z(o) = -o - 1. Let f be 7/(-9) + (-4)/18. Let j(s) = -2*s**2 + 6*s. Let h(y) = f*j(y) - 2*z(y). What is l in h(l) = 0?
1
Let n(k) = -k**2 - k + 3. Let z be n(0). Suppose 3*u + 3*a + 4 = 2*u, u - 4*a = 10. Solve -4*b**2 + 3*b**u + b**3 - 2*b**z = 0 for b.
-1, 0
Let g = 57/4 + -14. Let z = 515/4 - 128. What is k in -7/4*k + 13/4*k**2 + g + z*k**3 - 9/2*k**4 = 0?
-1, 1/3, 1/2
Factor 0 + 1/5*t**2 - 1/5*t.
t*(t - 1)/5
Factor -2/17*v**2 - 2/17*v + 0.
-2*v*(v + 1)/17
Solve -1 + 1/4*y**2 + 0*y = 0 for y.
-2, 2
Let k(c) be the first derivative of -c**3/3 + 7*c**2 - 49*c + 6. Determine a, given that k(a) = 0.
7
Let d be 2/2 - (-6)/(540/(-78)). Factor -d*n**2 - 4/15 + 2/5*n.
-2*(n - 2)*(n - 1)/15
What is b in 9/2*b**2 + 3/2 + 9/2*b + 3/2*b**3 = 0?
-1
Let q = -7 + 9. Solve -t**4 - q + 2 + 0 + t**3 = 0.
0, 1
Let b(u) be the third derivative of u**5/80 + 3*u**4/32 - 41*u**2. Let b(s) = 0. What is s?
-3, 0
Factor 2/5*p + 0 + 1/2*p**2 + 1/10*p**3.
p*(p + 1)*(p + 4)/10
Let z(a) be the second derivative of -1/6*a**4 + 1/15*a**6 + 0 + 0*a**2 + 1/10*a**5 + a - 1/3*a**3. Determine o, given that z(o) = 0.
-1, 0, 1
Let c(p) be the third derivative of p**7/490 - 3*p**6/280 + p**5/70 + 19*p**2. Find w, given that c(w) = 0.
0, 1, 2
Suppose -8/5*y**4 - 8/15*y + 22/15*y**3 - 14/15*y**5 + 0 + 8/5*y**2 = 0. What is y?
-2, -1, 0, 2/7, 1
Let w be (-9)/(-24)*4/90. Let r(d) be the third derivative of 1/24*d**4 - 1/6*d**3 + 0*d + 0 - 1/120*d**6 - d**2 + w*d**5. Factor r(m).
-(m - 1)**2*(m + 1)
Let f(s) be the first derivative of s**5/20 + s**4/24 - 4*s + 2. Let p(u) be the first derivative of f(u). Factor p(c).
c**2*(2*c + 1)/2
Let z be 20/(-110) - (-57)/132. Let n = -3 - -3. Factor z*j**4 + 0*j**2 + n + 0*j - 1/4*j**3.
j**3*(j - 1)/4
Let x = -3779/210 - -18. Let d(u) be the third derivative of -1/1008*u**8 - 1/180*u**5 + 0*u**4 + 0*u**3 + 0 + 0*u - 1/120*u**6 - x*u**7 + u**2. Factor d(t).
-t**2*(t + 1)**3/3
Let d(y) be the first derivative of -7/6*y**2 - 1/6*y**4 + 4 - 2/3*y - 7/9*y**3. Factor d(m).
-(m + 1)*(m + 2)*(2*m + 1)/3
Factor 162/7 - 34/7*o**2 + 18*o + 2/7*o**3.
2*(o - 9)**2*(o + 1)/7
Let l(h) be the first derivative of 1/18*h**4 + 1/3*h**2 - 2/9*h**3 - 2/9*h + 1. Let l(z) = 0. Calculate z.
1
Suppose -y = -2*a + 10, 3*y + a + 2*a = 15. Factor 4*x - 2*x + y*x - 2*x**2.
-2*x*(x - 1)
Suppose -5*h + 108 - 36 = -3*m, -3*m - 12 = 0. Let c be 10/h + 4/6. Suppose -5/2*o**5 + 7/2*o**3 + 0 + 3/2*o**4 - c*o**2 - o = 0. What is o?
-1, -2/5, 0, 1
Let a be 4/3 - (3 + -2 + 0). Let i(x) be the first derivative of x**2 + x - 2 + a*x**3. Factor i(u).
(u + 1)**2
Let h(x) be the third derivative of x**8/6720 - x**6/720 + x**4/12 + x**2. Let j(c) be the second derivative of h(c). Factor j(m).
m*(m - 1)*(m + 1)
Determine p, given that -9 - 115*p**3 - 57*p - 27*p**4 + 7*p**3 - 126*p**2 + 3*p**4 = 0.
-3, -1/2
Suppose -r = -3*z - 4, -z = -3*z. Suppose j = 6*j - 25. Factor -3*h**r + 0*h**j + 0*h**5 + 2*h**3 - 3*h + h**5 + 1 + 2*h**2.
(h - 1)**4*(h + 1)
Find y, given that 2/7*y + 2/7*y**3 + 0 + 4/7*y**2 = 0.
-1, 0
Suppose 21*z - 42 = -0*z. Factor 2/9*s**z - 2/3*s + 4/9.
2*(s - 2)*(s - 1)/9
Let r(v) be the third derivative of 7*v**5/30 + 3*v**4/4 + 2*v**3/3 + 2*v**2. Factor r(p).
2*(p + 1)*(7*p + 2)
Let 0 - 2/15*y**4 - 2/15*y + 2/15*y**3 + 2/15*y**2 = 0. What is y?
-1, 0, 1
Let g(q) = 3*q**2 - 3*q + 2. Let t(o) = 7*o**2 - 6*o + 5. Let u(f) = -5*g(f) + 2*t(f). Find v, given that u(v) = 0.
0, 3
Let n = 0 + 7. Let s be (2/n)/(63/49). Factor -s*h**2 + 0 + 2/9*h.
-2*h*(h - 1)/9
Factor 22*c**3 - 6 + 23*c**3 + 6*c**2 - 47*c**3 + 2*c.
-2*(c - 3)*(c - 1)*(c + 1)
Let z(q) = q**4 - 7*q**3 - q**2 + 7*q - 6. Let g(x) = -x**3 + x - 1. Suppose 2*m = -m + 18. Let i(u) = m*g(u) - z(u). Let i(w) = 0. Calculate w.
-1, 0, 1
Factor 2/13*a**2 + 4/13 + 6/13*a.
2*(a + 1)*(a + 2)/13
Suppose -1 = -3*c + 5. Let -2*a**4 - 5*a**c + 7*a**2 + 0*a**5 + a - a**5 = 0. What is a?
-1, 0, 1
Let w(z) be the second derivative of -z**7/42 - z**6/30 + 3*z**5/20 + z**4/12 - z**3/3 + z. Factor w(g).
-g*(g - 1)**2*(g + 1)*(g + 2)
Let a(t) be the second derivative of 7*t**6/180 - t**5/18 - t**4/18 + 3*t**2/2 - t. Let q(d) be the first derivative of a(d). Solve q(w) = 0 for w.
-2/7, 0, 1
Let x(m) = -m. Let i be x(1). Let t(h) = -6*h**2 - 7*h - 1. Let f(l) = -l**2 - l. Let a(d) = i*t(d) + 5*f(d). Let a(b) = 0. Calculate b.
-1
Let q(j) be the first derivative of -2*j**5/35 - 2*j**4/7 - 4*j**3/21 + 4*j**2/7 + 6*j/7 - 31. Find r, given that q(r) = 0.
-3, -1, 1
Let d(q) be the second derivative of 1/10*q**5 + 0 + 1/15*q**6 + 3*q - 1/2*q**4 - 2*q**2 - 5/3*q**3. Factor d(l).
2*(l - 2)*(l + 1)**3
Let z(b) be the second derivative of b**5/210 - b**4/14 + 3*b**3/7 - 2*b**2 - 3*b. Let w(y) be the first derivative of z(y). Determine x so that w(x) = 0.
3
Factor -8/5*m**4 - 8/5*m**2 + 4*m**3 + 0 + 0*m.
-4*m**2*(m - 2)*(2*m - 1)/5
Let r(l) be the third derivative of l**8/168 + l**7/30 + 3*l**6/40 + l**5/12 + l**4/24 + 10*l**2. Suppose r(q) = 0. Calculate q.
-1, -1/2, 0
Suppose -83*y - 12 = -87*y. Let i(z) be the second derivative of 1/18*z**4 - 1/3*z**2 + 0 + y*z + 0*z**3. Solve i(a) = 0.
-1, 1
Let t(b) = -b**5 + b**4 + b**3 + b**2 + b. Let g(r) = -5*r**5 + 9*r**4 - r**3 - r**2 + 9*r - 2. Let c(f) = 2*g(f) - 6*t(f). Find k, given that c(k) = 0.
-1, 1
Let n(o) be the third derivative of 1/30*o**5 - 1/6*o**4 + 0*o + 2*o**2 + 1/120*o**6 + 0 - 4/3*o**3. Factor n(p).
(p - 2)*(p + 2)**2
Let i = 17 + -14. Factor 2*x**4 + 9*x**i - 8*x - 5*x**2 + 2 + 17*x**2 - 17*x**3.
2*(x - 1)**4
Let k(b) = -14*b - 4. Let q(t) = -5*t - 1. Let y(f) = 6*k(f) - 17*q(f). Let g be y(7). Find l such that 0*l**3 + g + 0*l - 2/5*l**4 + 2/5*l**2 = 0.
-1, 0, 1
Let n(g) be the third derivative of g**8/5040 + g**7/2520 + g**3/3 + 4*g**2. Let u(m) be the first derivative of n(m). Suppose u(r) = 0. What is r?
-1, 0
Suppose 0 = 5*o + 5, -k + 2 = o - 1. Let m(b) be the first derivative of 0*b + 1/5*b**2 + 0*b**3 - 1/10*b**k + 2. Factor m(z).
-2*z*(z - 1)*(z + 1)/5
Let q(m) be the second derivative of 0 - 5*m + 7/48*m**4 + 1/4*m**2 + 3/8*m**3. Factor q(b).
(b + 1)*(7*b + 2)/4
Let i(a) be the first derivative of a**4/4 - a**3/3 + 11. Solve i(d) = 0.
0, 1
Let p = 73 - 72. Let l(g) be the first derivative of -10/21*g**3 - p + 0*g - 2/7*g**2. Let l(c) = 0. What is c?
-2/5, 0
Let r(n) be the third derivative of -n**9/45360 - n**8/30240 + n**7/7560 - n**5/20 + n**2. Let k(d) be the third derivative of r(d). Factor k(w).
-2*w*(w + 1)*(2*w - 1)/3
Let d be 148/814 + 2/(-11). Factor -1/6*b**2 + d + 1/3*b.
-b*(b - 2)/6
Let j(g) be the first derivative of g**4/14 + 2*g**3/7 + 2*g**2/7 + 1. Find l, given that j(l) = 0.
-2, -1, 0
Let a = 15/8 + -29/24. Factor -a*b - 4/3 + 2*b**3 + 8/3*b**2.
2*(b + 1)**2*(3*b - 2)/3
Let c(n) = 7*n**2 - 12*n + 15. Let l(q) = q**2 - q + 1. Let x(y) = -c(y) + 6*l(y). Find p such that x(p) = 0.
3
Let f(b) be the second derivative of -b**4/3 + 28*b**3/3 - 98*b**2 - 19*b. Suppose f(q) = 0. What is q?
7
Let o(c) be the second derivative of c**4/3 - 16*c**3 + 288*c**2 + 19*c. Factor o(k).
4*(k - 12)**2
Suppose -4*n = -3*g + 16, -3 - 13 = -2*g + 4*n. Let u = -215/4 + 54. Factor g + u*c**3 + 0*c - 1/4*c**2.
c**2*(c - 1)/4
Let l(a) = a**2 + 6*a + 2. Let j(t) = 2*t**2 + 13*t + 3. Let n be (2/2*4)/(-2). Let m(o) = n*j(o) + 5*l(o). Suppose m(w) = 0. What is w?
-2
Suppose -4*w - 2*y = 22, -4*y = -8*w + 3*w - 60. Let b = w + 6. Let x(r) = 3*r**3 + 5. Let m(f) = -f**3 - 2. Let o(g) = b*x(g) - 5*m(g). Factor o(q).
-q**3
What is s in -4/3 + 2*s**3 + 8/3*s**2 - 10/3*s = 0?
-2, -1/3, 1
Find c, given that -4/3 - 4/3*c + 2/3*c**3 - 1/3*c**4 + c**2 = 0.
-1, 2
Let d(u) be the first derivative of u**6/2340 - u**5/195 + u**4/39 + 5*u**3/3 - 2. Let r(s) be the third derivative of d(s). Find i, given that r(i) = 0.
2
Let a(l) be the third derivative of -l**5/60 - l**4/12 - l**3/6 - 12*l**2. Factor a(p).
-(p + 1)**2
Let m = 1/139 - -133/834. Determine x, given that 4/3*x - 2/3 - 5/6*x**3 + 1/6*x**5 - 1/6*x**2 + m*x**4 = 0.
-2, 1
Let t**2 + 0 + 2/5*t - 7/5*t**3 = 0. Calculate t.
-2/7, 0, 1
Let g(o) = o**5 - o**4 + o - 1. Let b(u) = 7*u**5 - 8*u**4 + 2*u**2 + 5*u - 6. Let i(m) = -b(m) + 6*g(m). Factor i(l).
-l*(l - 1)**3*(l + 1)
Let v(x) be the first derivative of -x**4/36 - 4*x**3/27 + x**2/18 + 4*x/9