et y(k) be the first derivative of -2/5*k + 2/15*k**3 + 0*k**2 - 2. Factor y(j).
2*(j - 1)*(j + 1)/5
Let r(i) be the third derivative of 0*i**3 - 1/270*i**5 + 0 + 4*i**2 + 0*i - 1/945*i**7 + 0*i**4 + 1/270*i**6. Factor r(h).
-2*h**2*(h - 1)**2/9
Let f(u) be the second derivative of 0*u**4 + 1/30*u**5 - 1/9*u**3 + 2*u + 0*u**2 + 0. Factor f(i).
2*i*(i - 1)*(i + 1)/3
Let f(a) = 15*a**2 - 5*a + 5. Let b(d) = -23*d**2 + 7*d - 8. Let k(p) = 5*b(p) + 8*f(p). Factor k(z).
5*z*(z - 1)
Let k = -2 + 5. Suppose 0 = 4*y + 5*g + 7, g + 12 = k*y - g. Find j such that 2/3*j**y + 2/3*j + 0 = 0.
-1, 0
Let k = 1009/4 + -251. Determine p so that k*p**3 + 1/4*p + 1/2 - 2*p**2 = 0.
-2/5, 1
Let f(x) be the third derivative of x**9/272160 - x**8/15120 + x**7/1890 - x**6/405 - x**5/15 - 6*x**2. Let n(u) be the third derivative of f(u). Factor n(w).
2*(w - 2)**3/9
Suppose 0 = -i - i + 24. Suppose t = -2*t + i. Solve 2*d**2 + d**2 + t*d - 4*d**2 - 3*d = 0 for d.
0, 1
Let b(r) be the first derivative of r**5/2 - 9*r**4/4 + 17*r**3/6 - 2*r + 5. Let b(a) = 0. What is a?
-2/5, 1, 2
Let g(i) be the third derivative of -i**7/945 + i**6/180 - i**5/90 + i**4/108 - 24*i**2. Let g(w) = 0. What is w?
0, 1
Let f(s) = -4*s**2 + 16*s - 8. Let j(n) be the second derivative of n**2/2 - 5*n. Let x(o) = -f(o) + 8*j(o). Factor x(h).
4*(h - 2)**2
Let l(w) be the first derivative of w**6/3 - w**4/2 - 24. Factor l(c).
2*c**3*(c - 1)*(c + 1)
Let q(a) be the second derivative of -1/105*a**7 + 0*a**4 + 1/75*a**6 + 0*a**3 + 0*a**5 + 0 + 0*a**2 + 2*a. Suppose q(c) = 0. Calculate c.
0, 1
Let u(t) = t**2 + 1. Let a be u(1). Factor 1/5 - 2/5*s**a + 0*s + 0*s**3 + 1/5*s**4.
(s - 1)**2*(s + 1)**2/5
Let h = 6 - 3. Factor -4*m**3 + 2*m**2 + 4*m**h + 2*m**3 + 0*m**3.
2*m**2*(m + 1)
Let p = 17 + -11. Suppose 0 = 4*q + 2*r - 6, p*q = 4*q + 4*r - 12. Suppose 0*a**2 + 6/7*a**4 + q + 2/7*a**3 + 0*a = 0. Calculate a.
-1/3, 0
Let o(j) be the second derivative of -j**5/180 + j**4/108 - 14*j. Solve o(i) = 0 for i.
0, 1
Let h(k) be the third derivative of -k**5/60 - k**4/8 + 9*k**2. Determine q, given that h(q) = 0.
-3, 0
Let d(k) be the second derivative of -3*k - 1/5*k**2 + 9/100*k**5 - 3/10*k**3 + 7/150*k**6 - 1/12*k**4 + 0. Factor d(t).
(t - 1)*(t + 1)**2*(7*t + 2)/5
Let h = -4/19 + 103/38. Let 2 + h*z**2 - 6*z = 0. What is z?
2/5, 2
Let p(n) = -3*n**2 - 36*n + 9. Let i(u) = 2*u**2 + 18*u - 5. Let l(x) = -9*i(x) - 5*p(x). Solve l(y) = 0.
0, 6
Let l(r) be the third derivative of -r**5/12 - 5*r**4/24 + 5*r**3/3 + 2*r**2. Find i such that l(i) = 0.
-2, 1
Let g(s) = 3*s**4 - s**3 - 3*s**2 + s. Let p(j) = j**4 - j**2. Let v(w) = -2*g(w) + 5*p(w). Find b such that v(b) = 0.
-1, 0, 1, 2
Let b(y) be the second derivative of -y**3 - 1/12*y**4 + 4*y - 9/2*y**2 + 0. Factor b(d).
-(d + 3)**2
Suppose 6*i + 2 = 14. Let 0*g**i + 0*g + 0 + 0*g**3 + 1/3*g**4 + 1/3*g**5 = 0. What is g?
-1, 0
Let n(k) = -k - 10. Let m be n(-11). Determine b, given that b - b**2 + m - 1 = 0.
0, 1
Let j(b) be the third derivative of b**5/100 - b**4/40 - b**3/5 + 4*b**2. Factor j(h).
3*(h - 2)*(h + 1)/5
Let c be (12*3/426)/4. Let a = 311/1278 - c. Factor a*g**4 - 2/9*g**2 - 2/9*g + 0 + 2/9*g**3.
2*g*(g - 1)*(g + 1)**2/9
Let -40*m**3 - 2*m**5 + 2*m**5 - 20*m**2 - 25*m**4 - 5*m**5 = 0. What is m?
-2, -1, 0
Let c be (3 - (-28)/(-10))*10. Factor l**4 - 16*l + l**2 + 15*l - 2*l**c + l**3.
l*(l - 1)*(l + 1)**2
Let p(r) be the third derivative of r**7/280 - r**6/45 + 7*r**5/120 - r**4/12 - r**3/3 - 2*r**2. Let b(x) be the first derivative of p(x). Factor b(v).
(v - 1)**2*(3*v - 2)
Determine r so that 8/3*r + 8/3 - 2/3*r**3 - 2/3*r**2 = 0.
-2, -1, 2
Let w(s) be the second derivative of -s**4/12 - s**3/3 - s**2/2 - 10*s. Factor w(n).
-(n + 1)**2
What is i in 12 - i**2 - 407*i - 3*i**2 + 415*i = 0?
-1, 3
What is q in -2*q**2 + 2006 + 2*q - 2006 = 0?
0, 1
Let d = 13 - 11. Let n(y) be the first derivative of 2/3*y**3 - 1 - y**4 + 0*y + y**d. Factor n(q).
-2*q*(q - 1)*(2*q + 1)
Find p such that 60*p + 15*p**3 - 99/2*p**2 - 3/2*p**4 - 24 = 0.
1, 4
Let s = -24 + 97/4. Let r(p) be the first derivative of 1/3*p**3 - 2 + 1/2*p**2 - s*p**4 - p. Factor r(d).
-(d - 1)**2*(d + 1)
Let y(w) be the third derivative of -w**6/600 + w**5/150 - w**4/120 + w**2. Factor y(x).
-x*(x - 1)**2/5
Let o = 65/8 + -61/8. Factor -o*u**2 - 1/2 + u.
-(u - 1)**2/2
Let g be 5/35 + (-202)/42 - -5. Let d be 0 + 4 + 2/(-1). Factor g*u**3 + u - 1/3 - u**d.
(u - 1)**3/3
Let q(w) be the second derivative of 5*w**4/12 + 10*w**3 + 90*w**2 - 16*w. Factor q(r).
5*(r + 6)**2
Let v = -7 + 9. Factor -2 - 6*b + 2*b - v*b**2 + 0.
-2*(b + 1)**2
Let u(h) = -h**3 + 2*h**2 + 2. Let o be u(2). Suppose -2*p**o - 2*p**2 - 16 + 16*p + 4 = 0. What is p?
1, 3
Let w = 4 + -4. Let h be 0/((-2 - -3) + -2). Solve h*v**2 + 1/3*v + w - 1/3*v**3 = 0.
-1, 0, 1
Let a(v) be the second derivative of 2*v**5/65 - 41*v**4/78 + 110*v**3/39 - 25*v**2/13 - v. Determine c, given that a(c) = 0.
1/4, 5
Let w(x) = x**3 + 8*x**2 + 7*x + 2. Let s be w(-7). Suppose q + s*q - 12 = 0. Factor -12*n**3 - 4*n**5 - 4*n**2 + 53*n**5 - 17*n**4 - 4*n**q - 12*n**3.
n**2*(n - 1)*(7*n + 2)**2
Let t(a) = -a**3 - 4*a**2 - 3*a + 2. Let c be t(-3). Suppose -x = -6*x. Factor -1/5*r**c + 1/5 + x*r.
-(r - 1)*(r + 1)/5
Let s = 42 + -40. Let u(c) be the first derivative of 1 + 2*c + 3*c**s + 2*c**3 + 1/2*c**4. Factor u(v).
2*(v + 1)**3
Let i(z) be the third derivative of -z**9/5040 - 3*z**8/2240 - z**7/420 - z**4/12 + z**2. Let f(m) be the second derivative of i(m). Find r such that f(r) = 0.
-2, -1, 0
Let t(h) = 13*h**3 - 15*h**2 - 2*h + 15. Let o(u) = 7*u**3 - 8*u**2 - u + 8. Let n(m) = -11*o(m) + 6*t(m). Factor n(d).
(d - 2)*(d - 1)*(d + 1)
Let h be (-4)/10*4 + (-4 - -6). Solve h*m**2 + 0 + 2/5*m**4 - 4/5*m**3 + 0*m = 0.
0, 1
Let o(y) = y + 2. Let l be o(-4). Let u(g) = 2*g**2 + 3*g + 2. Let w be u(l). Factor -2*z + 2*z**4 + w*z**2 - z**2 - 6*z**3 + 3*z**2.
2*z*(z - 1)**3
Let b(h) be the first derivative of h**5/40 - h**4/32 - h**3/12 - 64. Let b(n) = 0. Calculate n.
-1, 0, 2
Let a(x) be the second derivative of -3/40*x**5 + 0 + 0*x**2 + 0*x**4 + 1/56*x**7 + 0*x**6 + 3*x + 1/8*x**3. Suppose a(t) = 0. Calculate t.
-1, 0, 1
Let x be (-287)/(-70) - (-1 + 3). Let t = x - 8/5. What is j in j + t - j**3 - 1/2*j**4 + 0*j**2 = 0?
-1, 1
Let n(w) = -4*w**2 + w + 5. Suppose 0 = -b + 2*b + 7. Let c(h) = 9*h**2 - 2*h - 11. Let x(p) = b*n(p) - 3*c(p). Determine s so that x(s) = 0.
-1, 2
Determine q so that -6*q**3 + 3*q**4 - 2*q**2 - 9*q**3 - q**2 + 9*q**3 + 6*q = 0.
-1, 0, 1, 2
Let v(f) be the second derivative of -f**5/50 - 11*f. Factor v(h).
-2*h**3/5
Let j = 117/14 + -34/7. Let h = -3 + j. Determine f, given that h*f + 0 + 7/4*f**2 = 0.
-2/7, 0
Let a = 10 + -8. Factor -a*c**2 + 4*c**2 - 3*c**2.
-c**2
Let x(o) be the first derivative of 0*o**3 + 0*o**2 + 0*o + 1/3*o**6 - 4/5*o**5 + 1/2*o**4 + 2. Factor x(y).
2*y**3*(y - 1)**2
Let z(s) be the first derivative of 4/21*s**3 + 5/7*s**2 - 4/7*s - 5/14*s**4 - 1. What is g in z(g) = 0?
-1, 2/5, 1
Let j be (-350)/(-88) + 54/198. Factor -j*g - 10*g**2 - 1/2 - 4*g**3.
-(g + 2)*(4*g + 1)**2/4
Let g(x) = -x**5 - 9*x**4 + x**3 + 20*x**2 - 11*x + 11. Let r(c) = c**5 + 4*c**4 - c**3 - 10*c**2 + 6*c - 6. Let f(j) = 6*g(j) + 11*r(j). Factor f(v).
5*v**2*(v - 2)*(v - 1)*(v + 1)
Let u(q) = -3*q**3 + 12*q**2 + 3*q - 6. Let b = 29 + -35. Let n(i) = -5*i**3 + 23*i**2 + 6*i - 11. Let k(o) = b*n(o) + 11*u(o). Factor k(f).
-3*f*(f + 1)**2
Let k(r) be the second derivative of 0 - r**2 + r + r**3 - 1/3*r**4. Suppose k(o) = 0. What is o?
1/2, 1
Let j(c) be the second derivative of -c - 1/12*c**4 + 2/3*c**3 - 2*c**2 + 0. Factor j(u).
-(u - 2)**2
Let a(h) = -h**2 - 7*h - 2. Let t be a(-6). Let n(j) be the second derivative of 1/20*j**t - 9/10*j**2 + 1/5*j**3 + 0 + j. Factor n(k).
3*(k - 1)*(k + 3)/5
Let m(z) be the second derivative of z**6/30 + z**5/4 + 3*z**4/4 + 7*z**3/6 + z**2 + 22*z. Determine n so that m(n) = 0.
-2, -1
What is v in 0*v**3 - 55*v**4 - 3*v**2 + 52*v**4 - 8*v**3 + 2*v**3 = 0?
-1, 0
Let o(q) = -2*q**4 + 6*q**3 - 8*q**2 - 3*q + 4. Let h(l) = 3*l**4 - 11*l**3 + 15*l**2 + 6*l - 8. Let n(a) = 3*h(a) + 5*o(a). Factor n(v).
-(v - 1)**2*(v + 1)*(v + 4)
Let s(v) be the first derivative of -v**4/28 + v**3/7 + v**2/14 - 3*v/7 - 20. 