**2 - 25*f + 8. Let k(x) = -13*d(x) + 6*g(x). Factor k(u).
2*(u - 2)*(u - 1)**2*(u + 1)
Let f(v) = -v + 5. Let w be f(0). Factor -4 - g**4 + 4 + w*g**2 - 3*g**2 - 1.
-(g - 1)**2*(g + 1)**2
Determine g so that 0*g + 0 - 3/4*g**4 + 1/4*g**5 + 1/2*g**3 + 0*g**2 = 0.
0, 1, 2
Let i = -841 + 844. Factor 2/7*o**4 - 6/7*o**i + 6/7*o**2 - 2/7*o + 0.
2*o*(o - 1)**3/7
Let k be (6 - 12)/(-6) + 1. Factor -1/3*x**5 + x**3 + 1/3*x**4 - 5/3*x**k + 2/3*x + 0.
-x*(x - 1)**3*(x + 2)/3
Let q be 4/(-14) + 111/609. Let i = q - -35/58. Factor i*w**2 + 3/2*w + 1.
(w + 1)*(w + 2)/2
Let w be (-2)/6 + (-1 - -2). Let i = 33 - 30. Suppose -2*f**5 + 4/3*f**i + 4*f**2 - w + 2/3*f - 10/3*f**4 = 0. What is f?
-1, 1/3, 1
Let r(f) be the second derivative of -1/3*f**3 - 5/6*f**4 + 0 + 0*f**2 - 2/5*f**5 - 6*f. Factor r(b).
-2*b*(b + 1)*(4*b + 1)
Let t be (-3)/2 + 3159/1890. Let s(d) be the first derivative of -t*d**5 - 5/14*d**4 + 2 - 2/21*d**3 + 1/7*d**2 + 0*d. Let s(u) = 0. Calculate u.
-1, 0, 1/3
Let g(k) = -k**4 + 4*k**3 + 2*k**2 - 4*k - 1. Let t(y) = y**3 + y**2 - y - 1. Let o(x) = g(x) - 2*t(x). Find l, given that o(l) = 0.
-1, 1
Suppose 0 = -5*s + 12 + 18. Suppose s*k - k = 20. Factor 1/5*b**2 + 0 + 1/5*b - 1/5*b**k - 1/5*b**3.
-b*(b - 1)*(b + 1)**2/5
Find h, given that 17*h**2 + 16 - 16 - 22*h**2 + 5*h = 0.
0, 1
Let o(z) be the first derivative of -z**8/112 + z**7/35 - z**2 - 4. Let v(u) be the second derivative of o(u). Solve v(a) = 0 for a.
0, 2
Suppose 17*p - 96 = -15*p. Solve -6/7*i**4 + 4/7 - 2/7*i - 22/7*i**2 - 22/7*i**p = 0.
-2, -1, 1/3
Let z be 1 + (6/2)/(-21). Let l be 12/(-15)*10/(-28). Factor z*v - l*v**2 - 4/7.
-2*(v - 2)*(v - 1)/7
Let r = 271 - 539/2. Factor 3/4*v + 3/4*v**4 + 3/4 - r*v**2 + 3/4*v**5 - 3/2*v**3.
3*(v - 1)**2*(v + 1)**3/4
Factor 0*u**3 + 0*u - 2/9 + 4/9*u**2 - 2/9*u**4.
-2*(u - 1)**2*(u + 1)**2/9
Let u be (9/12)/(1/4). Let w be 44/10 + 4/(-10). Solve 2*x**w + 0*x**4 + 2*x**3 - 4*x**u = 0 for x.
0, 1
Let r(x) be the second derivative of x**8/672 - x**7/210 + x**6/240 + 5*x**2/2 - 7*x. Let d(a) be the first derivative of r(a). What is h in d(h) = 0?
0, 1
Let s be 182/392 + 4/14. Let h(v) be the first derivative of s*v**4 - 3/2*v**2 + 0*v**3 + 0*v + 4. Factor h(g).
3*g*(g - 1)*(g + 1)
Let o(s) be the second derivative of s**7/91 - 7*s**6/195 - 3*s**5/130 + 11*s**4/78 - 4*s**2/13 + 11*s. Solve o(x) = 0 for x.
-1, -2/3, 1, 2
Suppose 0 = -0*q + q - 5. Factor 8 - r**4 + 3*r**3 + 2*r - q*r**3 - 7.
-(r - 1)*(r + 1)**3
Suppose -2193*l**3 + 4*l**2 + 2193*l**3 - 2*l**4 - 2 = 0. What is l?
-1, 1
Let l(j) be the second derivative of j**6/20 + 39*j**5/40 + 57*j**4/8 + 95*j**3/4 + 75*j**2/2 - 3*j. Solve l(c) = 0.
-5, -2, -1
Let l(z) be the first derivative of 1/6*z**6 + 0*z + 2/3*z**3 + 5/4*z**4 + 0*z**2 - 4 + 4/5*z**5. Factor l(d).
d**2*(d + 1)**2*(d + 2)
Let g(i) = -4*i**4 + 4*i**3 - 8*i**2 + 2*i - 6. Let q(k) = 3*k**4 - 4*k**3 + 7*k**2 - k + 5. Let p(c) = -5*g(c) - 6*q(c). What is r in p(r) = 0?
-2, -1, 0, 1
Let x(k) be the third derivative of 0 + 0*k**3 - 5*k**2 + 0*k**4 + 1/90*k**5 - 1/180*k**6 + 0*k. Factor x(r).
-2*r**2*(r - 1)/3
Factor 0 - 6/7*r**2 - 2/7*r.
-2*r*(3*r + 1)/7
Suppose 13 = 19*p - 25. Factor -1/2*s**4 + 0 + 1/2*s**p - 3/2*s**3 + 1/2*s**5 + s.
s*(s - 2)*(s - 1)*(s + 1)**2/2
Determine d so that 4/5*d**4 + 4/15 + 28/15*d**3 + 6/5*d + 2/15*d**5 + 32/15*d**2 = 0.
-2, -1
Let q = -4 + 14. Suppose q = 3*j - 5. Factor -3*l**4 + 1 + 0*l**5 + 3*l**5 + 3*l + 2*l**2 - 2*l**3 - 4*l**j.
-(l - 1)*(l + 1)**4
Let h(o) be the second derivative of 2*o**7/63 - 14*o**6/45 + 2*o**5/3 + 2*o**4 - 6*o**3 - 18*o**2 - 2*o. Factor h(t).
4*(t - 3)**3*(t + 1)**2/3
Let u(y) be the second derivative of y**5/10 + y**4/3 + y**3/3 - 15*y. Factor u(s).
2*s*(s + 1)**2
Let m(l) be the second derivative of -l**6/45 + 2*l**5/15 - l**4/3 + 4*l**3/9 - l**2/3 + 18*l. Factor m(k).
-2*(k - 1)**4/3
Factor 5*h**4 - 5*h**2 + 10 + 9*h**3 - 10*h**2 - 11*h**3 - 3*h**3 + 5*h.
5*(h - 2)*(h - 1)*(h + 1)**2
Let d(g) be the second derivative of -g**6/80 + g**5/32 + 11*g**4/96 + g**3/16 + 6*g. Factor d(s).
-s*(s - 3)*(s + 1)*(3*s + 1)/8
Let r(s) be the third derivative of s**7/1575 - s**5/450 + 21*s**2. Suppose r(l) = 0. Calculate l.
-1, 0, 1
Let h be (-8)/4 + 0 + 6. Factor 6*n**3 + 3*n**2 + 3*n**h + 12 - 12.
3*n**2*(n + 1)**2
Let a(s) be the third derivative of s**11/33264 + s**10/9450 + s**9/30240 - s**8/5040 + s**5/60 - s**2. Let o(g) be the third derivative of a(g). Factor o(q).
2*q**2*(q + 1)**2*(5*q - 2)
Let s(j) be the third derivative of j**5/210 + j**4/42 + j**3/21 + 12*j**2. Factor s(m).
2*(m + 1)**2/7
Let y(o) be the second derivative of -1/2*o**5 + 0 + 3*o - 5*o**2 - 1/12*o**4 - 1/6*o**3. Let m(g) = g**3 + 1. Let a(c) = -22*m(c) - 2*y(c). Factor a(j).
-2*(j - 1)**2*(j + 1)
Let j(m) be the first derivative of -m**3/18 - m**2/3 - m/2 + 8. Factor j(y).
-(y + 1)*(y + 3)/6
Let d(p) be the second derivative of 0*p**3 + 4*p + 1/6*p**4 + 0*p**5 + 0 + 0*p**2 - 1/15*p**6. Factor d(f).
-2*f**2*(f - 1)*(f + 1)
Let t be ((-2)/31)/(40/(-20)). Let m = 277/62 + t. Factor -27/4 - m*o - 3/4*o**2.
-3*(o + 3)**2/4
Let i(w) be the second derivative of 1/54*w**4 + w - 1/9*w**3 + 0 + 2/9*w**2. Find o such that i(o) = 0.
1, 2
Let a(p) be the second derivative of -p**4/24 + 2*p**3/3 - 4*p**2 + 26*p. Find n, given that a(n) = 0.
4
Let w be 8/32 - 19/(-4). Solve 0 + p**2 + 0*p - p**3 + 3/4*p**w - 5/4*p**4 = 0.
-1, 0, 2/3, 2
Suppose -5*i = 3*z - z - 11, -3*z = -4*i - 28. Factor -4*c**2 - 16*c + 0*c + 4*c - z.
-4*(c + 1)*(c + 2)
Let q be (-60)/18*4/(-10). Solve 2/3*m + 2/3*m**3 + 0 + q*m**2 = 0 for m.
-1, 0
Let q(h) be the second derivative of h**5/16 + 5*h**4/12 + 5*h**3/6 - 72*h. Let q(y) = 0. Calculate y.
-2, 0
Let u be (-136)/(-6)*18/4. Solve -d**5 - 81*d**4 - 14*d**5 + 3*d**2 - 111*d**2 - 252*d**3 + u*d**3 - 24*d = 0.
-2, -1, -2/5, 0
Let n be (2/24)/((-1)/(-8)). Factor n - 10/3*l - 2/3*l**5 - 20/3*l**3 + 20/3*l**2 + 10/3*l**4.
-2*(l - 1)**5/3
Factor -2/9*h - 4/9*h**4 + 0 + 2/9*h**5 + 4/9*h**2 + 0*h**3.
2*h*(h - 1)**3*(h + 1)/9
Let j be (-6)/(-3 + (-1 - -2)). Solve r**j + r - r - 3*r + r + r**2 = 0 for r.
-2, 0, 1
Suppose -19*r + 4*r = 0. Let p(z) be the second derivative of -1/3*z**4 - 3*z + r*z**2 + 1/10*z**5 + 0 + 1/3*z**3. Factor p(x).
2*x*(x - 1)**2
Let h(n) = 90*n**5 - 88*n**4 - 4*n**3 + 20*n**2 + 4*n - 4. Let w(z) = -90*z**5 + 87*z**4 + 5*z**3 - 19*z**2 - 3*z + 3. Let b(p) = 3*h(p) + 4*w(p). Factor b(c).
-2*c**2*(3*c - 2)**2*(5*c + 2)
Suppose 0 = 2*q + q. Suppose q = 4*o - 20 + 4. Factor 2*i**o + 6*i**3 - i**3 - 3*i**3 - 6*i**2 - 2*i - 1 + 5.
2*(i - 1)**2*(i + 1)*(i + 2)
Suppose 2*i + 0 + 5/2*i**3 + 6*i**2 = 0. Calculate i.
-2, -2/5, 0
Let y(m) be the first derivative of m**3 - 9*m**2/2 + 6*m + 14. Find g, given that y(g) = 0.
1, 2
Let n(p) be the first derivative of -p**5/40 - p**4/24 - p - 1. Let x(b) be the first derivative of n(b). What is w in x(w) = 0?
-1, 0
Let w(k) = -4*k**3 - 7*k**2 - 2*k + 1. Let o(b) be the second derivative of b**5/20 + b**4/6 + b**3/6 + 3*b. Let s(m) = 14*o(m) + 4*w(m). Factor s(u).
-2*(u - 2)*(u + 1)**2
Factor -2*w - 1/3*w**2 + 7/3.
-(w - 1)*(w + 7)/3
Let d be -5*(2 - (-26)/(-10)). Let a(p) be the third derivative of 1/480*p**6 - 1/24*p**d + 1/32*p**4 + 0*p - 1/80*p**5 + 0 - p**2. Factor a(m).
(m - 1)**3/4
Let a(c) be the second derivative of -c**4/72 + c**3/18 - 7*c. Find p, given that a(p) = 0.
0, 2
Let r(p) = 17*p**2 - 9*p. Let c(d) = -d**2 + d. Let l(x) = 5*c(x) + r(x). Let l(u) = 0. What is u?
0, 1/3
Let g(j) be the third derivative of 0*j - 3*j**2 + 0*j**5 + 1/28*j**4 - 1/420*j**6 + 0 + 2/21*j**3. Factor g(k).
-2*(k - 2)*(k + 1)**2/7
Let q(j) = -5*j**4 + j**3 + 14*j**2 - 4*j + 2. Let o(g) = -6*g**4 + g**3 + 15*g**2 - 4*g + 3. Let y(n) = -4*o(n) + 6*q(n). Factor y(c).
-2*c*(c - 2)*(c + 2)*(3*c - 1)
Let f(a) be the first derivative of -a**6/720 + a**5/120 - a**3/3 - 3. Let u(h) be the third derivative of f(h). Factor u(q).
-q*(q - 2)/2
Let z(q) be the second derivative of -q**6/345 - 2*q**5/115 - q**4/23 - 4*q**3/69 - q**2/23 - 24*q. Let z(w) = 0. What is w?
-1
Let f = -2561/6 + 428. Let q(i) be the first derivative of 1/3*i**2 - 8/9*i**6 + 22/9*i**3 - 2/3*i + f*i**4 - 4/3*i**5 + 3. Suppose q(d) = 0. What is d?
-1, -1/2, 1/4, 1
Let 0*i**3 + 2*i**3 - 17*i + 35*i