3. Let q(y) be the first derivative of 0*y + 1/4*y**2 - 5/12*y**u + 1 + 3/16*y**4. Factor q(x).
x*(x - 1)*(3*x - 2)/4
Suppose -5*t + 2 = -3. Let p be (t/(-3))/(2/(-18)). Factor k + p + k**3 + 2*k - 2 + 3*k**2.
(k + 1)**3
Let m(c) = 6*c**2 - 3. Let k(v) = -11*v**2 + v + 5. Let t(r) = 3*k(r) + 5*m(r). Factor t(w).
-3*w*(w - 1)
Let -80/3*k**3 + 0 + 55/3*k**2 + 35/3*k**4 - 10/3*k = 0. What is k?
0, 2/7, 1
Suppose 0 = 4*l - 20, -5*k + 33 = -k + 5*l. Factor 0*r + 4/9*r**k - 2/9*r**3 + 0 - 2/3*r**4.
-2*r**2*(r + 1)*(3*r - 2)/9
Factor -810*o**2 - 375 - 324*o**3 - 900*o - 243/5*o**4.
-3*(3*o + 5)**4/5
Let v(j) = -2*j + 40. Let m be v(21). Let p be (-57)/(-135) - m/(-10). Let -2/9*y**3 + p*y**2 + 4/9*y + 0 = 0. Calculate y.
-1, 0, 2
Let p(w) be the third derivative of 5*w**5/4 - 15*w**4/4 + 9*w**3/2 + 13*w**2. Factor p(y).
3*(5*y - 3)**2
Let d(r) = -r**3 - 7*r**2 + 5*r - 3. Let k = -5 - 1. Let n be 5/4*(2 + k). Let s(b) = b**3 + 13*b**2 - 9*b + 5. Let a(v) = n*d(v) - 3*s(v). Factor a(h).
2*h*(h - 1)**2
Let z(j) be the first derivative of -j**7/1680 + j**6/360 - j**5/240 + j**3 + 3. Let v(p) be the third derivative of z(p). Let v(i) = 0. What is i?
0, 1
Let h = -54 + 56. Factor 1/2*g**4 - g**h + 1/2 + 0*g + 0*g**3.
(g - 1)**2*(g + 1)**2/2
Let h(c) = -14*c**3 - 26*c**2 + 15*c - 2. Let r(i) = 1 + 0 - i**2 + i**3 - 1. Let u(f) = -2*h(f) + 4*r(f). Let u(g) = 0. What is g?
-2, 1/4
Let k(s) be the first derivative of s**4/4 - s**3 - s**2/2 + 3*s + 34. Factor k(y).
(y - 3)*(y - 1)*(y + 1)
Let y = -18 - -14. Let w(h) = -3*h**5 - 5*h**3. Let k(v) = 2*v**5 + 4*v**3. Let p(f) = y*k(f) - 3*w(f). Factor p(n).
n**3*(n - 1)*(n + 1)
Let x = 15 + -14. Let r(j) = -j**3 - j**2 + j + 1. Let u(p) = 7*p**3 - 9*p**2 + 9*p - 7. Let v(s) = x*u(s) + 3*r(s). Solve v(d) = 0.
1
Suppose 0 = -4*f + 8 + 16. Factor f*n + 3*n**3 + 15/2*n**2 + 3/2.
3*(n + 1)**2*(2*n + 1)/2
Suppose 20*t - 16*t = 12. Let r(v) be the second derivative of 1/75*v**6 + 1/5*v**2 + 1/15*v**t - 1/15*v**4 + 0 + 2*v - 1/25*v**5 + 1/105*v**7. Factor r(j).
2*(j - 1)**2*(j + 1)**3/5
Let j(f) be the third derivative of f**5/300 + f**4/60 - f**3/10 - f**2. Suppose j(x) = 0. What is x?
-3, 1
Let f(x) be the first derivative of -2*x**5/55 + x**4/11 - 2*x**3/33 - 6. Factor f(z).
-2*z**2*(z - 1)**2/11
Determine b so that -b - 2*b + b**4 - 3*b**2 - 3*b**3 + 2*b**4 + 6*b**3 = 0.
-1, 0, 1
Let q = 14 + -8. Let i be -1 + 3/q*2. Factor -2/3*x**4 + 0*x + 2/3*x**2 + i + 0*x**3.
-2*x**2*(x - 1)*(x + 1)/3
Suppose -p = 2*k - 4, 0*k - p - 4 = -2*k. Factor -2*w**2 + 11*w**k - 2*w**4 - w**4 - w - 5*w.
-3*w*(w - 1)**2*(w + 2)
Let c(d) be the third derivative of d**8/3080 - d**7/660 + d**6/396 - d**5/660 + 7*d**3/6 + 7*d**2. Let o(w) be the first derivative of c(w). Factor o(a).
2*a*(a - 1)**2*(3*a - 1)/11
Let n(k) be the third derivative of -k**7/525 + 2*k**5/25 + 4*k**4/15 - 18*k**2. Find r, given that n(r) = 0.
-2, 0, 4
Let i(r) = 3*r**3 - 3*r**2 + 2*r + 2. Let c(m) = 10*m**3 - 10*m**2 + 7*m + 7. Suppose -4*p + 16 = -8. Let s(u) = p*c(u) - 21*i(u). Solve s(w) = 0.
0, 1
Let y = -51 - -54. Factor 0 + 11/2*r**3 + y*r**4 - 9/2*r**5 - 2*r**2 - 2*r.
-r*(r - 1)**2*(3*r + 2)**2/2
Suppose 5*k + 27 = q, -3*q + 16 = -k + 5. Solve -2*r**q + 8 + 5*r**2 - 5*r**2 = 0.
-2, 2
Let x be ((-10)/(6 + -1))/(-1). Let 0 - 4/5*f - x*f**2 = 0. What is f?
-2/5, 0
Let i = -163 + 165. Suppose -3/5*c**i - 6/5*c + 0 = 0. Calculate c.
-2, 0
Suppose -2 = 3*l + 7. Let t be l/(-6) - 7/(-2). Suppose 0*m**3 + 5*m**2 + m**3 - 5*m**4 - m + t*m**4 - 4*m**2 = 0. What is m?
-1, 0, 1
Let s(t) = -34*t**3 - t**2 + 3*t - 1. Let o be s(1). Let c = 36 + o. Factor 2/3*y**2 - 2/3 + 2/3*y - 2/3*y**c.
-2*(y - 1)**2*(y + 1)/3
Suppose t - 2*t**2 + 0 - 5/4*t**3 = 0. What is t?
-2, 0, 2/5
Let o(v) be the second derivative of 2*v**6/15 + v**5/4 - 7*v**4/12 - v**3/3 + 8*v. Factor o(x).
x*(x - 1)*(x + 2)*(4*x + 1)
Let n(d) be the first derivative of d**5 - 5*d**4/2 + 5*d**2 - 5*d + 15. Factor n(v).
5*(v - 1)**3*(v + 1)
Let c(f) be the second derivative of f**7/1440 + f**6/576 - f**5/240 - f**4/4 - 2*f. Let m(k) be the third derivative of c(k). What is a in m(a) = 0?
-1, 2/7
Let w(p) = -p**3 - 6*p**2 - p. Let v(u) = -u**3 - u. Let j(y) = 2*v(y) + w(y). Factor j(a).
-3*a*(a + 1)**2
Suppose -3*g + 2*f = 3 - 17, g + 10 = -3*f. Suppose 0*x**2 + 0*x**g - 2*x**5 + 0*x**5 + 2*x**3 + 2*x**2 - 2*x**4 = 0. Calculate x.
-1, 0, 1
Let s(r) = 3*r**2 + 3*r + 2. Let q be s(-1). Find z, given that -8*z**2 - 2*z + q*z - 10*z - 4 - 2*z**3 = 0.
-2, -1
Let z be ((2 - 1) + 1)*3/18. Solve 1/6*d**2 - 1/2*d + z = 0.
1, 2
Let g(i) be the first derivative of -3 - 9*i - 1/3*i**3 + 3*i**2. Let g(t) = 0. Calculate t.
3
Let y(t) be the first derivative of -t**5/15 + t**4/6 - t**3/9 - 13. Determine f so that y(f) = 0.
0, 1
Let u(y) be the second derivative of -y**7/21 + y**6/15 + y**5/10 - y**4/6 + 9*y. Factor u(w).
-2*w**2*(w - 1)**2*(w + 1)
Let t(m) be the third derivative of m**8/252 - 2*m**7/63 + m**6/40 + 13*m**5/90 + m**4/9 + 22*m**2. Find h such that t(h) = 0.
-1/2, 0, 2, 4
Let w(g) be the third derivative of g**6/40 + 3*g**5/20 + 3*g**4/8 + g**3/2 - 41*g**2. Factor w(x).
3*(x + 1)**3
Let i(t) = t**3 - 4*t**2 + 5*t - 4. Let l be i(3). Suppose 0*v + 2*v = 4*w, 0 = 5*w - 15. Factor -d**2 - 6 - l*d + v.
-d*(d + 2)
Let s(w) = 2*w**2 + w - 1. Let y(g) = 2*g - 4. Let t be y(3). Let a be (-4 - 0)/t + 8. Let k(d) = 9*d**2 + 5*d - 4. Let l(f) = a*k(f) - 26*s(f). Factor l(i).
2*(i + 1)**2
Let q(x) be the third derivative of x**6/300 - x**5/30 - x**4/10 - 53*x**2. Factor q(c).
2*c*(c - 6)*(c + 1)/5
Let n(u) = 6*u**2 - 16*u + 16. Let q(g) = 2*g**2 - 5*g + 5. Let y be (-2 + 0 - 4)/(-2). Let b be -9 + -1*(-1 + 0). Let c(r) = b*q(r) + y*n(r). Factor c(i).
2*(i - 2)**2
Let b be 24/(-10)*(-10)/4. Suppose -2*w + b*o = 2*o + 4, 1 = -4*w + o. Factor -1/3*i**2 + w + 1/3*i.
-i*(i - 1)/3
Suppose 6*u - 4 = -4. Factor -2/3*q**2 + u*q + 2/3.
-2*(q - 1)*(q + 1)/3
Let p(x) = 10*x**5 + x**4 + 4*x**3 - x**2 + 7*x. Let u(o) = -3*o**5 - o**3 - 2*o. Let d(z) = -2*p(z) - 7*u(z). Factor d(i).
i**2*(i - 2)*(i - 1)*(i + 1)
Let i(y) be the second derivative of -y**4/12 - 3*y**3/2 - 5*y**2/2 - 2*y. Let o be i(-8). Factor -4*l**5 + l + 2*l**o - l + 2*l**5.
-2*l**3*(l - 1)*(l + 1)
Let g be 69/21 + 4/(-14). Let d be 1*(-6)/(-9)*g. Determine o so that o**2 - 2*o - 2*o + d*o = 0.
0, 2
Let f(o) be the third derivative of o**6/24 + o**5/12 - 5*o**4/24 - 5*o**3/6 - 5*o**2. Solve f(m) = 0 for m.
-1, 1
Let c be ((-52)/455)/(4/(-30)). Factor 6/7*a + 2/7*a**3 + 2/7 + c*a**2.
2*(a + 1)**3/7
Let m(c) be the first derivative of 2*c**3/3 + 3*c**2 - 9. Suppose m(d) = 0. Calculate d.
-3, 0
Solve -99/2*h**2 - 3/2*h**4 + 33/2*h**3 + 15/2*h + 75 = 0 for h.
-1, 2, 5
Find a such that -6*a**3 - 3*a**4 + 3*a**2 + 6*a - 63 + 63 = 0.
-2, -1, 0, 1
Suppose 3/7*d**2 + 30/7*d + 75/7 = 0. Calculate d.
-5
Let z be (-16)/28*(-21)/6. Let r(i) be the first derivative of 1/3*i**3 + 1/16*i**4 + 0*i + z + 1/2*i**2. Let r(c) = 0. Calculate c.
-2, 0
Suppose 18*y = -21*y + 117. Solve -2/3*s**5 + 0*s + 2*s**y - 4/3*s**2 + 0*s**4 + 0 = 0 for s.
-2, 0, 1
Let v(q) be the first derivative of -2 + 2/3*q**3 + q**2 - 4*q. Suppose v(u) = 0. What is u?
-2, 1
Let w(d) = d**2 - d - 1. Let y(u) = -4*u**2 + 12*u + 9. Let r(b) = -5*b**2 + 11*b + 9. Let l(p) = -4*r(p) + 3*y(p). Let o(s) = 2*l(s) - 18*w(s). Factor o(k).
-2*k*(k - 1)
Factor -8/9*a**3 + 2/3 - 32/9*a + 34/9*a**2.
-2*(a - 3)*(a - 1)*(4*a - 1)/9
Let g(r) be the first derivative of -2*r**5/5 - 2*r**4 - 4*r**3 - 4*r**2 - 2*r + 10. Let g(s) = 0. What is s?
-1
Let q(k) be the first derivative of -2*k**3/15 + 8*k/5 + 21. Determine a, given that q(a) = 0.
-2, 2
Let s = 372 + -6685/18. Let h = 1/18 + s. Solve 0 - 2/3*o**3 - 4/3*o**2 - h*o = 0 for o.
-1, 0
Let s be 2/8 - 3*(-3)/60. Factor -2/5*u**3 + 0*u + 0 + s*u**5 - 2/5*u**2 + 2/5*u**4.
2*u**2*(u - 1)*(u + 1)**2/5
Let w(s) be the third derivative of 0 + 1/6*s**4 - 1/30*s**6 + 1/105*s**7 - 1/30*s**5 + 0*s**3 - 3*s**2 + 0*s. Factor w(a).
2*a*(a - 2)*(a - 1)*(a + 1)
Let p(q) be the second derivative of q**4/3 - 16*q**3/3 + 32*q**2 - 10*q. Factor p(r).
4*(r - 4)**2
Let v(s) be the third derivative of 2*s**7/735 - 2*s**6/105 + s**5/21 - s**4/21 - 8*s**2. Suppose v(p) = 0. Calculate p.
0, 1, 2
Let x = -475 - -4