 - 1)*(b + 1)**2
Suppose 2/7*u**2 + 50/7 - 20/7*u = 0. What is u?
5
Let p(b) be the first derivative of -5/2*b**2 - 3/4*b**4 + 7/3*b**3 + b - 3. What is v in p(v) = 0?
1/3, 1
Suppose i - 3*p + 5 = 0, -4*i = 4*p - 7 - 21. Suppose -4 = -a + 4*j, i*a + 5 = -2*j + 3. Let 2/7*t + a + 2/7*t**3 - 4/7*t**2 = 0. What is t?
0, 1
Factor -1/10*v**4 - 1/10*v**2 - 1/2*v**3 + 9/5 + 21/10*v.
-(v - 2)*(v + 1)*(v + 3)**2/10
Let q = 3 - 0. Let r(a) = 5*a**2 - 1 + 0 - 3*a**3 - 1 + 5*a**q - a. Let k(s) = 10*s**3 + 26*s**2 - 4*s - 10. Let j(o) = -2*k(o) + 11*r(o). Factor j(g).
(g - 1)*(g + 2)*(2*g + 1)
Let z be (-4)/(-7) - (-48)/63. Let q(j) be the first derivative of -3*j**2 + z*j**3 + 2*j + 3. What is u in q(u) = 0?
1/2, 1
Let p(m) be the second derivative of 5*m**4/32 - 13*m**3/48 - m**2/8 + 13*m. Solve p(n) = 0 for n.
-2/15, 1
Let n(c) be the second derivative of -4*c**4/3 + 6*c**3 - 4*c**2 + 10*c. Factor n(x).
-4*(x - 2)*(4*x - 1)
What is d in 4/3*d**5 + 0*d**2 + 0*d + 0*d**4 - 4/3*d**3 + 0 = 0?
-1, 0, 1
Let t(j) be the third derivative of -j**8/840 + j**7/105 - 3*j**6/100 + 7*j**5/150 - j**4/30 - 16*j**2. Solve t(r) = 0 for r.
0, 1, 2
Let x(j) = -3*j**2 + j + 4. Let z(q) = q**2 - 1. Let t(f) = -x(f) - 4*z(f). Factor t(c).
-c*(c + 1)
Let s(l) = -8*l**5 + 56*l**4 - 129*l**3 + 63*l**2 - 9. Let i(g) = -2*g**5 + 14*g**4 - 32*g**3 + 16*g**2 - 2. Let d(c) = -18*i(c) + 4*s(c). Factor d(x).
4*x**2*(x - 3)**2*(x - 1)
Let f(n) be the first derivative of -5*n**3/18 + 5*n/6 + 31. Suppose f(b) = 0. Calculate b.
-1, 1
Let f = 18 + -16. Suppose 1 + 3/2*p + 1/2*p**f = 0. What is p?
-2, -1
Let m(p) be the second derivative of 0*p**4 + 3/80*p**5 - 3/8*p**3 - 3/4*p**2 + 0 + p. Find u such that m(u) = 0.
-1, 2
Let a(y) be the second derivative of -y**5/10 + y**4/3 - y**3/3 - 8*y. Solve a(o) = 0.
0, 1
Let s = -12 + 17. Suppose 4*w + 4*q = 36, 0*w + 11 = 3*w - s*q. Factor 3 - 2*o + 2*o**3 + 9*o**2 - 5*o**3 - w*o.
-3*(o - 1)**3
Let b(y) be the first derivative of y**8/1680 - y**7/1050 - y**6/600 + y**5/300 + y**2 + 2. Let w(l) be the second derivative of b(l). Factor w(m).
m**2*(m - 1)**2*(m + 1)/5
Let o(d) be the second derivative of 2*d**6/5 + 19*d**5/5 + 7*d**4 + 10*d**3/3 + 63*d. Factor o(u).
4*u*(u + 1)*(u + 5)*(3*u + 1)
Factor 2*g**5 + 0*g**4 - 6*g**4 + 6*g**2 + g**5 - 3*g.
3*g*(g - 1)**3*(g + 1)
Let h(j) be the first derivative of 4 + 1/7*j**2 + 0*j - 1/28*j**4 - 1/21*j**3. Factor h(g).
-g*(g - 1)*(g + 2)/7
Let x be ((-8)/(-5))/((-8)/(-20)). Solve -x*u + 6*u**2 - 8*u + 8*u + 4*u**3 = 0.
-2, 0, 1/2
Determine a, given that -3*a**5 - 4*a**4 + 3*a**4 + 7*a**4 = 0.
0, 2
Let p(x) be the second derivative of x**8/3840 - x**7/630 + 11*x**6/2880 - x**5/240 + x**4/6 + 2*x. Let s(f) be the third derivative of p(f). Factor s(c).
(c - 1)**2*(7*c - 2)/4
Let g be 0 + 2 - (0 - 1). Factor -2*k**4 + 4*k + 3*k**2 - 4*k**3 + k**g - 2*k.
-k*(k - 1)*(k + 2)*(2*k + 1)
Let c = 2801/7 - 399. Suppose 8/7 - 6/7*a**2 - c*a = 0. What is a?
-2, 2/3
Factor -2/3 - 4/3*a - 2/3*a**2.
-2*(a + 1)**2/3
Let a(y) = -y**3 + 8*y**2 - y + 8. Let l be a(8). Let i(m) be the first derivative of 1/15*m**6 + 4/25*m**5 + 0*m**4 + 3 + l*m**3 + 0*m + 0*m**2. Factor i(o).
2*o**4*(o + 2)/5
Let 7/2*g**3 - 8*g - 2 - 5/2*g**2 = 0. Calculate g.
-1, -2/7, 2
Let d be (1 - 2) + 6 + -5. Factor -2/9*x**3 + d - 2/9*x - 4/9*x**2.
-2*x*(x + 1)**2/9
Let i(n) be the third derivative of 4*n**2 + 0*n + 2/35*n**7 + 1/40*n**6 + 0*n**4 + 0*n**5 - 5/112*n**8 + 0 + 0*n**3. Let i(d) = 0. What is d?
-1/5, 0, 1
Factor -16/3*n**5 - 40/3*n**2 - 80/3*n**3 + 4/3 + 0*n - 20*n**4.
-4*(n + 1)**4*(4*n - 1)/3
Let a(k) be the second derivative of k**6/10 - 21*k**5/20 + 15*k**4/4 - 9*k**3/2 - 11*k. Solve a(x) = 0.
0, 1, 3
Suppose -8 + 6 = -n. Let j be (-5)/(-2) + -2 + 0. Find l such that 0 + j*l**3 + 0*l**2 + 0*l + n*l**4 + 3/2*l**5 = 0.
-1, -1/3, 0
Let c(j) = 11*j - 11. Let r be c(-4). Let t be 33/r*20/(-22). Determine s so that -2/11*s**3 - 6/11*s - 2/11 - t*s**2 = 0.
-1
Let p(o) be the first derivative of 4*o**3/3 - 22*o**2 + 17. Factor p(v).
4*v*(v - 11)
Let y(c) be the second derivative of c**8/588 - 2*c**7/245 + c**6/70 - c**5/105 - 4*c**2 + 5*c. Let f(z) be the first derivative of y(z). Factor f(n).
4*n**2*(n - 1)**3/7
Let x = -17/114 - -6/19. Let q(d) = d**3 + 5*d**2 - 2*d - 7. Let h be q(-5). Solve 0*a + 0*a**2 - 1/6*a**h + 1/3*a**4 - x*a**5 + 0 = 0.
0, 1
Let j(c) be the third derivative of c**6/80 - 3*c**5/40 + c**4/8 - 8*c**2. Factor j(z).
3*z*(z - 2)*(z - 1)/2
Let j(l) = -l**2 + 0*l**2 - 9*l - 1 + 14*l. Let x be j(4). Factor 0*c**2 - x*c - 2*c**2 + c.
-2*c*(c + 1)
Let m(t) be the third derivative of t**8/84 - 2*t**7/105 - 11*t**6/120 + t**5/15 + 5*t**4/24 - t**3/3 + 7*t**2. Solve m(c) = 0 for c.
-1, 1/2, 2
Let s(a) be the first derivative of -4/5*a - 2 + 2/15*a**3 - 1/5*a**2. What is z in s(z) = 0?
-1, 2
Factor 3/4*w**2 + 0 - 3/4*w.
3*w*(w - 1)/4
Factor -12/7*j**3 + 0 - 3/7*j**4 - 15/7*j**2 - 6/7*j.
-3*j*(j + 1)**2*(j + 2)/7
Let -6 - 420*p**2 - 144*p - 392*p**3 + 6 - 16 = 0. Calculate p.
-1/2, -2/7
Let y(x) = -5*x**2 + 88*x - 405. Let c(t) = 20*t**2 - 351*t + 1620. Let h(r) = -2*c(r) - 9*y(r). Factor h(v).
5*(v - 9)**2
Let a be (-2)/3*(0 + -3). Factor -42*u**2 + 42*u**2 - 2*u**5 - a*u**4.
-2*u**4*(u + 1)
Factor 5/4*o**2 + 1/2*o + 1/4*o**4 + o**3 + 0.
o*(o + 1)**2*(o + 2)/4
Find p such that -8/9*p - 2/3*p**2 - 1/3 + 1/9*p**4 + 0*p**3 = 0.
-1, 3
Suppose 1 = -4*s + 3*b - 22, -4*s - 4*b - 16 = 0. Let n = 7 + s. What is p in -n + 4*p**2 - p**2 - 5*p**2 + 4*p = 0?
1
Let t(j) be the first derivative of -125*j**6/24 - 65*j**5/4 - 145*j**4/8 - 53*j**3/6 - 17*j**2/8 - j/4 - 22. Let t(z) = 0. Calculate z.
-1, -1/5
Let f(g) be the second derivative of -g + 0 + 2/5*g**3 - 9/5*g**2 - 1/30*g**4. Factor f(o).
-2*(o - 3)**2/5
Factor -36 - 3*l**3 + 8 + 15 + 19 + 9*l.
-3*(l - 2)*(l + 1)**2
Let r(t) be the third derivative of -t**2 + 0 - 1/180*t**6 - 1/90*t**5 + 0*t**3 + 1/18*t**4 + 0*t. Factor r(u).
-2*u*(u - 1)*(u + 2)/3
Let c(z) = 3*z - 70. Let t be c(24). Determine o, given that -88/3*o + 16/3 - 10/3*o**3 + 44*o**t - 50/3*o**4 = 0.
-2, 2/5, 1
Factor 3/2*k**2 + 0*k - 15/4*k**4 - 9/4*k**3 + 0.
-3*k**2*(k + 1)*(5*k - 2)/4
Let n(b) be the second derivative of b**5/4 + 5*b**4/4 - 5*b**3 - 20*b**2 - 26*b. Factor n(p).
5*(p - 2)*(p + 1)*(p + 4)
Let v(c) = -12*c**2 - 15*c - 9. Let z(j) = 3*j**2 + 4*j + 2. Let q(g) = -2*v(g) - 9*z(g). Factor q(r).
-3*r*(r + 2)
Let o(u) be the second derivative of -1/9*u**2 + 2*u + 2/27*u**3 + 0 - 1/54*u**4. Factor o(p).
-2*(p - 1)**2/9
Suppose 1 = 2*c - 5. Factor 4/7*m**c - 2/7 - 4/7*m + 0*m**2 + 2/7*m**4.
2*(m - 1)*(m + 1)**3/7
Let h be 7/((-28)/6)*7. Let k = h - -79/6. Determine m so that -4/3*m**2 + 2/3 - 16/3*m**3 + 2/3*m**4 + 8/3*m + k*m**5 = 0.
-1, -1/4, 1
Let k be 31/(-4) + 32/4. Factor 1/4*n**4 + 0 + 3/4*n - 5/4*n**2 + k*n**3.
n*(n - 1)**2*(n + 3)/4
Suppose -55*b - 13*b - 35*b**5 - 12*b - 2*b**4 + 20 - 23*b**4 + 115*b**3 + 5*b**2 = 0. What is b?
-2, -1, 2/7, 1
Let y be (-12)/42 - (-55)/70. Factor b - 1/2*b**2 - y.
-(b - 1)**2/2
Let g(o) be the first derivative of o**4/10 + 2*o**3/15 - o**2/5 - 2*o/5 + 16. Factor g(q).
2*(q - 1)*(q + 1)**2/5
Suppose -3*g - 2*j = -10, -4 = g - 5*j + 2*j. Let h = -2/131 + 135/262. Determine v so that -h*v**3 + 0 + v**g - 1/2*v = 0.
0, 1
Let t be (104/50)/((-6)/(-15)). Let u = 28/5 - t. Let 4/5*k + 0 + u*k**2 = 0. What is k?
-2, 0
Let u(l) be the second derivative of -l**6/360 - l**5/60 - l**4/24 - l**3/6 - 2*l. Let o(d) be the second derivative of u(d). Suppose o(n) = 0. What is n?
-1
Let c be (-1)/((-21)/6 - -3). Factor -z - 9*z**2 + z - 3 + 12*z**c.
3*(z - 1)*(z + 1)
Let v(t) be the third derivative of t**7/420 - t**6/48 + 7*t**5/120 - t**4/16 + t**2 - 2*t. Find y such that v(y) = 0.
0, 1, 3
Let u(g) be the second derivative of -25*g**4/12 - 65*g**3/6 + 15*g**2 - 17*g - 1. Determine s so that u(s) = 0.
-3, 2/5
Let x(l) = l**2 - 23*l + 134. Let j be x(11). Factor z + 3/2*z**j + 0 + 1/2*z**3.
z*(z + 1)*(z + 2)/2
Let g(r) be the third derivative of -3*r**5/80 + 13*r**4/32 - r**3/2 + 8*r**2. Factor g(f).
-3*(f - 4)*(3*f - 1)/4
Let l = -105 + 107. Let x(s) be the third derivative of 1/6*s**4 - 3*s**l + 0*s - 1/60*s**5 + 0 - 2/3*s**3. Factor x(v).
-(v - 2)**2
Determine r so that 0*r - 1/3*r**2 + 0 + 5