- 4*t**5 + 40*t**4/3 - 80*t**3/3 + 32*t**2 + 2*t. Factor u(f).
-2*(f - 2)**5
Suppose 5*q + 2*n = 11, q = n - 3*n - 1. Suppose -2*s + 2*a = -6, -15 = -2*s - q*s + a. Suppose -3*i**s - 7*i**4 + i**3 + 5*i**4 = 0. What is i?
-1, 0
Let y(p) be the third derivative of -p**8/70560 - p**7/17640 + 3*p**5/20 - 9*p**2. Let h(k) be the third derivative of y(k). What is j in h(j) = 0?
-1, 0
Suppose 7*t = t + 12. What is m in -8/5*m**4 + 8/5*m**3 - 2*m + 4/5*m**t + 2/5*m**5 + 4/5 = 0?
-1, 1, 2
Solve -44*k**2 - 22*k**5 + 42*k**4 + 23*k**4 + 30*k - 4 - 17*k**4 - 8*k**3 = 0 for k.
-1, 2/11, 1
Let g be (-7)/7 - (0 - 3). Let k = -2 + g. Factor 1/3*a**3 + k + 1/3*a - 2/3*a**2.
a*(a - 1)**2/3
Let x(w) be the third derivative of -1/48*w**4 + 0 - 7*w**2 - 1/12*w**3 + 1/120*w**5 + 1/240*w**6 + 0*w. What is m in x(m) = 0?
-1, 1
Let a(x) be the second derivative of x**5/40 - x**4/12 - x**3/3 + 2*x**2 - 3*x. Factor a(h).
(h - 2)**2*(h + 2)/2
Let s(l) be the third derivative of l**8/336 - l**7/168 + l**6/480 - 21*l**2. Let s(v) = 0. What is v?
0, 1/4, 1
Let l(n) = -6*n**3 + n. Let c(x) = -7*x**3 + x. Let t(u) = -5*c(u) + 6*l(u). Factor t(s).
-s*(s - 1)*(s + 1)
Let c(k) be the second derivative of -k**5/20 + 11*k**4/12 - 4*k**3 - 18*k**2 + 34*k. What is b in c(b) = 0?
-1, 6
Let k be (22/3)/(2/3). Suppose k*l = 6*l. Factor 4/7*u + 2/7*u**2 + l.
2*u*(u + 2)/7
Let a be 3/(-39)*-17 - 1. Determine q so that 6/13*q**2 + 10/13*q - 2/13*q**4 - 2/13*q**3 + a = 0.
-1, 2
Let g(z) = -5*z**4 - 15*z**3 - 9*z**2 + z. Let y(a) = -15*a**4 - 44*a**3 - 27*a**2 + 2*a. Let c(s) = 8*g(s) - 3*y(s). Factor c(m).
m*(m + 1)**2*(5*m + 2)
Suppose -4*r - 12 = -7*r. Let z be ((-28)/r)/(-2 + 0). Suppose -j**3 + 0 - 2*j**5 - 1/2*j**2 + 0*j + z*j**4 = 0. Calculate j.
-1/4, 0, 1
Determine d, given that -16/7 + 2/7*d**3 - 8/7*d + 4/7*d**2 = 0.
-2, 2
Let h(o) be the first derivative of o**6/8 + 9*o**5/20 + 3*o**4/8 + 11. Factor h(v).
3*v**3*(v + 1)*(v + 2)/4
Let m(i) = -i**3 + i**2 + 2. Let o be m(2). Let w be (-1)/(o/(2 - 0)). Solve -3 - r + r**2 - 4 + w + 4 = 0.
-1, 2
Suppose 0 = 2*c - 3 + 5. Let b be (1 - c) + (-5)/(-20). Factor 1/4 + b*u**2 + 3/2*u.
(3*u + 1)**2/4
Let p(z) = -5*z**3 - 16*z**2 - 11*z - 6. Let n(o) = -5*o**3 - 17*o**2 - 12*o - 7. Let i(k) = -6*n(k) + 7*p(k). Factor i(y).
-5*y*(y + 1)**2
Let v = -33 + 58. Let c be (-10)/v + 12/5. Factor -3*q**2 - q**2 - c + 6*q**2.
2*(q - 1)*(q + 1)
Let l be (1/2)/((-1)/4). Let g(j) = -4*j**2 - 2*j. Let a(u) = -u**2 - u - 1. Let m(f) = l*a(f) + g(f). Factor m(p).
-2*(p - 1)*(p + 1)
Let g(u) = u**2 - 12*u + 11. Let c be g(9). Let q be c/12*(-9)/30. What is v in 0 - 4/5*v**4 - q*v**5 + 2/5*v + 0*v**3 + 4/5*v**2 = 0?
-1, 0, 1
Suppose -2 - 2 = 2*w. Let h(g) = -g + 2. Let p be h(w). Let x(u) = -u**2 + 2. Let b(c) = 2*c**2 + c - 3. Let y(m) = p*b(m) + 6*x(m). Factor y(n).
2*n*(n + 2)
Let m(o) be the second derivative of -2*o**6/195 + 3*o**5/130 - o**4/78 - 3*o. Let m(y) = 0. What is y?
0, 1/2, 1
Let u(c) be the first derivative of c**6/900 + 5*c**3/3 + 4. Let x(q) be the third derivative of u(q). Factor x(j).
2*j**2/5
Let r be 6 - (-3)/(2 + -1). Factor -4*g**2 + 26*g**4 + r*g**3 + 16*g**3 - 4*g - g**4.
g*(g + 1)*(5*g - 2)*(5*g + 2)
Let p(l) = -5*l**3 - 3*l**2 + 10*l. Let v(s) = 21*s**3 + 12*s**2 - 39*s. Suppose 5*o - 45 = 8*o. Let k(c) = o*p(c) - 4*v(c). Solve k(q) = 0 for q.
-1, 0, 2/3
Let d(h) = -6*h**4 - 29*h**3 - 18*h**2 + 29*h + 24. Let i(o) = -3*o**4 - 15*o**3 - 9*o**2 + 15*o + 12. Let u(f) = -3*d(f) + 5*i(f). Factor u(p).
3*(p - 1)*(p + 1)*(p + 2)**2
Let q(x) be the first derivative of 1/3*x**2 + 2 + 1/6*x**4 - 4/9*x**3 + 0*x. Let q(u) = 0. What is u?
0, 1
Suppose -2/5*n**2 + 16/5 + 4/5*n = 0. What is n?
-2, 4
Let o(b) = 65*b**3 - 547*b**2 - 77*b + 59. Let y(x) = -x**3 + x**2 - x - 1. Let d(z) = -o(z) + 5*y(z). Factor d(c).
-2*(c - 8)*(5*c + 2)*(7*c - 2)
Let b be (-1114)/1*6/(-84). Let x = -79 + b. Determine o so that 0*o**2 + 6/7*o**5 - 2/7*o**4 - x*o**3 + 0 + 0*o = 0.
-2/3, 0, 1
Let s(k) be the third derivative of -2*k**7/105 + k**6/5 - 4*k**5/5 + 5*k**4/3 - 2*k**3 - 15*k**2. Factor s(a).
-4*(a - 3)*(a - 1)**3
Factor -1 - 4*o**2 - 2*o**3 - 10/3*o - 1/3*o**4.
-(o + 1)**3*(o + 3)/3
Let j(o) be the first derivative of -4*o**6/3 + 32*o**5/5 - 25*o**4/2 + 38*o**3/3 - 7*o**2 + 2*o + 12. Factor j(u).
-2*(u - 1)**3*(2*u - 1)**2
Suppose 6*b = 2*b - 8. Let u be ((-1)/2)/(b/12). Factor 2*a + u*a**3 - 3*a - 2*a**3.
a*(a - 1)*(a + 1)
Factor 40*s**3 - 4 + 4 + 36*s**2 + 8*s + 12*s**4 + 0*s.
4*s*(s + 1)*(s + 2)*(3*s + 1)
What is k in 9/2*k + 3/2*k**2 + 0 = 0?
-3, 0
Let g(r) be the third derivative of r**6/420 + r**5/35 + r**4/7 + 8*r**3/21 + 7*r**2. Factor g(w).
2*(w + 2)**3/7
Let s = 172/267 + 2/89. What is w in 4/3*w + s + 2/3*w**2 = 0?
-1
Let -16*z**4 + 4*z - 9*z**3 - 8*z**4 - 19*z**3 = 0. What is z?
-1, -1/2, 0, 1/3
Let y(u) = -5*u**3 + 9*u - 6. Let o(v) = 6*v**3 - 9*v + 6. Let d(r) = 3*r**2 + r. Let w be d(-1). Let t(b) = w*o(b) + 3*y(b). Factor t(g).
-3*(g - 1)**2*(g + 2)
Suppose -4*m + m = -9. Let f = 7 - m. Solve -2*o**3 + 0 + f + 4*o**3 - 6*o = 0.
-2, 1
Let c be (-124)/(-42) + -2 + 24/(-84). Factor -v + 1/3*v**2 + c.
(v - 2)*(v - 1)/3
Let i(q) be the third derivative of q**5/210 - q**3/21 - 14*q**2. Factor i(r).
2*(r - 1)*(r + 1)/7
Let i be 1/4*(-4)/(-18)*4. Factor -2/9*w**3 + 0*w + 0 + i*w**2.
-2*w**2*(w - 1)/9
Suppose 0 = 5*q - 12 - 13. Suppose 0 = -7*m + 2*m + 15. Let 0*i**5 - m*i**2 - i**4 + i**3 - i**q + 4*i**2 = 0. What is i?
-1, 0, 1
Let j(m) be the first derivative of 2 + 0*m**3 + 1/24*m**6 + 0*m**5 + 0*m**4 + 0*m + 0*m**2. What is l in j(l) = 0?
0
Let f(x) be the second derivative of x**5/70 - x**4/14 + 2*x**3/21 - 3*x. Find b, given that f(b) = 0.
0, 1, 2
Let a be (-1142)/(-1146) - 0 - 1. Let c = a - -770/1719. Suppose -14/9*j**2 - c*j + 0 = 0. Calculate j.
-2/7, 0
Let x(r) be the first derivative of 3/4*r - 1/4*r**3 - 5 + 3/16*r**4 - 3/8*r**2. Factor x(t).
3*(t - 1)**2*(t + 1)/4
Let t = 5 - 5. Factor t*b**4 + b**2 + 5*b**3 + 14*b**4 + b**2 + 5*b**3 + 6*b**5.
2*b**2*(b + 1)**2*(3*b + 1)
Let g(r) = 15*r**5 + 15*r**4 - 15*r**3 - 20*r**2 + 15*r + 10. Let q(v) = -7*v**5 - 7*v**4 + 8*v**3 + 10*v**2 - 7*v - 5. Let f(s) = 2*g(s) + 5*q(s). Factor f(t).
-5*(t - 1)**2*(t + 1)**3
Let v(d) be the third derivative of d**7/630 + d**6/180 + d**2. Determine l, given that v(l) = 0.
-2, 0
Let j(c) = 45*c**5 - 129*c**4 - 83*c**3 - 7*c**2 - 9*c. Let o(w) = -11*w**5 + 32*w**4 + 21*w**3 + 2*w**2 + 2*w. Let n(y) = 4*j(y) + 18*o(y). Factor n(l).
-2*l**2*(l - 4)*(3*l + 1)**2
Suppose 4*j - 1 + 9 = 0. Let u = j + 5. Factor -3*g**3 - 6*g - 3*g**u + 2*g**4 + 4*g + 6*g**2.
2*g*(g - 1)**3
Suppose 8*r = -5*r + 65. Let p(y) = -2*y**2 + 25*y - 2. Let f(i) = -1 - 6*i + i + 22*i - i**2. Let j(s) = r*p(s) - 7*f(s). Factor j(o).
-3*(o - 1)**2
Let n(f) = 2*f**2 + f**3 - f - 4*f + 2*f. Let i(l) = l**3 + 3*l**2 - 4*l. Let m(o) = -4*i(o) + 6*n(o). Factor m(y).
2*y*(y - 1)*(y + 1)
Suppose 3*o + 4*t = 21, 0*o - 4*t + 3 = -3*o. What is d in -d**2 - 2*d + o*d**2 - 4*d**2 = 0?
-1, 0
Let 2/3*w**2 - 2/9*w**3 + 2/9*w - 4/9 - 2/9*w**4 = 0. What is w?
-2, -1, 1
Let q(l) = 2*l**2 - 19*l + 25. Let h(m) = -3*m**2 + 29*m - 38. Let b(j) = 5*h(j) + 8*q(j). Determine s so that b(s) = 0.
2, 5
Let v be (256/24 - 8)*3/12. Let -4/3*q + 10/3*q**3 - 2*q**5 - 2/3*q**2 + 0 + v*q**4 = 0. What is q?
-1, -2/3, 0, 1
Let n be -2*9/24*8/(-18). Determine r, given that 4/3*r**2 + n*r**3 + 5/3*r + 2/3 = 0.
-2, -1
Let o be (-11)/44 + 9/18. Find a such that -1/4*a**3 + 0 + 1/2*a + o*a**2 = 0.
-1, 0, 2
Factor 2/7*u**3 + 6/7*u - 8/7*u**2 + 0.
2*u*(u - 3)*(u - 1)/7
Let n(i) be the second derivative of -2*i + 1/15*i**6 + 2/9*i**4 - 1/5*i**5 + 0 + 0*i**2 - 1/126*i**7 + 0*i**3. Suppose n(q) = 0. Calculate q.
0, 2
Suppose 6*w**3 + 3/5*w**4 + 72/5*w**2 - 384/5 - 96/5*w = 0. What is w?
-4, 2
Suppose 4*b = 12 + 8. Factor -18*x**2 + 14*x**2 + 2 + 2*x**b + 2 + 6*x - 8*x**3.
2*(x - 2)*(x - 1)*(x + 1)**3
Let l(v) = 9*v**5 + 5*v**4 - 7*v**3 - 7*v + 7. Let j(u) = 5*u**5 + 3*u**4 - 4*u**3 - 4*u + 4. Let r(x) = 7*j(x) - 4*l(x). Suppose r(h) = 0. What is h?
0, 1
Let 1148*y**5 - 96 - 1392*y - 8351*y**5 - 22638*y**4 - 11812*y**3 + 5065*y**3 - 7728*y**2 - 13245*y**3 = 0. Calculate y.
-2, -2/7
Let c = -1 + 7. Let -1 + 2*v**2 - 3 - c*v + 8 = 0.