 3/2*r**2 + 0*r**3 + 0. Let c(w) be the first derivative of z(w). Factor c(y).
-2*y*(y + 1)/5
Let d(v) be the first derivative of 2*v**5/65 - 3*v**4/26 + 4*v**3/39 - 33. Factor d(x).
2*x**2*(x - 2)*(x - 1)/13
Let u(k) be the first derivative of -2*k**3/27 + 2*k/9 + 2. Find y, given that u(y) = 0.
-1, 1
Let k(t) be the second derivative of -1/24*t**4 + 0*t**2 - 1/12*t**3 - t + 0. Factor k(y).
-y*(y + 1)/2
Suppose 2*c = 4*c - 6. Suppose 0 = -g + c - 1. What is w in 8*w**4 - 2*w**3 + w - 3*w**g + w**3 - w**3 - 4*w**3 = 0?
-1/2, 0, 1/4, 1
Let w(u) = u**3 - 3*u**2 - 5*u + 6. Suppose 3*r + 5 + 6 = 5*p, 5*r = -2*p + 23. Let v be w(p). Factor v*h**2 + 4/3 - 10/3*h.
2*(h - 1)*(3*h - 2)/3
Let n(a) be the first derivative of -1/96*a**4 - 1/240*a**5 + 1/3*a**3 - 1 + 0*a**2 + 0*a - 1/1440*a**6. Let i(j) be the third derivative of n(j). Factor i(u).
-(u + 1)**2/4
Let l(a) be the third derivative of 2*a**6/15 + 8*a**5/15 - a**4/2 - 6*a**3 + 11*a**2. Find m, given that l(m) = 0.
-3/2, 1
Let b(j) = -j**2 - 9*j + 12. Let c be b(-10). Solve 2*o**4 - o**4 + 6*o - 4 + c*o**4 + 1 - 6*o**3 = 0.
-1, 1
Let f(z) = -54*z**4 - 124*z**3 - 18*z**2 + 49*z - 13. Let g(h) = -1 - 8 - h**3 + 8 - h**4 + h. Let w(p) = f(p) - 5*g(p). Factor w(b).
-(b + 1)*(b + 2)*(7*b - 2)**2
Find g such that 3/4*g**4 + 0 + 0*g**2 + 0*g + 3/4*g**3 = 0.
-1, 0
Let w(s) be the first derivative of -7 + 2/65*s**5 - 2/39*s**3 - 1/39*s**6 + 1/26*s**4 + 0*s**2 + 0*s. Factor w(c).
-2*c**2*(c - 1)**2*(c + 1)/13
Find g, given that -2/9*g**3 + 0 + 4/9*g - 2/9*g**2 = 0.
-2, 0, 1
Let h(v) = v**3 - 11*v**2 + 22*v - 33. Let g be h(9). Factor 4/3*a + a**2 + 0 - 1/3*a**g.
-a*(a - 4)*(a + 1)/3
Let j(z) be the third derivative of -z**6/300 - 2*z**5/75 - z**4/15 + z**2. Solve j(n) = 0 for n.
-2, 0
Factor 40*t**2 - 15*t**3 - 12 + t + 45*t - 3*t**3.
-2*(t - 3)*(t + 1)*(9*t - 2)
Let r(x) be the second derivative of x**6/18 - 5*x**4/12 + 5*x**3/9 - 25*x. Let r(n) = 0. What is n?
-2, 0, 1
Let 4 - 3*g + 1/2*g**2 = 0. What is g?
2, 4
Find v, given that -48 - 12*v + 3/4*v**4 - 33/4*v**3 + 27*v**2 = 0.
-1, 4
Suppose 0 = -31*k + 32*k. Factor 2/7*b**2 + k - 2/7*b.
2*b*(b - 1)/7
Let r(g) be the third derivative of -g**8/1680 - g**7/210 - g**6/72 - g**5/60 + 5*g**3/6 - 2*g**2. Let d(c) be the first derivative of r(c). Factor d(w).
-w*(w + 1)**2*(w + 2)
Let k(t) = t**2 + 2. Let d be k(2). Let w(z) be the third derivative of 1/40*z**5 - 3*z**2 + 0*z + 0*z**3 + 1/16*z**4 - 1/80*z**d + 0 - 1/140*z**7. Factor w(g).
-3*g*(g - 1)*(g + 1)**2/2
Factor -16*m - m**4 + 56*m**2 + 2*m**4 + 37*m**3 - 62*m**3 + 2*m**4.
m*(m - 4)**2*(3*m - 1)
Let o(z) = 2*z. Let c be o(-2). Let j be ((-12)/18)/(c/18). Find l, given that l**j + 3*l - 2*l + l**4 - l = 0.
-1, 0
Let l(w) be the second derivative of -w**7/1050 - w**6/150 - w**5/60 - w**4/60 + 3*w**2/2 - w. Let u(s) be the first derivative of l(s). Factor u(a).
-a*(a + 1)**2*(a + 2)/5
Let w(k) be the second derivative of -k**5/5 + k**4/3 + k. Factor w(l).
-4*l**2*(l - 1)
Let v(u) = 9*u**2 + 10*u + 1. Let b(w) = -w**2 - w. Let c(n) = -3*b(n) - v(n). Find j, given that c(j) = 0.
-1, -1/6
Let t be (-6)/8*4/(-6). Let a(r) be the second derivative of 3/5*r**6 + 0 - 2*r - 3/2*r**4 - 2/3*r**3 - t*r**5 + 0*r**2 + 1/3*r**7. Let a(s) = 0. Calculate s.
-1, -2/7, 0, 1
Let p(t) be the third derivative of t**7/420 + t**6/180 - t**5/30 + t**3/3 - t**2. Let j(g) be the first derivative of p(g). Find n, given that j(n) = 0.
-2, 0, 1
Let h(y) be the third derivative of -y**8/1344 + y**7/560 - y**6/960 + 5*y**2. Factor h(u).
-u**3*(u - 1)*(2*u - 1)/8
What is z in z**4 - 8*z - 2*z**2 + 3*z**4 + 0*z**4 + 8*z**3 - 2*z**2 = 0?
-2, -1, 0, 1
Let 0*a**3 + 0 - 1/2*a + 1/2*a**5 + a**4 - a**2 = 0. Calculate a.
-1, 0, 1
Let 18/7 - 12/7*u + 2/7*u**2 = 0. Calculate u.
3
Suppose o = 2*o - 2. Suppose -17 - 2*t**o - t**2 - 10 + 18*t = 0. What is t?
3
Factor -2*d + 2*d**3 - 5*d**3 - 4 + 10 + 12*d**2 - 13*d.
-3*(d - 2)*(d - 1)**2
Suppose 0 = -0*w - 4*w + 5*o + 9, 2*o - 1 = -3*w. Let m(y) be the first derivative of -w + 0*y - 1/3*y**3 + 1/2*y**2. Factor m(a).
-a*(a - 1)
Let v(a) be the third derivative of -a**8/560 + a**6/60 - a**4/8 - a**3/3 - 2*a**2. Let t(r) be the first derivative of v(r). Find c such that t(c) = 0.
-1, 1
Let f(c) = -5*c**3 + 16*c**2 + 20*c + 17. Let o(m) = -2*m**3 + 8*m**2 + 10*m + 8. Let l(k) = 4*f(k) - 9*o(k). Let l(w) = 0. What is w?
-2, -1
Let w(x) be the first derivative of -x**4/8 + x**3/3 + x**2/4 - x - 4. Factor w(a).
-(a - 2)*(a - 1)*(a + 1)/2
Let i(a) = -a**2 + 3*a + 31. Let z be i(-4). Let n(m) be the first derivative of 1/28*m**4 + 2 - 1/21*m**z + 0*m - 1/7*m**2. Factor n(w).
w*(w - 2)*(w + 1)/7
Let g(m) be the first derivative of -2 - 2/27*m**3 + 0*m + 1/9*m**2. Factor g(r).
-2*r*(r - 1)/9
Suppose -9*c + 4*c = 0. What is a in -3/5*a**3 + 0*a**2 + 6/5*a**4 + 0 - 3/5*a**5 + c*a = 0?
0, 1
What is r in -1/2*r**2 - 1/2*r**3 + 1/2*r + 0 + 1/2*r**4 = 0?
-1, 0, 1
Let l(p) = 25*p**3 + p**2 - p + 1. Let b be l(1). Factor -25*h + h**4 + b*h + 0*h**4 - h**3 + 4*h**3 + 3*h**2.
h*(h + 1)**3
Let m = 13 + -9. Factor -100*o**2 - 26*o**2 - m - 52*o - 43*o**2.
-(13*o + 2)**2
Let v = 46 + -46. Let p(k) be the third derivative of -2/9*k**3 + 1/12*k**4 - 1/90*k**5 + v*k + 0 - 3*k**2. Factor p(z).
-2*(z - 2)*(z - 1)/3
Let l(h) be the first derivative of -4/15*h**3 + 2/25*h**5 + 0*h + 0*h**2 + 1/10*h**4 - 1. Find p, given that l(p) = 0.
-2, 0, 1
Let k(f) = f**3 + 2*f**2 - 3*f - 4. Let h = -10 + 14. Suppose -2*y - h = -y. Let r(t) = -2*t**3 - 4*t**2 + 7*t + 9. Let g(i) = y*r(i) - 9*k(i). Factor g(s).
-s*(s + 1)**2
Let n(l) be the first derivative of l**5/140 - l**4/42 - 2*l + 1. Let w(g) be the first derivative of n(g). Solve w(o) = 0.
0, 2
Suppose 4*o = 4 + 24. Determine j, given that -2*j**2 - 2*j**3 + 7*j - o*j = 0.
-1, 0
Let i(m) be the second derivative of 0*m**5 - 1/84*m**7 + 0*m**3 - 1/60*m**6 - 3*m + 0*m**2 + 0*m**4 + 0. Factor i(p).
-p**4*(p + 1)/2
Let x be 4/8 + (-2)/4. Let 2*s**3 - s**4 - 2*s**3 - 2*s**3 - s**2 + x*s**4 = 0. Calculate s.
-1, 0
Let c(o) be the first derivative of -3*o**4 - 15*o**3 - 12*o**2 + 9*o - 11. Solve c(y) = 0.
-3, -1, 1/4
Factor 3 + 2*k**4 - 3 - 12*k**3 + 24*k**2 - 16*k.
2*k*(k - 2)**3
Let t = -39 + 27. Let r be 5/(-2)*t/45. Find b such that r - 2/3*b**2 + 0*b = 0.
-1, 1
Factor 0 + 10/3*u**5 + 34/3*u**4 + 4/3*u + 14*u**3 + 22/3*u**2.
2*u*(u + 1)**3*(5*u + 2)/3
Let m(x) be the third derivative of x**6/720 - x**5/72 + x**4/18 - x**3/9 + 7*x**2. Factor m(c).
(c - 2)**2*(c - 1)/6
Let h = 11 - 5. Let s(j) = j**4 + j**3 - j**2 - j. Let i(k) = 28*k**4 + 8*k**3 - 19*k**2 + k. Let m(o) = h*s(o) - 2*i(o). Suppose m(p) = 0. What is p?
-1, 0, 2/5
Let v = -1/59 - -181/236. Factor -1/4*c**3 + 0*c + 0*c**2 + 0 - 1/2*c**4 + v*c**5.
c**3*(c - 1)*(3*c + 1)/4
Let f = -10 + 21/2. Factor -2*z**2 + f*z + 0.
-z*(4*z - 1)/2
Let w be (5 - -1)*(-5)/(-10). Factor 0*o**3 - 2*o**2 - 2*o**2 + 2*o + 2*o**w.
2*o*(o - 1)**2
Let m = -1 + 3. Let w(x) = 2*x - 33. Let v be w(18). Suppose 2/3*l**4 + 4/3*l**v - l**5 - 2/3*l**m - 1/3*l + 0 = 0. Calculate l.
-1, -1/3, 0, 1
Let f(o) be the first derivative of -2/9*o**3 - 5/6*o**2 + 1/3*o**4 + 1/18*o**6 - 4 + 4/15*o**5 - 2/3*o. Factor f(r).
(r - 1)*(r + 1)**3*(r + 2)/3
Let u(k) = k**3 - 6*k**2 - 6*k - 4. Let f be u(7). Let o be f/(1 - 10)*-1. Factor o*i + 0 + 1/3*i**2.
i*(i + 1)/3
Suppose -4*a + 3*i = -2 - 7, 2*i + 6 = 0. Factor a - q**2 + 2/5*q**3 + 2/5*q.
q*(q - 2)*(2*q - 1)/5
Factor -3*r**5 - 26*r**3 + 5*r**5 + 3*r**4 + 27*r**3.
r**3*(r + 1)*(2*r + 1)
Let h(x) = -3*x**3 - 6*x**2 - 5*x. Let s(k) = -3 + 0 + 3 - k. Let a(d) = -h(d) + 2*s(d). Factor a(b).
3*b*(b + 1)**2
Let d(p) be the first derivative of -p**3/9 + p**2/2 + 4*p/3 - 1. Suppose d(o) = 0. What is o?
-1, 4
Let p(a) = -7*a**2 + 15*a + 2. Let v(h) = -50*h**2 + 105*h + 15. Let w(b) = 15*p(b) - 2*v(b). What is o in w(o) = 0?
0, 3
Let i(l) = -l**2 - 5*l - 4. Let c be i(-3). Let g = -25/2 - -79/6. Factor -2/3*h**3 + 2/3*h + g - 2/3*h**c.
-2*(h - 1)*(h + 1)**2/3
Let k = -869/4 - -218. Factor 7/4*u + 1/4*u**3 + 5/4*u**2 + k.
(u + 1)**2*(u + 3)/4
Let q(u) = u**3 - 2*u**2 + u + 2. Let k be q(2). Solve -4*l**k + 2*l**3 + 3*l**4 + 2*l**4 - 5*l - 1 + 3*l = 0 for l.
-1, 1
Let b(k) be the third derivative of -4/45*k**5 + 0*k**3 + 1/72*k