 - 1/150*x**5 + i*x - 1/525*x**7 + 0 + 1/150*x**6 + 0*x**3 + 0*x**4. Find p, given that m(p) = 0.
0, 1
Let r = -52 + 54. Factor 0*o + 2/5*o**r + 2/5*o**3 + 0.
2*o**2*(o + 1)/5
Suppose 6*o = -12 + 24. Let 0 - 4/11*s - 14/11*s**o + 8/11*s**3 = 0. What is s?
-1/4, 0, 2
Let i(x) = 7*x**2 + 8*x + 5. Let m(h) = -85*h**2 - 95*h - 60. Let s(n) = -25*i(n) - 2*m(n). Factor s(b).
-5*(b + 1)**2
Let h(m) be the second derivative of 2/39*m**3 - 1/78*m**4 + 3/13*m**2 + 0 + m. Solve h(y) = 0 for y.
-1, 3
What is f in -8/3*f**2 + 0 - 8/9*f + 14/9*f**3 = 0?
-2/7, 0, 2
Let u = -452 - -905/2. Let x be (-7)/(-4) + 0 + 0. Factor -u*v + x*v**2 + 0.
v*(7*v - 2)/4
Suppose 4*q + 20 = -4*t, 2*t = 5*t + 5*q + 25. Suppose -2*r + 4 = 0, -8*z - 2*r = -6*z - 8. Determine l, given that -49/2*l**3 + t + 14*l**2 - z*l = 0.
0, 2/7
Let f(s) be the second derivative of -s**8/1680 + s**7/840 + s**6/360 - s**5/120 + 7*s**3/6 - 3*s. Let l(b) be the second derivative of f(b). Factor l(r).
-r*(r - 1)**2*(r + 1)
Let h = 55 + -35. Let w be (-24)/(-20) + (-12)/h. Find x such that -3*x**2 - 12/5 - 24/5*x - w*x**3 = 0.
-2, -1
Let w(a) be the first derivative of a**5/60 + a**2/2 - 2. Let q(k) be the second derivative of w(k). Let h(g) = g - 1. Let s(u) = -4*h(u) + q(u). Factor s(z).
(z - 2)**2
Let r be 2*1/(-2) - (-9)/6. Suppose r*v**5 + 0*v**2 + 1/2*v**3 + 0*v - v**4 + 0 = 0. What is v?
0, 1
Let y(r) = r**3 + 8*r**2 + 8*r + 7. Let i be y(-7). Suppose 0 = k - i*k - 2. Solve 0*v**4 - 6/5*v - 2/5*v**k + 14/5*v**3 + 2/5 - 8/5*v**5 = 0 for v.
-1, 1/2, 1
Let y(c) be the third derivative of -1/150*c**5 - 1/30*c**4 + 0*c**3 + 0 + 3*c**2 + 1/300*c**6 + 0*c. Factor y(b).
2*b*(b - 2)*(b + 1)/5
Suppose 2*y = 4*y. Factor n**4 - n - 1 + 3*n + y - 2*n**3.
(n - 1)**3*(n + 1)
Let s(b) be the second derivative of -1/5*b**6 - 5/6*b**4 + 0 - 7/10*b**5 + 2*b + 0*b**2 - 1/3*b**3. Suppose s(d) = 0. Calculate d.
-1, -1/3, 0
Factor 5/3*y**2 + 0 - 5/3*y.
5*y*(y - 1)/3
Let q(n) = 7*n**4 - 5*n**3 + 3*n**2 + 5*n + 5. Let u(g) = -g**4 + g**3 - g**2 - g - 1. Let b(t) = q(t) + 5*u(t). Factor b(m).
2*m**2*(m - 1)*(m + 1)
Let k be (-4)/(-12) - (-3)/(-9). Suppose k = s - 4 + 1. Factor -6*l**4 + 3*l**s + l**5 + 0*l**5 + l**5 + l**3.
2*l**3*(l - 2)*(l - 1)
Let x = 3 - 0. Let d be (1/(-6))/((-1)/3). Factor -3/2*g - d*g**x + 3/2*g**2 + 1/2.
-(g - 1)**3/2
Suppose 6 = -2*i + 8*i. Solve i - 3/2*b + 1/2*b**2 = 0.
1, 2
Factor 1/10*q - 2/5*q**2 + 3/5 + 1/10*q**3.
(q - 3)*(q - 2)*(q + 1)/10
Let g(y) = -y**2 + 3*y - 3. Let v be g(3). Let b = v - -5. Factor p**3 + 0 + 0*p - 1/2*p**b - 1/2*p**4.
-p**2*(p - 1)**2/2
Let i(h) be the second derivative of 0*h**2 + 0 + 1/6*h**4 + 0*h**3 + 4*h + 1/10*h**5. Find f, given that i(f) = 0.
-1, 0
Determine p so that 0 + 6*p**3 + 21/2*p**4 - 6*p**2 + 3*p**5 + 0*p = 0.
-2, 0, 1/2
Let l(r) be the first derivative of 49*r**3/5 - 12*r/5 - 7. Solve l(a) = 0 for a.
-2/7, 2/7
Let m be 1/3 + 2/(-18). Suppose m*v**5 + 4/9*v**4 + 0*v + 0 + 2/9*v**3 + 0*v**2 = 0. What is v?
-1, 0
Let u = -12 - -12. Factor -2*m**4 + 8*m**2 - 4*m**5 + u*m**4 - 6*m**4 + 3*m + m.
-4*m*(m - 1)*(m + 1)**3
Let k(r) = -3*r**4 + 5*r**3 - r**2 - 9*r + 5. Let f(y) = -2*y**4 + 3*y**3 - 5*y + 3. Let g(l) = 5*f(l) - 3*k(l). Find d such that g(d) = 0.
-1, 0, 2
Let n(a) = -a**3 + 3