 be a(4). Let g be k/11 - (-48)/22. Let 13 - 13 + z**5 - g*z**3 + z = 0. What is z?
-1, 0, 1
Let k(g) be the second derivative of g**7/420 - g**6/80 + g**5/40 - g**4/48 + g**2/2 - 8*g. Let c(u) be the first derivative of k(u). Factor c(y).
y*(y - 1)**3/2
Let m(y) = y + 1. Let l(h) = -h**2 + 1. Let k(w) = l(w) - 2*m(w). Find t such that k(t) = 0.
-1
Let y be 6 - (-1 - -2) - 11/3. Determine r so that -4/3*r**4 - 1/3*r**5 + 0 + 0*r + 0*r**2 - y*r**3 = 0.
-2, 0
Let u(g) be the first derivative of 8*g**5/5 + 9*g**4 + 16*g**3/3 - 21. Let u(t) = 0. What is t?
-4, -1/2, 0
Let n(u) be the first derivative of -4/3*u + 4 - 1/3*u**2 + 2/9*u**3. Factor n(c).
2*(c - 2)*(c + 1)/3
Suppose 0 = -g - 0 + 10. Let i(a) = a - 8. Let t be i(g). Factor 0*s + 3*s**2 + 2*s + s**3 + s**t + s**3.
2*s*(s + 1)**2
Let q be (-3)/(9/14)*(-192)/224. Find w such that 4/7*w**3 + 4/7 + 4/7*w**q - 2/7*w**5 - 8/7*w**2 - 2/7*w = 0.
-1, 1, 2
Let -3*k + 2*k**2 - 3*k**5 - 2*k**4 + 4*k + 2*k**5 = 0. Calculate k.
-1, 0, 1
Let o(v) = -v**2 + 9. Let h be o(3). Let c(n) be the second derivative of h + 1/48*n**4 + 0*n**3 + 3*n - 1/8*n**2. Let c(q) = 0. What is q?
-1, 1
Let y(w) be the second derivative of w**7/280 - w**5/40 + w**3/8 - w**2 - 2*w. Let x(h) be the first derivative of y(h). Let x(c) = 0. What is c?
-1, 1
Let n(s) be the first derivative of 2*s**3/39 - 5*s**2/13 + 8*s/13 + 21. Factor n(r).
2*(r - 4)*(r - 1)/13
Suppose -4*m + 0*m = -5*x + 16, 2*m - 2 = 0. Suppose 2/5*s**x + 2/5*s**5 + 0 + 0*s**3 + 0*s + 0*s**2 = 0. Calculate s.
-1, 0
Let n(p) be the first derivative of p**8/1120 + p**7/1120 - p**6/240 - p**5/160 + p**3/3 - 4. Let o(f) be the third derivative of n(f). Solve o(u) = 0.
-1, -1/2, 0, 1
Let y(f) be the second derivative of -f**9/7560 - f**8/1120 - f**7/630 + 5*f**4/12 - 3*f. Let l(z) be the third derivative of y(z). Factor l(d).
-2*d**2*(d + 1)*(d + 2)
Let u be (18/3 + 1)/1. Let x(h) = h**2 - 7*h + 2. Let k be x(u). Let -5*b**2 + 2*b**2 + 5*b**k = 0. What is b?
0
Let g(o) be the first derivative of 3*o**5/40 + 3*o**4/16 - 3*o**2/8 - 3*o/8 + 2. What is n in g(n) = 0?
-1, 1
Let o be (6/5)/(3/(-80)). Let f = -32 - o. Suppose 0 - 1/2*t**5 + 1/2*t**3 + 0*t + f*t**4 + 0*t**2 = 0. What is t?
-1, 0, 1
Let b(m) be the first derivative of 0*m**3 + 0*m**5 + 1 - 1/15*m**6 + 1/10*m**4 + 0*m + 0*m**2. Factor b(t).
-2*t**3*(t - 1)*(t + 1)/5
Let n be (-17)/(-3) - 1/(-3). Factor -4*u**4 - u**5 - u**4 + n*u**4.
-u**4*(u - 1)
Let d = -2/17 - -25/68. Let f(n) be the first derivative of 0*n + 0*n**2 - 1 + 0*n**3 + d*n**4. Suppose f(k) = 0. Calculate k.
0
Factor -7*h**2 - h**2 - 562 + 280 + 280 + 10*h.
-2*(h - 1)*(4*h - 1)
Let g(i) = i**2 - 9*i - 20. Let o be g(-2). What is q in 0*q + 1/4*q**o + 0 - 1/4*q**5 - 3/4*q**3 + 3/4*q**4 = 0?
0, 1
Factor 1 + 5*g - 2*g + 5*g**2 - 3*g**3 - 2*g**2 - 4.
-3*(g - 1)**2*(g + 1)
Factor 3/5*f**3 + 6/5*f + 9/5*f**2 + 0.
3*f*(f + 1)*(f + 2)/5
Let x(q) be the first derivative of 1/9*q**3 + 2/3*q - 1/2*q**2 - 1. Factor x(i).
(i - 2)*(i - 1)/3
Let a(x) be the second derivative of x**7/70 - 2*x**6/25 + 9*x**5/50 - x**4/5 + x**3/10 + 16*x - 2. Let a(c) = 0. What is c?
0, 1
Let u be (5 - 2/4) + -4. Let z(d) be the first derivative of -u*d + 1/6*d**3 - 1/4*d**2 - 1 + 1/8*d**4. Find b, given that z(b) = 0.
-1, 1
Let -r**4 - 2*r - 3*r**3 + 2*r**3 + 2*r**4 + 2 - 3*r**2 + 3*r = 0. Calculate r.
-1, 1, 2
Let k be (5/20)/(1/((-8)/(-5))). Let w(x) be the first derivative of k*x**2 + 0*x - 14/15*x**3 - 1 + 1/2*x**4. What is d in w(d) = 0?
0, 2/5, 1
Let r(f) be the third derivative of -f**4/24 - f**3/6 - f**2. Let k be r(-3). Solve 0 - 2*c + 1 - 1 - k*c**2 = 0.
-1, 0
Let t be -4 + ((-111)/(-108) - -3). Let b(g) be the third derivative of 1/45*g**5 + t*g**4 + 1/180*g**6 + 0 + 2*g**2 + 0*g**3 + 0*g. Factor b(h).
2*h*(h + 1)**2/3
Factor -4 + 7*a + 5*a**2 - 22*a + 4.
5*a*(a - 3)
Suppose 0*z + 5*z = -5*s - 905, z + 3*s + 173 = 0. Let x = 929/5 + z. Suppose -2/5*n**2 - 6/5*n**3 + 6/5*n + x - 2/5*n**4 = 0. What is n?
-2, -1, 1
Let n(v) be the second derivative of v**4/30 - v**3/15 + 7*v. What is j in n(j) = 0?
0, 1
Let z(f) be the first derivative of 0*f + 1/6*f**2 + 1 + 1/30*f**5 - 1/6*f**3 + 0*f**4. Factor z(d).
d*(d - 1)**2*(d + 2)/6
Let k = 67/524 - -16/131. What is u in 0*u - 1/4*u**2 + k = 0?
-1, 1
Let j(m) be the first derivative of -m**2/2 + 6*m + 3. Let q be j(4). Factor o**q + 3/5*o**3 - 9/5*o**4 + 0 + 1/5*o.
-o*(o - 1)*(3*o + 1)**2/5
Let y = -1/18 + 11/36. Factor -l**2 - 1/4*l**5 - 3/2*l**3 - l**4 - y*l + 0.
-l*(l + 1)**4/4
Let u = 0 + 6. Factor u*t**2 + 6 - 5 + 2*t**3 + 6*t + 1.
2*(t + 1)**3
Determine v, given that 1/4*v**4 + 33*v + 18 + 15/4*v**3 + 37/2*v**2 = 0.
-6, -2, -1
Let o(g) be the second derivative of -g**4/18 + 7*g**3/9 + 4*g. Factor o(c).
-2*c*(c - 7)/3
Let z = -139 - -142. Factor -5/3*k**z + k**4 - 1/3*k**2 + 5/3*k - 2/3.
(k - 1)**2*(k + 1)*(3*k - 2)/3
Let i be 18/45*15/18. Factor 0*u + 0 - 2/3*u**2 - i*u**3.
-u**2*(u + 2)/3
Let c(a) be the first derivative of -2/5*a**2 - 1/15*a**3 + 2 + 4*a + 1/30*a**4. Let u(l) be the first derivative of c(l). Factor u(p).
2*(p - 2)*(p + 1)/5
Let x be (3/27)/(2/3964). Let v = x - 220. Factor 4/9*w**3 + v*w + 2/3*w**2 + 0.
2*w*(w + 1)*(2*w + 1)/9
Let k(l) be the first derivative of 2*l**3 + 3/2*l**2 + 1 + 3/4*l**4 + 0*l. Factor k(o).
3*o*(o + 1)**2
Let o(n) = 2*n**2 - 2*n - 2. Let p be o(2). Let d = 12 + -7. Let 0*q**3 - q**3 + p*q**4 + 2*q**3 + q**d + 0*q**3 = 0. What is q?
-1, 0
Let a be 0*((-7)/(-35) - 7/10). Let y = -4 - -6. What is z in a*z**2 + 5*z**y - 4*z**2 = 0?
0
Let w(o) be the first derivative of -o**4/42 + 2*o**3/21 - o**2/7 - 4*o - 2. Let z(n) be the first derivative of w(n). Let z(x) = 0. Calculate x.
1
Let p be (-2)/(-8) + (-6)/(-8). Let v be (-1 + 2)*p*2. Determine q, given that q + 1/3*q**3 - q**v - 1/3 = 0.
1
Let u(b) be the third derivative of -b**8/560 + b**6/120 - 5*b**3/6 - b**2. Let t(w) be the first derivative of u(w). Factor t(a).
-3*a**2*(a - 1)*(a + 1)
Let f(k) = -12*k**3 + 8*k**2 + 152*k - 192. Let u(l) = 8*l**3 - 5*l**2 - 101*l + 128. Let m(y) = 5*f(y) + 8*u(y). Let m(z) = 0. Calculate z.
-4, 2
Let v(r) = -r**2 + 5*r + 2. Let c be v(5). Let s(b) = -2*b + 1 + b + c*b. Let y(x) = -x**3 + x**2 - x - 1. Let d(l) = s(l) + y(l). Factor d(j).
-j**2*(j - 1)
Let h be 2621/(-12)*112/(-21). Let j = -1154 + h. Let 16/3*o - j*o**3 + 14/3*o**2 + 8/9 = 0. Calculate o.
-2/7, 1
Let v be (-2)/(-3) - (-518)/(-21). Let y be ((-2)/4)/(3/v). Determine l, given that 0*l**2 + 2/3*l**y - 2/3 + 4/3*l**3 - 4/3*l = 0.
-1, 1
Let m = 139 - 136. Let t(q) be the second derivative of 0*q**2 + 0 + 0*q**4 - 2*q - 1/60*q**5 + 1/18*q**m. Factor t(f).
-f*(f - 1)*(f + 1)/3
Let q be (3 - 65/20)/(-1). Solve 0 + g**2 + 1/4*g**3 - g**4 - q*g = 0 for g.
-1, 0, 1/4, 1
Let y = -4 + 1. Let z be 6/9*y/(-4). Factor z - 5/4*r + 3/4*r**2.
(r - 1)*(3*r - 2)/4
Factor -3 + 12*l**4 - 7*l**3 + 12*l - 8*l**2 - l**3 - 1 - 3*l**5 - l**5.
-4*(l - 1)**4*(l + 1)
Suppose -6 = 70*b - 73*b. Factor 0*k + 2/5 - 2/5*k**b.
-2*(k - 1)*(k + 1)/5
Let z(y) be the third derivative of -y**5/80 - y**4/16 + 9*y**2. Determine a, given that z(a) = 0.
-2, 0
Let g be 4/16 - 3/12. Let x(o) be the second derivative of -1/3*o**3 + 0*o**2 + 2*o + g + 1/5*o**5 + 0*o**6 - 1/21*o**7 + 0*o**4. Factor x(j).
-2*j*(j - 1)**2*(j + 1)**2
Suppose -4*i - 3*s + 23 = 0, -2*s + 5 = i - 7. Let a be 2 + (-1 - (-1 - -1)). Factor -f - f**3 + 2*f + 0*f**3 + a - f**i.
-(f - 1)*(f + 1)**2
Let k = -1104/7 + 158. What is v in -2/7*v**3 - k*v - 4/7*v**2 + 0 = 0?
-1, 0
What is i in 0 - 6/7*i**3 - 2*i**4 - 4/7*i**5 + 0*i + 0*i**2 = 0?
-3, -1/2, 0
Let k = -1 + -7. Let h be (k/(-42))/(12/14). Find m such that -2/3*m - h*m**2 - 4/9 = 0.
-2, -1
Let h be (3 - 6) + 1 + 6. Find n such that h*n**4 + 5*n**3 + 1 + 10*n**2 - 10*n**4 - 5 - 3*n**3 - 2*n = 0.
-1, -2/3, 1
Let a = 2/15 - -11/30. Let x(t) = -t**2 + 7*t - 5. Let r be x(6). Suppose -a*i**2 + r - 1/2*i = 0. Calculate i.
-2, 1
Let q(k) be the third derivative of k**6/660 + k**5/165 + k**4/132 + k**2. Factor q(t).
2*t*(t + 1)**2/11
Suppose 3 = -t - 7. Let m be (16/t)/((-10)/25). Find r such that -21*r**m + 15*r**3 + 27*r**2 - 12*r - 3*r - 2 - 5 + 1 = 0.
-1, -2/7, 1
Let k(g) be the second derivative of g**5/150 - g**4/10 + 3*g**3/5 - g**2 + 4*g. Let n(l)