Solve 6*q - 45/4*q**2 - 1 + d*q**3 = 0.
1/3, 2/3
Let m be (-2)/(-8) - (-18)/(-180). Let d(n) be the first derivative of 0*n + 1/5*n**3 + 1/25*n**5 + 1/10*n**2 + m*n**4 + 3. Factor d(r).
r*(r + 1)**3/5
Let u(j) = -j**2 - j - 1. Let m(a) = 5*a**2 + a - 3. Let t(i) = m(i) + u(i). Factor t(z).
4*(z - 1)*(z + 1)
Factor 2/9*p - 2/9*p**3 + 2/9*p**2 + 0 - 2/9*p**4.
-2*p*(p - 1)*(p + 1)**2/9
Let f = -5 - -9. Suppose -3*a + a - f*i = -16, -3*a - i + 9 = 0. Factor 3*p**3 + 4*p**2 - 3*p**2 + p**4 + p + 2*p**a.
p*(p + 1)**3
Let p(b) = -19*b**2 - 1. Let u be p(-1). Let w be (-184)/u + 1/(-5). Suppose 9*k**3 + 3*k**4 + 3*k + 0 + w*k**2 + 0 = 0. Calculate k.
-1, 0
Let c = -6 - -6. Suppose c*w - 16 = -4*w. Let -41*u + u**w - u**5 - u**2 + 41*u + u**3 = 0. What is u?
-1, 0, 1
Let r(y) = 0 + 0 + 3 - 2*y - y**2. Let c = -20 + 17. Let k(v) = v**2 - 1. Let l(g) = c*k(g) - r(g). Find u such that l(u) = 0.
0, 1
Let r(m) be the first derivative of 0*m**2 + 1/10*m**4 - 1 + 0*m**3 + 0*m. Suppose r(s) = 0. What is s?
0
Suppose 4*p = -3*v + 3*p + 10, 2*v = -p + 7. Determine l so that -v*l**2 + 3*l**4 - 12*l**2 + 15*l - 6 - 3*l**3 + 3*l**2 + 3*l**2 = 0.
-2, 1
Let 7/3*a**4 + 3*a**2 - 5*a**3 + 0*a + 0 - 1/3*a**5 = 0. Calculate a.
0, 1, 3
Let z(q) be the third derivative of q**9/5040 + q**8/560 + q**7/175 + q**6/150 - 5*q**3/6 - 6*q**2. Let b(n) be the first derivative of z(n). Factor b(k).
3*k**2*(k + 1)*(k + 2)**2/5
Suppose 3*i + 4 = 5*i. Factor 0*p - 4/7*p**i + 0 - 2/7*p**3.
-2*p**2*(p + 2)/7
Suppose -s + 1 + 2 = 0. Let l be (-1 - s) + 8 + -1. Factor o**4 - l*o**3 + 13/4*o**2 - 3/2*o + 1/4.
(o - 1)**2*(2*o - 1)**2/4
Let t(u) = 5*u**2 - 11 - 11*u + 2*u**2 - u**2. Let v be (-24)/2 + 1/1. Let p(y) = -y**2 + 2*y + 2. Let h(k) = v*p(k) - 2*t(k). Let h(r) = 0. What is r?
0
Suppose 12 = 2*p + 4. Let k = -2 + p. Let 2 + t**k - 2 = 0. What is t?
0
Let t(y) be the second derivative of -3*y - 1/2*y**3 + 0 + 0*y**4 + 3/20*y**5 + 0*y**2. Factor t(r).
3*r*(r - 1)*(r + 1)
Suppose -2*f + 7 + 1 = 0. Let k(i) be the third derivative of 1/120*i**5 - 1/48*i**f - 3*i**2 + 0*i**3 + 0 + 0*i. Factor k(s).
s*(s - 1)/2
Factor 8/17*n + 2/17*n**2 + 6/17.
2*(n + 1)*(n + 3)/17
Let g(p) be the third derivative of p**7/84 + p**6/12 + p**5/4 + 5*p**4/12 + 5*p**3/12 - 3*p**2. Solve g(y) = 0.
-1
Let j = 37 + -32. Let h be -1*7*6/(-21). Factor -1/4*x**4 + 0*x + 1/4*x**3 + 0 + 1/4*x**h - 1/4*x**j.
-x**2*(x - 1)*(x + 1)**2/4
Factor 1 - 4 + 1 + v + 2*v**2 - v**2.
(v - 1)*(v + 2)
Let r = 17 - 14. Factor -r*j**2 - 13 + 13 - 3*j**3 + 3*j + 3*j**4.
3*j*(j - 1)**2*(j + 1)
Let c = 1303486/219 - 5952. Let h = c - -661/438. Factor -3/4*d**3 + 0 - h*d**2 - 3/4*d.
-3*d*(d + 1)**2/4
Let u(n) = -n**2 + 9*n. Let v(l) = 8*l**2 - 80*l. Let p(m) = 28*u(m) + 3*v(m). Factor p(t).
-4*t*(t - 3)
Let p(k) be the third derivative of 0 + 1/630*k**7 - 1/180*k**6 + 0*k**4 - k**2 + 0*k + 0*k**3 + 1/180*k**5. Factor p(y).
y**2*(y - 1)**2/3
Find l, given that 0*l - 5*l**3 + 20/3*l**4 - 5/3*l**5 + 0*l**2 + 0 = 0.
0, 1, 3
What is c in 2/3*c**2 - 2/3*c**4 - 2/3*c**3 + 2/3*c + 0 = 0?
-1, 0, 1
Let s be 7/((-7)/(-4))*(-3)/(-6). Let c(a) be the first derivative of -2/3*a**3 + 2*a**s - 2*a + 1. Factor c(z).
-2*(z - 1)**2
Let z(n) be the second derivative of -2*n**6/75 + 4*n**4/15 + 6*n. Solve z(m) = 0 for m.
-2, 0, 2
Suppose -4*u - 16 = -3*a, 4*u - 68 = -4*a - 0*u. What is d in 88/3*d**2 + 14/3*d**3 + a + 50*d = 0?
-3, -2/7
Let q(i) be the second derivative of i**4/12 - i**2/2 - i. What is z in q(z) = 0?
-1, 1
Suppose 0 = -5*u + 25, -5*d - 3*u = -7*u + 20. Factor -2/3*l**3 - 2/9*l**5 + d*l - 2/9*l**2 + 0 - 2/3*l**4.
-2*l**2*(l + 1)**3/9
Let c(x) be the third derivative of -x**9/2016 + x**7/560 + x**3/3 - 5*x**2. Let n(a) be the first derivative of c(a). Factor n(f).
-3*f**3*(f - 1)*(f + 1)/2
Let q(g) = -g**3 + 5*g**2 - 4*g + 2. Let v be q(4). Factor 2*z**4 - z**3 - 2*z**2 - v*z + 3*z**3 + 0*z**3.
2*z*(z - 1)*(z + 1)**2
Let q(p) be the second derivative of 0 + 11*p + 0*p**2 + 1/10*p**6 + 1/10*p**5 + 0*p**4 + 0*p**3 + 1/42*p**7. Suppose q(y) = 0. Calculate y.
-2, -1, 0
Factor 0 + 0*v**2 + 8/3*v - 2/3*v**3.
-2*v*(v - 2)*(v + 2)/3
Let s(i) be the second derivative of 3*i**5/20 - 32*i. What is j in s(j) = 0?
0
Let s(r) be the third derivative of -r**8/20160 - r**7/1260 - r**6/180 - 3*r**5/20 + 6*r**2. Let p(f) be the third derivative of s(f). What is n in p(n) = 0?
-2
Let g(b) be the first derivative of b**6/210 + 2*b**5/105 - b**4/42 - 4*b**3/21 - 3*b**2 + 9. Let r(t) be the second derivative of g(t). Solve r(y) = 0 for y.
-2, -1, 1
Let i = 2807/421 - 1/1263. Suppose -20*t**3 + i*t + 5/3 + 15*t**4 - 10/3*t**2 = 0. Calculate t.
-1/3, 1
Let w = -7783391/111 + 70120. Let f = 1/37 - w. Factor f*z - 2/9*z**3 + 4/9 + 0*z**2.
-2*(z - 2)*(z + 1)**2/9
Let p(m) = 3*m - 4*m - 2 - m**2 + 0. Let j(l) = -3*l**2 - 3*l - 3. Suppose 0 = -2*z + 4*z - 18. Let t(c) = z*p(c) - 4*j(c). Solve t(f) = 0 for f.
-2, 1
Let u(x) be the third derivative of x**8/672 - x**7/210 - x**6/48 + x**5/12 + x**4/12 - 2*x**3/3 + 29*x**2. Determine z, given that u(z) = 0.
-2, -1, 1, 2
Let s be 0*((-126)/(-140) - (-4)/(-10)). Factor 2/7*x**5 + 0*x + 0*x**3 + s*x**2 + 0 - 2/7*x**4.
2*x**4*(x - 1)/7
Factor -54*c**3 + 3 + 6*c**2 - 11 + 56*c**3.
2*(c - 1)*(c + 2)**2
Suppose -33 + 39 = 3*k. Let w(a) be the third derivative of 0 + 0*a**3 + 0*a - 1/180*a**5 - 1/72*a**4 - 3*a**k. Factor w(u).
-u*(u + 1)/3
What is g in -200/7 - 2/7*g**2 - 40/7*g = 0?
-10
Let l(m) = -3*m**2 + 15*m + 15. Let v(g) = -3*g**2 + 16*g + 15. Let u(r) = 4*l(r) - 3*v(r). Factor u(n).
-3*(n - 5)*(n + 1)
Let t(h) be the first derivative of 3 + 23/7*h**4 + 0*h - 4/5*h**5 - 80/21*h**3 + 8/7*h**2. What is f in t(f) = 0?
0, 2/7, 1, 2
Let y(n) be the third derivative of n**5/390 - n**3/39 - 31*n**2. Factor y(o).
2*(o - 1)*(o + 1)/13
Let f = -19/24 - -301/360. Let g(z) be the first derivative of 1 - 1/9*z**2 + f*z**5 + 0*z - 2/27*z**3 + 1/18*z**4. Factor g(o).
2*o*(o - 1)*(o + 1)**2/9
Let r(o) be the second derivative of -o**7/2520 + o**6/180 - o**5/30 - 5*o**4/12 - 4*o. Let n(v) be the third derivative of r(v). What is h in n(h) = 0?
2
Suppose 0 = -3*w + 5*n + 32, 3*w = -0*w - 3*n. Suppose -5*l - 15 = -5*j, -w*l + 3*j - 9 = l. Factor 3*k**2 + l + 4*k**3 + 2/3*k + 5/3*k**4.
k*(k + 1)**2*(5*k + 2)/3
Let g(r) be the second derivative of 1/30*r**3 + 0*r**2 + 4*r + 1/60*r**4 + 0. Suppose g(d) = 0. Calculate d.
-1, 0
Let t(i) = -2*i - 5. Let u be t(-4). What is k in 0 - 15*k**u - 2*k**2 + 0 - 16*k**5 + k - k**4 + 33*k**4 = 0?
-1/4, 0, 1/4, 1
Let k(w) be the first derivative of 2*w**3/63 - 2*w**2/21 + 31. Factor k(o).
2*o*(o - 2)/21
Let c(m) = -7*m**4 + 18*m**3 - 16*m**2 - 2*m + 2. Let x(a) = -15*a**4 + 35*a**3 - 30*a**2 - 5*a + 5. Let g(j) = -5*c(j) + 2*x(j). Find f such that g(f) = 0.
0, 2
Let x(n) be the first derivative of -n**4/3 + 2*n**3 - 9*n - 1. Let g(i) be the first derivative of x(i). Factor g(p).
-4*p*(p - 3)
Let k(p) = 3*p**3 + 17*p**2 + 22*p + 10. Let d(r) = 6*r**3 + 35*r**2 + 43*r + 19. Let c(l) = -2*d(l) + 5*k(l). Let c(t) = 0. Calculate t.
-2, -1
Let d(j) be the first derivative of -j**6/240 - j**5/480 + j**2/2 - 7. Let k(n) be the second derivative of d(n). Determine b, given that k(b) = 0.
-1/4, 0
Let g(v) = -v**3 - 4*v**2 + 3*v - 6. Let m be g(-5). Let p(j) be the second derivative of -2*j + 1/75*j**6 + 0*j**3 + 0 + 0*j**2 + 0*j**m + 0*j**5. Factor p(x).
2*x**4/5
Let a(l) = -2*l**3 - 21*l**2 + 13*l + 22. Let c be a(-11). Factor c + 0*p - 2/7*p**2.
-2*p**2/7
Suppose 0 = 9*p - 8*p - 2. Let o(v) be the second derivative of 0 - 1/40*v**5 + 1/2*v**p + 0*v**4 + 2*v + 1/4*v**3. Find d such that o(d) = 0.
-1, 2
Let k(r) be the third derivative of r**7/1785 - r**6/510 + r**5/510 + 3*r**2. Suppose k(m) = 0. Calculate m.
0, 1
Let k be 0/((0 + -5)*(-8)/(-20)). Let k + 2/3*i**2 + i**5 - 2/3*i**4 + 1/3*i - 4/3*i**3 = 0. What is i?
-1, -1/3, 0, 1
Factor -7*a + 7*a**3 - 24*a**2 + 3*a**5 + 6*a**4 - 19*a**3 + 7*a.
3*a**2*(a - 2)*(a + 2)**2
Let i(q) = 48*q**4 + 148*q**3 + 344*q**2 + 316*q + 112. Let m(x) = -7*x**4 - 21*x**3 - 49*x**2 - 45*x - 16. Let u(l) = 3*i(l) + 20*m(l). Factor u(h).
4*(h + 1)**2*(h + 2)**2
Determine r, given that -r**2 + 15*r - 9*r**2 - 9*r**2 + 14*r**2 = 0.
0, 3
Let t(r) = -r**3 + 2*r**2 - 2*r + 3. Let c be t(3). 