uppose -5*p + 12 = -11*p. Let l(w) = 16*w**2 - 20*w. Let q(j) be the second derivative of -5*j**4/12 + 7*j**3/6 + 2*j. Let y(r) = p*l(r) - 7*q(r). Factor y(a).
3*a*(a - 3)
Let y(z) be the first derivative of -5*z**3/6 + 15*z**2/4 + 6. What is u in y(u) = 0?
0, 3
Suppose 0 = -5*d + 144 - 39. Suppose d*u - 25*u = 0. Factor -2/5*p**4 + 0 + u*p**2 - 2/5*p**5 + 0*p + 0*p**3.
-2*p**4*(p + 1)/5
Let m(p) be the second derivative of -3*p**5/140 + p**4/14 - p**3/14 + 9*p. Factor m(o).
-3*o*(o - 1)**2/7
Let t = -6 - -6. Let g(z) be the third derivative of 0*z**5 + 2*z**2 + 0*z + t + 0*z**3 + 1/120*z**6 - 1/24*z**4. Factor g(a).
a*(a - 1)*(a + 1)
Let k(n) = 9*n**2 - 6*n - 6. Let i(d) = 10*d**2 - 6*d - 7. Let v(j) = -6*i(j) + 7*k(j). Determine z, given that v(z) = 0.
0, 2
Let o(q) be the first derivative of -6*q**5/5 - 5*q**4/4 + q**3/3 + 3*q - 4. Let w(d) = d**4 + d**3 - 1. Let y(l) = 2*o(l) + 6*w(l). Factor y(x).
-2*x**2*(x + 1)*(3*x - 1)
Let w(f) be the first derivative of -f**4/24 + 2*f**3/9 + f**2/12 - 2*f/3 - 22. Factor w(r).
-(r - 4)*(r - 1)*(r + 1)/6
Let y(q) be the second derivative of q**10/181440 + q**9/90720 - q**8/40320 - q**7/15120 + q**4/3 + 3*q. Let i(s) be the third derivative of y(s). Factor i(k).
k**2*(k - 1)*(k + 1)**2/6
Let c(j) be the second derivative of 4*j + 1/168*j**7 + 0 + 0*j**6 - 1/40*j**5 + 0*j**4 + 1/24*j**3 + 0*j**2. Suppose c(m) = 0. What is m?
-1, 0, 1
Let i be (-56)/(-16) - 2/(-4). Let f(o) be the first derivative of -4/39*o**3 + 0*o - 1/26*o**i - 1 - 1/13*o**2. What is j in f(j) = 0?
-1, 0
Let m(k) be the third derivative of 1/9*k**3 - 1/36*k**6 - 5*k**2 + 5/36*k**4 - 5/252*k**7 + 0 + 7/120*k**5 + 0*k. Suppose m(f) = 0. What is f?
-1, -2/5, 1
Let z(f) be the third derivative of -5*f**2 + 0*f - 1/10*f**5 + 0 - 1/3*f**3 + 1/4*f**4 + 1/60*f**6. Factor z(x).
2*(x - 1)**3
Let l be (2/(-4))/((-1)/2). Suppose 4*h = -l + 9. Factor -2/9*q**3 + 2/9*q**h + 0 + 0*q.
-2*q**2*(q - 1)/9
Factor 1/6*i**2 - 1/3*i + 1/6.
(i - 1)**2/6
Let v(r) = -r - r + 7*r**2 + 4*r - r. Let u(g) = -g**2 - g. Let y(x) = -5*u(x) - v(x). Solve y(m) = 0 for m.
0, 2
Let f(b) be the second derivative of b**5/110 - b**3/11 + 2*b**2/11 + 9*b. Determine n so that f(n) = 0.
-2, 1
Let j(y) be the second derivative of -y**6/30 - y**5/4 - 3*y**4/4 - 7*y**3/6 - y**2 - 12*y. Factor j(q).
-(q + 1)**3*(q + 2)
Let f(t) = 4*t**4 + 5*t**3 - 2*t**2 - 5*t. Let u(o) = 17*o**4 + 19*o**3 - 10*o**2 - 21*o. Let l(a) = -9*f(a) + 2*u(a). Factor l(d).
-d*(d + 1)*(d + 3)*(2*d - 1)
Let d(y) be the second derivative of -y**4/24 - y**3/12 - 6*y. Let d(n) = 0. Calculate n.
-1, 0
Let k(u) be the third derivative of u**7/4200 - u**6/900 - 7*u**5/600 - u**4/30 - 5*u**3/6 - 7*u**2. Let v(m) be the first derivative of k(m). Factor v(d).
(d - 4)*(d + 1)**2/5
Let g = -8/145 + 48/29. Suppose -4/5*n**3 + g*n**2 + 2/5*n**5 - 4/5 + 2/5*n - 4/5*n**4 = 0. What is n?
-1, 1, 2
Let k(j) be the third derivative of -j**6/120 + j**5/60 - j**4/24 + j**3/2 + 2*j**2. Let t be k(0). Solve -1/4*a**t + 0*a**2 + 3/4*a + 1/2 = 0 for a.
-1, 2
Let r be 4*(1 - (-2)/(-4)). Let i(u) = 3*u**3 - u**2 + u. Let m be i(1). Determine l so that -r*l**m - 9*l**2 + 5*l**2 + l - 3*l = 0.
-1, 0
Let z(h) be the second derivative of h**6/150 - h**5/50 + 7*h. Factor z(l).
l**3*(l - 2)/5
Let n = 1497/2 - 748. Factor 0 + 0*r - n*r**2.
-r**2/2
Let a(d) = -5*d**3 + 4*d**2 + 5*d + 4. Let s(q) = -q**3 + q**2 + q + 1. Let j(t) = a(t) - 4*s(t). Factor j(h).
-h*(h - 1)*(h + 1)
Let f(t) = -t**3 + 10*t**2 + 10*t + 11. Let n be f(11). Solve n*q + 1/5*q**3 - 1/5*q**2 + 0 = 0.
0, 1
Let t = 18 - 36. Let z be 69/27 + 4/t. Factor -2/3*g**2 - 5/3*g**4 + 0*g + 0 - z*g**3.
-g**2*(g + 1)*(5*g + 2)/3
Let k(l) be the first derivative of l**5/4 + 13*l**4/16 - l**3/2 - 5*l**2/2 + 2*l + 8. Determine c so that k(c) = 0.
-2, 2/5, 1
Let m(g) be the second derivative of 1/6*g**4 + 1/6*g**3 + 9*g - g**2 + 0 - 1/20*g**5. Determine r so that m(r) = 0.
-1, 1, 2
Let a(v) be the third derivative of 0*v + 1/50*v**5 + 0 - 1/300*v**6 + 1/15*v**3 - 1/20*v**4 - v**2. What is w in a(w) = 0?
1
Let u(i) = 6*i**4 + 10*i**3 + 8*i**2 - 4*i - 5. Let z(n) = -5*n**4 - 9*n**3 - 7*n**2 + 5*n + 4. Let c(v) = -4*u(v) - 5*z(v). Factor c(y).
y*(y - 1)*(y + 3)**2
Suppose 21*i**3 + 2*i**2 - 29*i**3 + 2*i**2 - 4*i**4 + 8*i = 0. Calculate i.
-2, -1, 0, 1
Let s be (0/(1/(-2)*2))/2. Let p(d) be the first derivative of 2 + 2/5*d**5 + s*d**3 - 2*d + 2*d**2 - d**4. What is r in p(r) = 0?
-1, 1
Let n(i) be the first derivative of -i**6/40 + 4*i**5/45 - 5*i**4/72 - i**3/9 + i**2/2 - 2. Let k(g) be the second derivative of n(g). Solve k(u) = 0.
-2/9, 1
Let y(k) be the first derivative of k**4 + 8*k**3/3 - 6*k**2 - 22. Determine v so that y(v) = 0.
-3, 0, 1
Factor -7 + 2 + 4*s**2 - 4*s - 3.
4*(s - 2)*(s + 1)
Let s(m) be the second derivative of -5*m**7/42 + 3*m**5/4 - 5*m**4/6 + 18*m. Factor s(x).
-5*x**2*(x - 1)**2*(x + 2)
Let k(u) be the first derivative of 3 + 1/7*u**2 + 0*u**3 + 0*u - 1/14*u**4. Factor k(l).
-2*l*(l - 1)*(l + 1)/7
Let h(t) be the second derivative of t**7/1260 - t**5/180 + t**3 + 3*t. Let y(s) be the second derivative of h(s). Factor y(z).
2*z*(z - 1)*(z + 1)/3
Let f(i) be the second derivative of i**5/70 + 5*i**4/42 + 37*i. Factor f(w).
2*w**2*(w + 5)/7
Let i(n) be the first derivative of n**5/10 - 3*n**4/8 + n**3/6 + 3*n**2/4 - n + 2. Solve i(s) = 0.
-1, 1, 2
Suppose 0 = -19*t + 24*t. Solve -2/3*v**4 + 2/3*v - 2*v**2 + 2*v**3 + t = 0 for v.
0, 1
Let d(y) = 5*y - 25. Let l(m) = -m + 5. Let t(w) = 2*d(w) + 11*l(w). Let x be t(0). Factor 2*j**3 + j**4 + j**5 - 5*j**4 + j**x.
2*j**3*(j - 1)**2
Let k(b) be the second derivative of -b**6/55 + 7*b**5/55 - 10*b**4/33 + 8*b**3/33 - 5*b. Suppose k(d) = 0. What is d?
0, 2/3, 2
Factor 0 - 1/3*a**2 + 1/6*a**3 + 1/6*a.
a*(a - 1)**2/6
Let h(z) be the second derivative of -5*z**4/24 - 5*z**3/12 + 5*z**2/2 + 10*z. Determine l so that h(l) = 0.
-2, 1
Factor -50*g**2 - 135*g**4 + 50*g**2 - 10*g**3.
-5*g**3*(27*g + 2)
Let b = -2/499 + 60389/2495. Factor -4/5 - 44/5*a - b*a**2.
-(11*a + 2)**2/5
Let q(z) be the first derivative of z**4/10 - 4*z**3/5 + z**2 + 67. Factor q(j).
2*j*(j - 5)*(j - 1)/5
Let m(w) be the third derivative of -w**6/40 - w**5/10 - w**4/8 + 7*w**2. Let m(l) = 0. Calculate l.
-1, 0
Let i(h) be the first derivative of -h**5/90 - h**4/18 + h**2/2 + 1. Let b(w) be the second derivative of i(w). Let b(j) = 0. Calculate j.
-2, 0
Let q(r) = -2*r + 6. Let z be q(-5). Let d be -4*(-4)/(z/3). Factor -b**2 + d*b**2 + b - b**5 - 2*b**4 + 0*b.
-b*(b - 1)*(b + 1)**3
Let l be -6*((-2)/(-1))/(-6). Suppose 0*p - 84 = -l*p. Factor -10*i**2 - 4 + 27*i**2 + 30*i**2 - 6*i + p*i**3 - 7*i**2.
2*(i + 1)*(3*i - 1)*(7*i + 2)
Let d(w) be the first derivative of -w**6/30 + 2*w**5/25 + w**4/20 - 2*w**3/15 + 42. Find b such that d(b) = 0.
-1, 0, 1, 2
Let z = -7 + 15. Suppose 4*k + 7*v - 13 = 2*v, -5*k + 2*v + z = 0. Solve 2/3*n - 4/9 - 2/9*n**k = 0.
1, 2
Suppose 5*r = 4*i - 19, -5*r = -i + 5*i + 11. Let u be (5/10)/((-1)/r). Factor -27/4*o**2 - u*o + 0.
-3*o*(9*o + 2)/4
Let x(c) be the first derivative of c**6/51 - 6*c**5/85 + 3*c**4/34 - 2*c**3/51 - 5. Factor x(l).
2*l**2*(l - 1)**3/17
Suppose -a + 4*m - 18 = 0, a + m + 2 - 9 = 0. Determine z, given that -z**2 - 3*z**a - 2*z + 2*z**2 = 0.
-1, 0
Suppose 3*a = -5*g + 27, -3*g - 1 = -3*a + 2. Suppose f = a*f - 6. Factor n**2 - f*n**2 + 1 - 2*n + 2*n**2.
(n - 1)**2
Let j = 1 + -3/4. Let h(r) be the first derivative of -j*r**3 + 1/2*r + 5/8*r**2 - 1. Determine t, given that h(t) = 0.
-1/3, 2
Let u be (-1)/((-10)/30 - (-2)/(-12)). Solve -2/7*d - 2/7*d**3 + 0 - 4/7*d**u = 0.
-1, 0
Let m(n) be the first derivative of 3*n**5/25 - 3*n**4/20 - n**3/5 + 3*n**2/10 + 4. What is w in m(w) = 0?
-1, 0, 1
Let q = -5 + 8. Let g(a) be the first derivative of 2/7*a**2 + 2 + 2/21*a**q + 2/7*a. Factor g(u).
2*(u + 1)**2/7
Let u(g) = -g + 11. Let z be u(5). Let 3/2*i**3 + 15/2*i**2 + z + 12*i = 0. Calculate i.
-2, -1
Let f(l) be the third derivative of l**6/80 + l**5/40 - l**4/4 - l**3 + 35*l**2. Suppose f(g) = 0. Calculate g.
-2, -1, 2
Let h(q) = 0 + 7*q**2 - 4 - 4*q + q. Let c(m) be the second derivative of m**4/3 - m**3/3 - m**2 - m. Let b(f) = -11*c(f) + 6*h(f). Factor b(a).
-2*(a - 1)**2
Let s(i) be the first derivative of