2
Let y(a) = 12*a**4 - 18*a**3 + 6*a**2 + 12*a - 3. Let q = 11 - 14. Let g(c) = -25*c**4 + 35*c**3 - 11*c**2 - 25*c + 5. Let u(s) = q*g(s) - 7*y(s). Factor u(t).
-3*(t - 1)**3*(3*t + 2)
Suppose 6*n = -12 + 12. Suppose -2*p + 8*p = n. Factor -2/5 + 2/5*x**2 + p*x.
2*(x - 1)*(x + 1)/5
Let p(x) be the second derivative of -x**8/2016 + 11*x**7/3780 - x**6/540 + 11*x**4/6 + 15*x. Let j(l) be the third derivative of p(l). Solve j(h) = 0.
0, 1/5, 2
Let q = -376 - -11303/30. Let g(l) be the third derivative of -q*l**5 + 0 + 0*l - 5/63*l**7 - 4/9*l**3 + 3*l**2 + 7/9*l**4 + 7/18*l**6. Factor g(n).
-2*(n - 1)**2*(5*n - 2)**2/3
Let v(l) be the second derivative of -1/21*l**7 + 0*l**2 + 1/2*l**4 + 18*l - 1/5*l**6 + 0*l**3 + 0 + 1/10*l**5. Find w such that v(w) = 0.
-3, -1, 0, 1
Factor -26*z + 12*z**4 + 13*z**5 - 19*z - 40*z**3 + 90*z**2 - 22*z**4 - 8*z**5.
5*z*(z - 3)*(z - 1)**2*(z + 3)
Let w(k) = -2*k**2 + 13*k - 11. Let u be w(13). Let l be (26/(-8))/(5/u). Determine m so that -9*m - 117 + l - 12*m**2 = 0.
-3/4, 0
Let b = -47486 - -807264/17. Factor 12/17*l**2 - b*l**3 + 0 + 0*l.
-2*l**2*(l - 6)/17
Let o = 70 + -20. Let a = o + -50. Factor 0*v + a + 0*v**2 - 2/9*v**4 + 0*v**3.
-2*v**4/9
Let h(g) = g**3 - 7*g**2 + 9*g + 9. Let m be h(5). Factor 5*r**5 - 2*r**4 + 15*r**m - r**3 - r**4 - 8*r**4.
r**3*(r + 1)*(5*r - 1)
Let 29/6*z - 11/6*z**3 + 7/3*z**4 - 1 - 13/3*z**2 = 0. What is z?
-3/2, 2/7, 1
Let x(s) be the third derivative of s**5/12 - 155*s**4/12 + 4805*s**3/6 - 20*s**2 - 3. Solve x(q) = 0 for q.
31
Let w(k) be the second derivative of 4*k**5/45 + 3*k**4/2 - 14*k**3/9 + 27*k**2 - 17*k. Let m(a) be the first derivative of w(a). Factor m(o).
4*(o + 7)*(4*o - 1)/3
Let x(n) be the first derivative of 0*n**2 - 1/2*n**5 - 2/3*n**3 + 7/6*n**4 + 5 + 14*n. Let i(z) be the first derivative of x(z). Let i(y) = 0. What is y?
0, 2/5, 1
Find k, given that -10*k**2 + 65/2 - 255/2*k = 0.
-13, 1/4
Let l(f) be the third derivative of -5*f**5/24 - 5*f**4/3 - 16*f**3/3 - 288*f**2. Factor l(r).
-(5*r + 8)**2/2
Let v = -7/6 - -47/30. Let m = 156/145 - 8/29. Factor v + 2/5*f**2 + m*f.
2*(f + 1)**2/5
Let n(i) be the third derivative of 2*i**7/105 - 7*i**6/30 + 17*i**5/15 - 17*i**4/6 + 4*i**3 + 5*i**2 + 6. Suppose n(a) = 0. What is a?
1, 2, 3
Let y = -186919/720 + -229/144. Let u = y - -262. Let 8/5*s + 0*s**3 + u*s**4 + 0 - 12/5*s**2 = 0. What is s?
-2, 0, 1
Let p(o) be the third derivative of o**5/120 - o**4/48 - o**3/2 + 72*o**2. Solve p(y) = 0.
-2, 3
Let v be (-33)/(-30) + 4 - (0 - -5). Let d(g) be the second derivative of 1/12*g**4 + 0 + 3/20*g**5 + 0*g**2 + 0*g**3 + 4*g + 1/42*g**7 + v*g**6. Factor d(p).
p**2*(p + 1)**3
Let z(a) be the first derivative of 18*a**5 - 425*a**4/4 + 90*a**3 - 20*a**2 + 74. What is v in z(v) = 0?
0, 2/9, 1/2, 4
Let d(p) be the third derivative of 15*p**8/112 + 9*p**7/14 + 7*p**6/12 - p**5 - 5*p**4/3 + 2*p**2 - 12. Solve d(u) = 0.
-2, -1, -2/3, 0, 2/3
Let g = -71 + 70. Let c be (g/7)/(1*3/(-6)). Determine d, given that -6/7*d**4 + 0 - 2/7*d**2 + 0*d - c*d**5 - 6/7*d**3 = 0.
-1, 0
Let f(s) = -s**5 + 39*s**4 + 38*s**3 - 29*s**2 - 91*s - 11. Let d(r) = r**5 - 19*r**4 - 18*r**3 + 14*r**2 + 46*r + 6. Let k(w) = 11*d(w) + 6*f(w). Factor k(t).
5*t*(t - 1)*(t + 2)**3
Suppose 0*r - 3/7*r**5 + 15/7*r**3 + 0 - 12/7*r**4 + 0*r**2 = 0. What is r?
-5, 0, 1
Let m(t) be the first derivative of -2*t**3/21 - t**2 - 58. Let m(g) = 0. What is g?
-7, 0
Let i(v) = -v**3 - 3*v**2 - 3*v. Let o be i(-3). Factor -4*y**2 - 27 - o + 13*y - 37*y.
-4*(y + 3)**2
Suppose 0 = -1156*a + 1154*a + 4. Let g(q) be the second derivative of -q - 2/5*q**5 + 4/3*q**3 + 0 + 0*q**a + q**4 - 2/5*q**6. Factor g(x).
-4*x*(x - 1)*(x + 1)*(3*x + 2)
Let r(d) = -10*d**4 - 16*d**3 + 20*d**2 + 74*d + 7. Let f(x) = 3*x**4 + 5*x**3 - 7*x**2 - 25*x - 2. Let k(c) = 21*f(c) + 6*r(c). What is z in k(z) = 0?
-3, 0, 3
Let t(f) = -f**2 + 9*f - 9. Let l be t(5). Suppose w = s - 2*w - l, 2*w + 4 = -s. Determine c, given that 0 + 10/9*c**3 - 8/9*c + 16/9*c**s = 0.
-2, 0, 2/5
Let w(a) be the third derivative of -a**6/48 + 7*a**5/30 - 15*a**4/16 + 3*a**3/2 - 187*a**2. Factor w(y).
-(y - 3)*(y - 2)*(5*y - 3)/2
Let v(f) = -2*f + 721*f**2 + 17*f - 18*f**3 - 733*f**2 - 12*f**4 + 7. Let m(i) = i**4 - i - 1. Let h(y) = -35*m(y) - 5*v(y). Suppose h(d) = 0. Calculate d.
-2, 0, 2/5
Factor 2/15*r**3 + 0 + 26/15*r - 28/15*r**2.
2*r*(r - 13)*(r - 1)/15
Let h = 303 - 298. Let i(y) be the first derivative of 0*y + 0*y**2 + 1/15*y**3 + 1/30*y**6 + 3/25*y**h + 6 + 3/20*y**4. Suppose i(o) = 0. Calculate o.
-1, 0
Let 7/5*f**4 + 22671/5*f**2 + 49005*f - 71874/5 + 691/5*f**3 = 0. What is f?
-33, 2/7
Let m be ((-6)/(-20) + (-9002)/140)*(-1)/18. Find i, given that 0*i - 2/3*i**4 + m*i**2 - 32/9 + 2/9*i**5 - 8/9*i**3 = 0.
-2, -1, 2
Let y be -1 - (2 + 1) - -8. Factor 3*v**4 + 14*v**3 - v**y - 18*v**3 + 2*v**2.
2*v**2*(v - 1)**2
Let j(a) = a**3 + 4*a**2 - 2*a - 5. Let k be j(-4). Factor -3*d**4 + 7*d**5 + 0*d**4 - d**2 + d**3 - 8*d**5 - 4*d**k.
-d**2*(d + 1)**3
Suppose 3*l - 2*z + 11 = 4*l, 5*l = -5*z + 80. Let m(d) be the first derivative of 7 - l*d**4 - 8/3*d**2 - 40/3*d**3 - 98/15*d**5 + 0*d. What is h in m(h) = 0?
-2, -2/7, 0
Let i(m) be the second derivative of 1/90*m**5 + 0*m**2 - m**3 + 0 + 5*m - 1/540*m**6 + 0*m**4. Let w(b) be the second derivative of i(b). Factor w(h).
-2*h*(h - 2)/3
Let y(w) = 3*w**3 + 372*w**2 - 23069*w + 476641. Let p(r) = -r**3 - 186*r**2 + 11534*r - 238322. Let o(a) = 10*p(a) + 4*y(a). Factor o(k).
2*(k - 62)**3
Let q(h) be the second derivative of -5/21*h**7 + 11*h**3 - 14/5*h**5 - 23/3*h**4 + 0 + 18*h**2 + 28/15*h**6 + 5*h. Let q(i) = 0. What is i?
-1, -2/5, 1, 3
Let d(k) = -k**2 + 7*k + 20. Let o be d(9). Factor o*s - 2*s**3 + 128*s**2 - 2 - 126*s**2 + 0.
-2*(s - 1)**2*(s + 1)
Let i be -1*3 + (-1918)/(-616). Let b = i - -23/572. Let -2/13*k**2 + 0 - b*k = 0. What is k?
-1, 0
Suppose 13 = 2*t + 3*d, 4*t + 13*d - 11*d - 14 = 0. Suppose 0 + 0*q - 2/3*q**3 + 0*q**t = 0. Calculate q.
0
Let p be (2/(-5))/(22/(-55)). Let v be (-2)/(4/(-3)) + 0/p. What is n in 5/2*n + v*n**3 - 1/4*n**4 - 3/4 - 3*n**2 = 0?
1, 3
Let j(b) = 2*b - 10. Let v be j(6). Let d(q) = -q**2 + 8*q + 12. Let i be d(9). Determine m so that -m - 43*m**3 + 5*m - 8*m**v - 2*m**i = 0.
-2/5, 0, 2/9
Let l(a) = -5*a**2 + 60*a - 59. Let f(p) = -10*p**2 + 120*p - 117. Let i(g) = 4*f(g) - 7*l(g). Factor i(h).
-5*(h - 11)*(h - 1)
Suppose -h - 2*m = 3 + 3, -h + 9 = -m. Find w such that -8*w + w**2 + h*w + 3*w**2 - 2*w**2 = 0.
0, 2
Let w(u) be the third derivative of u**7/280 - 13*u**6/480 + 11*u**5/240 + 5*u**4/96 - u**3/4 - 76*u**2. Solve w(n) = 0 for n.
-2/3, 1, 3
Let l(n) be the first derivative of 2*n**3 + 1/5*n**5 + 18 - 13/8*n**2 + 1/2*n - 17/16*n**4. Find t, given that l(t) = 0.
1/4, 1, 2
Suppose 3*x - 8*x = -55. Suppose 3 = -4*t + x. Factor 0*j**t + 0 + 1/4*j**3 - 1/4*j.
j*(j - 1)*(j + 1)/4
Let l be (1 + (-104)/90)/((-1919)/3534). Let m = -2/101 + l. Factor -2/15*f**2 - m - 2/5*f.
-2*(f + 1)*(f + 2)/15
Let n(f) be the third derivative of -f**9/36288 + f**8/30240 + f**7/3024 - f**6/1080 + f**5/6 - 2*f**2. Let w(s) be the third derivative of n(s). Factor w(x).
-(x - 1)*(x + 1)*(5*x - 2)/3
Let u(t) be the first derivative of 1681*t**3/9 + 82*t**2/3 + 4*t/3 + 673. Factor u(c).
(41*c + 2)**2/3
Let f(w) = -w**2 - 9*w. Let b(p) = -9*p + 9*p + p. Let g(a) = 18*b(a) + 2*f(a). Factor g(i).
-2*i**2
Let d = 15265/24 - 636. Let t(z) be the second derivative of 0*z**3 + 0*z**2 + 3/80*z**5 - 1/120*z**6 - d*z**4 - 6*z + 0. Determine y, given that t(y) = 0.
0, 1, 2
Let i be (-1)/(-3)*(-18)/(-72). Let n(s) be the second derivative of 0 + 0*s**3 + i*s**4 + s + 0*s**2 + 0*s**5 - 1/30*s**6. Factor n(q).
-q**2*(q - 1)*(q + 1)
Find a, given that -3*a**2 + 69*a**5 + 5*a**2 + 6*a**4 - 37*a**5 - 11*a**3 - 8 - 33*a**5 + 12*a = 0.
-1, 1, 2
Factor 17/6*h**3 - 17/6*h + 0 - 1/6*h**4 + 1/6*h**2.
-h*(h - 17)*(h - 1)*(h + 1)/6
Let o be (-1*1/(-5))/((-6)/(-5)). Suppose 0 = 4*c - 0*c. Determine r, given that o*r**2 - 1/2*r**3 + 1/2*r**4 + 0*r - 1/6*r**5 + c = 0.
0, 1
Let n(t) be the first derivative of -2*t**5/35 + 590*t**4/7 - 348100*t**3/7 + 102689500*t**2/7 - 15146701250*t/7 + 271. What is d in n(d) = 0?
295
Let b(v) be the first derivative of -2*v**5/5 - 16*v**4 - 178*