8 = -t - 2*i, -5 = -2*t - i. Find b such that 25*b**t + 4*b**3 - 17*b**2 - b + 5*b = 0.
-1, 0
Let x(u) = u**2 + 2*u. Let d be x(-3). Let t be 6 + (-1 - 1) + 1. What is g in -6*g**d + 2*g**4 - 2*g - g**2 - 5*g**4 - t*g**2 + g**4 = 0?
-1, 0
Suppose 4*o**2 - 11 - 5*o**2 - 5 + 5*o + 3*o = 0. What is o?
4
What is h in 4*h - 1/4*h**2 - 16 = 0?
8
Let r = 23/2 + -113/10. Factor -2/5 + 2/5*a**2 + 1/5*a**3 - r*a.
(a - 1)*(a + 1)*(a + 2)/5
Let u(x) = -x**2 + x + 3. Let a(n) = 3*n**2 - 3*n - 9. Let q(p) = 2*a(p) + 7*u(p). Let g(j) = -j**2 + j + 2. Let m(c) = -3*g(c) + 2*q(c). Factor m(b).
b*(b - 1)
Let s(v) be the second derivative of -v**7/168 + v**6/120 + v**5/40 + 14*v. Factor s(j).
-j**3*(j - 2)*(j + 1)/4
Let i(f) be the second derivative of 0 + 19/4*f**4 + 33/2*f**3 + 27/2*f**2 + 5*f + 9/20*f**5. Factor i(c).
3*(c + 3)**2*(3*c + 1)
Let h(g) = g**2 + 6*g - 15 + 5 + 4 + 5. Let n(a) = -a**2 - a - 1. Let k(m) = 3*h(m) + 6*n(m). Let k(r) = 0. What is r?
1, 3
Let t(a) be the first derivative of 0*a**2 + 1 + 1/9*a**3 - 1/3*a. Find y such that t(y) = 0.
-1, 1
Let a(s) be the third derivative of 1/12*s**6 + 0*s - 2*s**2 - 8/105*s**7 + 0 - 1/30*s**5 + 1/42*s**8 + 0*s**3 + 0*s**4. Factor a(n).
2*n**2*(n - 1)*(2*n - 1)**2
Let q(f) be the second derivative of f**4/28 + f**3/7 + 3*f**2/14 + 18*f. Factor q(v).
3*(v + 1)**2/7
Let m(l) be the first derivative of 0*l**2 - 2/5*l**5 - l**4 + 0*l - 2/3*l**3 + 1. Factor m(i).
-2*i**2*(i + 1)**2
Let n(f) be the first derivative of f**3/9 + f**2/3 - f - 12. Find s, given that n(s) = 0.
-3, 1
Let o(n) be the second derivative of -1/18*n**4 - 1/15*n**5 + 0 + 2/9*n**3 + 3*n + 1/3*n**2. Factor o(y).
-2*(y - 1)*(y + 1)*(2*y + 1)/3
Let b(x) be the second derivative of x**4/8 + x**3/4 + 11*x - 2. Suppose b(w) = 0. What is w?
-1, 0
Let d(b) be the first derivative of b**5/20 - b**4/16 - b**3/4 + 5*b**2/8 - b/2 + 13. Factor d(i).
(i - 1)**3*(i + 2)/4
Let y(s) = 4*s**4 + 25*s**3 + 36*s**2 + 28*s + 13. Let c(u) = -2*u**4 - 12*u**3 - 18*u**2 - 14*u - 6. Let o(z) = -10*c(z) - 4*y(z). Factor o(t).
4*(t + 1)**3*(t + 2)
Factor 1/3*c**2 - 1/3*c + 0.
c*(c - 1)/3
Let z(v) = 0 + 0*v**2 + 7*v - v**2 - 3. Let k be z(6). Suppose 12*p**2 + 6*p - 2 + 3 - 16*p**k - 3 = 0. What is p?
-1/2, 1/4, 1
Let t(x) = -x**4 + 12*x**3 - 4*x**2 - 9*x + 11. Let g(z) = 8*z**4 - 84*z**3 + 28*z**2 + 64*z - 76. Let y(w) = 3*g(w) + 20*t(w). Factor y(h).
4*(h - 2)*(h - 1)**2*(h + 1)
Let h = -4 + 2. Let y be (14/6 + h)*1. Let 1/3*p**4 + p**3 + y*p + p**2 + 0 = 0. Calculate p.
-1, 0
Let n = 23377/58 - 403. Let m = 131/290 - n. Factor m*s**2 + 0 + 2/5*s - 2/5*s**3 - 2/5*s**4.
-2*s*(s - 1)*(s + 1)**2/5
Let i(l) be the first derivative of 3 + 2*l**3 + 3/4*l**4 - 6*l - 3/2*l**2. Factor i(g).
3*(g - 1)*(g + 1)*(g + 2)
Let a(z) be the third derivative of z**8/784 + 9*z**7/490 + 4*z**6/35 + 2*z**5/5 + 6*z**4/7 + 8*z**3/7 + 16*z**2. Factor a(b).
3*(b + 1)*(b + 2)**4/7
Factor 1/5*a**2 + 0*a - 9/5.
(a - 3)*(a + 3)/5
Suppose 4*x = -9 - 3. Let k = 10 + x. Factor 7*m**2 - 3*m**2 + 5*m**2 + k*m**3 + 2*m.
m*(m + 1)*(7*m + 2)
Let o(a) be the second derivative of 0*a**4 - a**2 - 1/30*a**5 - a + 1/3*a**3 + 0. Let p(x) be the first derivative of o(x). Factor p(s).
-2*(s - 1)*(s + 1)
Suppose -k = -4*k + 15. Let v be k*2/4*2. Solve -2*q**2 + 2*q**4 - 2*q**v - q + q**5 + 2*q**5 = 0.
-1, 0, 1
Let v = 435/2 - 217. Find m such that m - v*m**2 + 0 = 0.
0, 2
Let n(x) be the first derivative of -x**9/13608 - x**8/7560 + x**7/3780 + x**6/1620 + x**3 - 6. Let p(r) be the third derivative of n(r). What is j in p(j) = 0?
-1, 0, 1
Let d(f) be the third derivative of -f**7/14 + 3*f**6/10 - 9*f**5/20 + f**4/4 - 3*f**2. Factor d(l).
-3*l*(l - 1)**2*(5*l - 2)
Let c(p) be the second derivative of p**6/360 + p**3/3 - 2*p. Let y(r) be the second derivative of c(r). Determine k, given that y(k) = 0.
0
Suppose 15 + 15 = 5*k. Let h(a) be the first derivative of 0*a - 3/5*a**5 + 2 + 0*a**2 - 1/2*a**k + 0*a**4 + 0*a**3. Factor h(g).
-3*g**4*(g + 1)
Factor 1/4*t**5 + 0 + 0*t**2 + 1/4*t**3 - 1/2*t**4 + 0*t.
t**3*(t - 1)**2/4
Suppose t = 4*t. Let p = 5 + -3. Factor 1/2*o**3 - 1/2*o**4 + 0*o + t*o**p + 0.
-o**3*(o - 1)/2
Factor 0 + 4/17*c**3 + 0*c + 0*c**2 - 14/17*c**4.
-2*c**3*(7*c - 2)/17
Let b(l) be the third derivative of -7*l**8/12 + 22*l**7/15 + 17*l**6/30 - 73*l**5/15 + 16*l**4/3 - 8*l**3/3 + 8*l**2. Solve b(j) = 0.
-1, 2/7, 1
Factor 40*y**3 - 7/10 + 83/10*y + 32/5*y**4 - 162/5*y**2.
(y + 7)*(4*y - 1)**3/10
Let 3/4*x**3 + 3/2*x**2 - 3/4*x - 3/2 = 0. What is x?
-2, -1, 1
Let s(q) be the first derivative of -q**4/24 + q**2/4 - 8*q + 2. Let g(c) be the first derivative of s(c). Find t, given that g(t) = 0.
-1, 1
Suppose -5*o - 126 - 29 = 0. Let u = o - -34. Let 8*z**2 + 1 - 11/2*z - 7/2*z**u = 0. Calculate z.
2/7, 1
Let c be (6/5)/((-1)/(-5)). Factor -c*b**3 - 11 + 3*b + 11 + 3*b**5.
3*b*(b - 1)**2*(b + 1)**2
Suppose 3*q = -0*z - 2*z - 2, q = z + 6. Find j such that -119*j**3 + j**2 + 9*j - 7*j**q + 116*j**3 = 0.
-3, 0, 1
Suppose -80 = -4*p - p. Let m = 19 - p. Determine d so that -1/6 - 1/3*d**m - 5/6*d**2 - 2/3*d = 0.
-1, -1/2
Let v = -193 + 193. Factor 2/5*b**2 + v*b - 4/5*b**3 + 2/5*b**4 + 0.
2*b**2*(b - 1)**2/5
Let h(p) be the first derivative of 1/15*p**5 + 1/12*p**4 - 1/9*p**3 + 8 + 0*p - 1/6*p**2. Factor h(r).
r*(r - 1)*(r + 1)**2/3
Let o be (-2)/((4/(-10))/(15 - 14)). Find k such that -6/5*k**3 + 4/5*k**4 + 4/5*k**2 - 1/5*k**o + 0 - 1/5*k = 0.
0, 1
Determine l, given that 0*l - 3*l**5 - 6*l**3 - 53*l**2 + 9*l + 9*l**4 + 47*l**2 - 3 = 0.
-1, 1
Let x(u) be the third derivative of u**7/630 - u**6/180 + 2*u**2. Find b, given that x(b) = 0.
0, 2
Factor -16/5*x**2 + 7/5*x**4 - 4/5*x - x**3 + 0.
x*(x - 2)*(x + 1)*(7*x + 2)/5
Let j = 98 - 96. Suppose 6/5*f**3 - 12/5*f**j - 3/5*f + 6/5*f**4 + 6/5 - 3/5*f**5 = 0. Calculate f.
-1, 1, 2
Let f(n) be the third derivative of -n**6/280 - n**5/420 + n**4/56 + n**3/42 - 3*n**2. Factor f(l).
-(l - 1)*(l + 1)*(3*l + 1)/7
Let w = 11/4 - 5/2. Suppose -w*b**2 + 0 + 0*b**3 + 0*b + 1/4*b**4 = 0. Calculate b.
-1, 0, 1
Let t be (4 - (-57)/(-15)) + 99/55. Suppose 0 = -0*n + 3*n. Factor 0*a + 2/3*a**t + n - 3*a**3.
-a**2*(9*a - 2)/3
Let k(c) be the third derivative of 0*c**6 + 4*c**2 + 0 + 0*c**5 + 0*c + 0*c**4 - 1/84*c**8 + 2/105*c**7 + 0*c**3. Factor k(u).
-4*u**4*(u - 1)
Let f(z) be the second derivative of z**4/28 + z**3/14 - 16*z. Factor f(w).
3*w*(w + 1)/7
Factor -2/3*v - 1/3*v**2 - 1/3.
-(v + 1)**2/3
Determine q so that 1/5*q**2 - 2/5 - 1/5*q = 0.
-1, 2
Factor 3*o - 790*o**2 + 786*o**2 + o.
-4*o*(o - 1)
Let i(q) be the second derivative of q**8/504 + q**7/315 - q**6/60 - q**5/18 - q**4/18 + 2*q**2 - 3*q. Let z(s) be the first derivative of i(s). Factor z(b).
2*b*(b - 2)*(b + 1)**3/3
Let z(j) = -j**3 + 7*j**2 - 5*j - 4. Let q be z(6). Find h such that -2*h**q - 2*h - 2/3*h**3 - 2/3 = 0.
-1
Let m be 38/4 - (-3)/(-6). Let b(q) = q**2 - q - 2. Let w(u) = 4*u**2 - 4*u - 9. Let h(t) = m*b(t) - 2*w(t). Solve h(n) = 0.
0, 1
Factor -7*f**4 + 36*f**3 - 12*f**4 - 2*f**4 + 11*f**2 + f**2.
-3*f**2*(f - 2)*(7*f + 2)
Let d(i) = -3*i**4 - 18*i**3 - 27*i**2 - 6*i + 6. Let l(r) = r + 1. Let p(f) = -d(f) + 6*l(f). Find k such that p(k) = 0.
-4, -1, 0
Let p(w) be the third derivative of 1/72*w**4 - 1/315*w**7 + 0*w**3 + 3*w**2 + 0*w + 1/90*w**5 + 0*w**6 + 0 - 1/1008*w**8. Find y, given that p(y) = 0.
-1, 0, 1
Let i(b) be the third derivative of b**5/160 - b**3/16 - 3*b**2. Factor i(o).
3*(o - 1)*(o + 1)/8
Let q(b) be the first derivative of -6*b + 5 - 3/2*b**2 + 2*b**3 + 3/4*b**4. Solve q(m) = 0 for m.
-2, -1, 1
Let f(y) = -y**4 + 4*y**3 - 2*y**2 + 2*y. Let a(n) = 3*n**4 - 11*n**3 + 5*n**2 - 5*n. Let j(t) = 3*a(t) + 8*f(t). Suppose j(x) = 0. Calculate x.
-1, 0, 1
Let c = -202 + 407/2. Find l, given that -3/4 - 3/4*l**4 + 0*l**3 + 0*l + c*l**2 = 0.
-1, 1
Let l be 20*2/(7 + -3). Let j be 2/(-10)*l/(-8). Solve 1/2*z - j*z**2 + 0 = 0.
0, 2
Let c(r) = 4*r**2 + 4*r - 2. Let v(z) = -7*z - 7 + 24*z + 2 + 17*z**2 - 3. Let j(f) = -26*c(f) + 6*v(f). Find d such that j(d) = 0.
-2, 1
Let q(r) be the second derivative of -r**7/70 - 7*r**6/150 - r**5/20 - r**4/60 + 20*r. Factor q(u).
-u**2*(u + 1)**2*(3*u + 1)/5
Let d be 0 - (1 - -3 - 14). Factor -v - 5*v + 8*v**3 - 2 - d*v**3 - 6*v**2.
-2*(v + 1)**3
Let y =