x**4 - 10*x**3 + 4*x**2 + 6*x + 7. Let s(u) = 3*t(u) - 21*y(u). Factor s(q).
-3*q*(q + 1)**3
Let 7*o**3 - 8*o**4 - 88*o**2 - 2*o**5 + 87*o**2 - 14*o**5 = 0. Calculate o.
-1, 0, 1/4
Suppose 0 = k + 5*h - 15, 6 = 3*h - 3. Let l(y) be the second derivative of 1/4*y**4 + 0 + k*y**5 - y + 0*y**2 + 1/3*y**3 - 1/30*y**6. Factor l(b).
-b*(b - 2)*(b + 1)**2
Let n(z) be the second derivative of -z + 0 + 0*z**2 + 1/24*z**3 - 1/12*z**6 + 3/20*z**5 + 1/56*z**7 - 1/8*z**4. Determine x, given that n(x) = 0.
0, 1/3, 1
Suppose t - 4 = j, -j - 10 = j - 4*t. Let y be (-75)/(-12) + -3 + j. Let 0*m - y*m**2 + 0 = 0. Calculate m.
0
Let r = 37/4 - 9. Solve -r*i**2 + 1/4 - 1/4*i**3 + 1/4*i = 0.
-1, 1
Find t, given that -18/5 - 3*t + 3/5*t**2 = 0.
-1, 6
Let j = 3280/11 + -298. Solve -j*l**2 + 4/11 - 2/11*l = 0.
-2, 1
Let w(r) be the third derivative of 0*r**4 + 0*r**5 + 0 + 5*r**2 + 0*r**3 - 1/30*r**6 + 0*r. Let w(z) = 0. Calculate z.
0
Let i(n) be the third derivative of -1/20*n**5 + 0*n - 2*n**2 + 0 - 1/40*n**6 + 1/8*n**4 + 1/2*n**3. Determine v, given that i(v) = 0.
-1, 1
Suppose 2*h - h - 15 = 4*f, -9 = -4*h - f. Let p(d) = 37*d**2 + 77*d - 19. Let l(c) = 18*c**2 + 39*c - 9. Let r(n) = h*p(n) - 5*l(n). Factor r(w).
3*(w + 2)*(7*w - 2)
Let k(s) be the third derivative of -1/27*s**3 - 4*s**2 + 0 + 1/270*s**5 + 0*s**4 + 0*s. Factor k(f).
2*(f - 1)*(f + 1)/9
Let l(o) = -2*o + 26. Let d be l(11). Let t(p) be the second derivative of 1/12*p**d - 1/18*p**3 + 0*p**2 + 3*p + 1/90*p**6 + 0 - 1/20*p**5. Factor t(k).
k*(k - 1)**3/3
Let k(v) be the second derivative of -v**4/24 - v**3/12 + v**2/2 + 12*v. Factor k(w).
-(w - 1)*(w + 2)/2
Suppose -8*q = -5*q - 3. Solve -q + 1/2*g**2 + 1/2*g = 0 for g.
-2, 1
Find q such that 36 - 4*q**2 + q**2 + 3*q**3 - 533*q + 509*q = 0.
-3, 2
Determine r, given that 15 + 143*r + 3*r**2 - 249*r + 130*r - 6*r**3 = 0.
-1, 5/2
Suppose 0*d + 2*d = 0. Let n be 6*(3/6 - d). Factor -n*z - 1 - 2*z**2 - z**3 + 0*z**3 - z**2 + 0*z**2.
-(z + 1)**3
Let l = -145 - -147. Solve -10/7*q**l + 8/7*q + 2/7 = 0.
-1/5, 1
Suppose 0 = -l + 2. Factor 0*h**3 + 0*h**l - 4 + 0*h**2 - 5*h**2 - h**3 - 8*h.
-(h + 1)*(h + 2)**2
Suppose -2*j - 4*p - 12 = 0, -4*j - p - 1 = -3*j. What is q in -q**j + 0*q**4 + 3*q**4 - 2*q**5 = 0?
0, 1
Let f(y) = y**3 - 2*y**2 - 11*y - 3. Let d be f(-2). Factor 2/3*u**5 - 4/3*u**d - 2/3*u**4 - 2/3 + 4/3*u**2 + 2/3*u.
2*(u - 1)**3*(u + 1)**2/3
Determine v, given that -15/2*v**2 + 9/2*v + 27/2 + 3/2*v**3 = 0.
-1, 3
Let j(y) = -y**2 - 11. Let u(h) = 1. Let t(b) = 4*j(b) + 44*u(b). Factor t(g).
-4*g**2
Let v(m) = -m**2 + m + 1. Let z(r) = 5*r**2 - 9*r - 8. Let k(p) = 30*v(p) + 5*z(p). Factor k(s).
-5*(s + 1)*(s + 2)
Solve 2/5*i + 0 - 2/5*i**3 + 2/5*i**2 - 2/5*i**4 = 0.
-1, 0, 1
Let p(q) = 3*q**2 + 5*q. Let z(h) = -3*h**2 - 6*h. Let r(b) = 5*p(b) + 4*z(b). Suppose r(s) = 0. What is s?
-1/3, 0
Let q = -21 + 5. Let x be (-44)/q - (-2)/8. Factor 0 + 0*f + 2/5*f**x + 2/5*f**2 - 2/5*f**4 - 2/5*f**5.
-2*f**2*(f - 1)*(f + 1)**2/5
Factor 82*t + 78*t - 140*t + 4*t**2.
4*t*(t + 5)
Let n(v) be the third derivative of v**5/660 - 5*v**4/132 + 25*v**3/66 + 24*v**2. Find b, given that n(b) = 0.
5
Let o(k) = 3*k**3 + 2*k**2 + k - 2. Let z(b) = 7*b**3 + 5*b**2 + 3*b - 5. Let i(p) = -5*o(p) + 2*z(p). What is g in i(g) = 0?
-1, 0, 1
Let u(b) be the second derivative of -1/12*b**4 - b + 0 - 1/6*b**3 + b**2. Determine r so that u(r) = 0.
-2, 1
Let y(l) = -98*l**4 + 140*l**3 + 99*l**2 + 16*l. Let c(x) = -49*x**4 + 70*x**3 + 49*x**2 + 8*x. Let h(q) = -5*c(q) + 3*y(q). Let h(p) = 0. What is p?
-2/7, 0, 2
Let b be 3/(87/6 - 1). Let x(d) = d**3 - 3*d**2 + d - 1. Let q be x(3). Solve 2/3*i**q + b + 2/9*i**3 + 2/3*i = 0.
-1
Let t(b) = -b**4 + b**3 + b**2 - b - 1. Let z(s) = -4*s**4 + 4*s**3 + 2*s**2 - 7. Let q(g) = 5*t(g) - z(g). Suppose q(d) = 0. Calculate d.
-2, 1
Let w = -14 + 26. Factor -7 + 0 - 4*l**2 - 2 + l**2 + w*l.
-3*(l - 3)*(l - 1)
Let s = -28 + 17. Let g(y) = -5*y**2 + 2*y - 5. Let k(f) = -9*f**2 + 4*f - 9. Let m(w) = s*g(w) + 6*k(w). Factor m(t).
(t + 1)**2
Let a = 100/693 - -6/77. Let j(y) be the first derivative of -1/27*y**6 + 2/9*y**5 + 14/27*y**3 - a*y**2 + 0*y - 1/2*y**4 + 1. Factor j(c).
-2*c*(c - 2)*(c - 1)**3/9
Let v(k) be the second derivative of 2*k**6/135 + k**5/45 - 2*k**4/27 - 7*k. Factor v(r).
4*r**2*(r - 1)*(r + 2)/9
Let a(n) = -11*n**2 + 3*n - 2. Let r be a(1). Let t be r/(-7) - 4/14. Factor 2/7*g**2 + 8/7*g + t.
2*(g + 2)**2/7
Let h = 113/270 + -1/54. Suppose -2*g + 0*g = -5*q + 23, 4*q - 5*g - 15 = 0. Factor -4/5*u**4 + 0 + 2/5*u + 4/5*u**2 + 0*u**3 - h*u**q.
-2*u*(u - 1)*(u + 1)**3/5
Let o be (-3 + (-52)/(-8))*(-5)/(-35). Let 1/2*y**2 - y + o = 0. Calculate y.
1
Let u(b) = b**5 + b + 1. Let z(w) = -4*w**5 + 2*w**4 - 4*w**3 - 4*w**2 - 4*w - 4. Let j = -4 - -5. Let p(c) = j*z(c) + 6*u(c). Factor p(a).
2*(a - 1)**2*(a + 1)**3
Suppose -30 = -4*r - 14. Let x(n) be the first derivative of -1 + 1/7*n**2 + 3/14*n**r - 2/35*n**5 - 2/7*n**3 + 0*n. Solve x(f) = 0 for f.
0, 1
Let n(w) be the second derivative of -2/15*w**5 - 5/18*w**4 - 1/9*w**3 + 0*w**2 + 6*w + 0. Factor n(r).
-2*r*(r + 1)*(4*r + 1)/3
Let n(k) be the first derivative of k**6/30 - 2*k**5/25 + 2*k**3/15 - k**2/10 + 6. Find m, given that n(m) = 0.
-1, 0, 1
Let g(i) be the first derivative of i**6/6 + 19*i**5/5 + 65*i**4/2 + 350*i**3/3 + 125*i**2/2 - 625*i + 21. Factor g(y).
(y - 1)*(y + 5)**4
Suppose -2*f + 37 = r, 3*f = -r - 0*r + 53. Let p be 54/10 + f/(-40). Suppose -65/4*i**3 + 0 - 45/4*i**p - 1/2*i + 19/4*i**2 + 93/4*i**4 = 0. What is i?
0, 1/3, 2/5, 1
Let s = 9/10 + -13/20. Determine t so that 1/4*t - 1/2*t**2 + 0 + s*t**3 = 0.
0, 1
Suppose 0 = 3*a - 7 - 8. Suppose 15 = a*h - 0*h. Find w such that w**3 + h*w**2 - 4*w**2 - 5*w**4 - w + 6*w**4 = 0.
-1, 0, 1
Let p be 2 - (2 - 9/3). Solve -3*b**p + 6*b**2 + 1 + 27*b - 7 - 24*b = 0 for b.
-1, 1, 2
Factor 4*p + 0*p**2 - 9*p + 5*p**2 + 0*p.
5*p*(p - 1)
Factor 0*q**2 + q**2 - 9*q - 3 + 0*q**2 - 3*q**3 - 10*q**2.
-3*(q + 1)**3
Let o(d) be the third derivative of d**4/12 + 2*d**3/3 + 2*d**2. Let p be o(-2). Let -2/3*j + p*j**3 + j**2 - 1/3*j**4 + 0 = 0. Calculate j.
-2, 0, 1
Let 0 - 2/5*j**3 + 4/5*j**2 + 0*j = 0. What is j?
0, 2
Suppose -2*o = -5*c - 4 - 13, 3*o + 9 = -4*c. Let s be (-1 - o) + 2 - -2. Let -2*v**s + 2*v**2 - v - v**2 = 0. What is v?
-1, 0
Suppose 2*p - 2*u + 4 = -p, 2*u = 4. Let n(l) be the first derivative of -1/2*l**4 + 0*l + 0*l**2 - 2 + p*l**3. Determine j, given that n(j) = 0.
0
Let l(w) be the second derivative of -w**5/50 - w**4/10 + w**3/15 + 3*w**2/5 - 8*w. Suppose l(f) = 0. What is f?
-3, -1, 1
Factor -2/7*h**2 + 4/7 - 2/7*h.
-2*(h - 1)*(h + 2)/7
Let w(l) = 23*l**2 - 220*l + 1197. Let z(v) = 11*v**2 - 110*v + 599. Let u(c) = 6*w(c) - 13*z(c). Find t, given that u(t) = 0.
11
Let r(t) be the second derivative of t**7/63 + 7*t**6/45 + 7*t**5/15 + 4*t**4/9 - 42*t. Let r(v) = 0. What is v?
-4, -2, -1, 0
Factor 14/9 + 2/9*c**2 - 16/9*c.
2*(c - 7)*(c - 1)/9
Let t = 269 - 1341/5. Solve -2/5*u**2 - 2/5*u + t = 0 for u.
-2, 1
Let h(s) = -4 + 5 - s + 0 + 6. Let k be h(5). Determine m so that -4/5 - 2/5*m**k - 6/5*m = 0.
-2, -1
Suppose 2*w + 24 = -6. Let y be (-9)/w + 1/(-5). Find u such that 0 - 6/5*u**3 - 6/5*u**2 - y*u - 2/5*u**4 = 0.
-1, 0
Let y(q) be the third derivative of -q**8/47040 - q**7/3920 - q**6/840 + q**5/15 - 4*q**2. Let j(z) be the third derivative of y(z). Factor j(w).
-3*(w + 1)*(w + 2)/7
Let d = 11 - 9. Suppose 0*l + 6 = -d*f - 2*l, -5*f - 6 = 2*l. Factor -4/5*g**3 + 2/5*g + 2/5*g**5 + 0 + f*g**4 + 0*g**2.
2*g*(g - 1)**2*(g + 1)**2/5
Suppose -3*m = -2*x - 6, -x + 6 = -m - 3*x. Factor 18/7*h**2 + 32/7*h**4 + 48/7*h**3 + m + 2/7*h.
2*h*(h + 1)*(4*h + 1)**2/7
Let p(w) = -w**3 + 7*w**2 - 3*w - 9. Let s(o) = -3*o**3 + 22*o**2 - 9*o - 27. Let r(m) = 14*p(m) - 4*s(m). Factor r(f).
-2*(f - 3)**2*(f + 1)
Let r(j) = 5*j + 4. Let m be r(-4). Let q = 91 + m. Find p, given that 125/2*p**3 + q*p**2 + 30*p + 4 = 0.
-2/5
Let t(i) be the second derivative of 5/28*i**4 - 1/7*i**3 + 0*i**2 - i + 3/20*i**5 + 0. Factor t(m).
3*m*(m + 1)*(7*m - 2)/7
Let z(v) be the first derivative of -49*v**4/38 + 182*v**3/19 - 144*v**2/19 + 40*v/19 + 9. What is k in z(k) = 0?
2/7, 5
Let q(m) be the second derivative of -m**8/7560 + m**6/540 + m*