Let w(q) be the second derivative of d(q). Find z such that w(z) = 0.
-2/5, 0, 1
Solve 7*t**4 - 16 - t**4 - 12*t**2 - 3*t**4 + 8*t**3 + t**4 - 32*t = 0 for t.
-2, -1, 2
Find k, given that 11*k**2 + 1 - 3*k**3 - 19/3*k = 0.
1/3, 3
Let h(l) be the second derivative of -l**7/14 + l**6/10 + 3*l**5/20 - l**4/4 + 11*l. Factor h(i).
-3*i**2*(i - 1)**2*(i + 1)
Let p(o) be the second derivative of o**7/336 + o**6/60 + o**5/32 + o**4/48 + 8*o. What is w in p(w) = 0?
-2, -1, 0
Let b(w) be the second derivative of -2*w + 0 + 1/24*w**4 - 1/60*w**6 + 0*w**3 + 1/40*w**5 + 0*w**2 - 1/84*w**7. Factor b(q).
-q**2*(q - 1)*(q + 1)**2/2
Let p(x) = 22*x**2 + 18*x + 1. Let o(u) = u**2 + 1. Let k(t) = -o(t) + p(t). Factor k(v).
3*v*(7*v + 6)
Let o(w) = w + 3. Let z(i) = -i**2 + 3*i + 1. Let k be z(4). Let u be o(k). Solve u + 2/7*t**3 - 2/7*t - 2/7*t**4 + 2/7*t**2 = 0 for t.
-1, 0, 1
Let n be (-16)/4*(-2)/4. Let b be -2 + (-1 - (-1 - n)). Suppose 1/4*g**3 + b + 1/4*g - 1/2*g**2 = 0. Calculate g.
0, 1
Let y(h) be the second derivative of -2*h**6/5 + 6*h**5/5 - 5*h**4/4 + h**3/2 - 3*h. Let y(k) = 0. Calculate k.
0, 1/2, 1
Let u be (-6)/1*-2*4/16. Factor 1/2*a**5 - 1/2 - 1/2*a**4 + 1/2*a - a**u + a**2.
(a - 1)**3*(a + 1)**2/2
Suppose 2 = -h + 2*h. Find k such that -10/7*k + 6/7*k**h - 4/7 = 0.
-1/3, 2
Let u be (-1*3)/((-15)/20). Suppose 6*z + 16 = 2*z + u*o, -12 = z - 3*o. Determine p so that z - 1/3*p - 1/3*p**3 - 2/3*p**2 = 0.
-1, 0
Let m be 8 + -3*3/3. Let x(y) be the first derivative of -2/5*y**2 - 3 + 0*y**4 + 2/5*y**3 + 0*y - 2/25*y**m. Factor x(h).
-2*h*(h - 1)**2*(h + 2)/5
Suppose -10 = -4*v - v. Let r be 0/(-5 + 7 + -3). Factor r - 1/4*g - g**v - g**3.
-g*(2*g + 1)**2/4
Determine l so that -5*l**3 + 0 + 9/4*l**4 + 13/4*l**2 - 1/2*l = 0.
0, 2/9, 1
Suppose i + 5*t - 7 = 0, 22 = 5*i + 5*t + 7. Let x**2 + 6*x + i*x - 6*x = 0. Calculate x.
-2, 0
Let x(c) be the second derivative of c**6/1620 - c**5/90 + c**4/12 + 7*c**3/6 + 2*c. Let q(f) be the second derivative of x(f). Factor q(i).
2*(i - 3)**2/9
Let t be (-3)/(-9) + (1 - 1). Let j be (5 + -10 + 5)*-1. Determine x, given that j - 1/3*x - t*x**2 = 0.
-1, 0
Suppose 0 = 3*m - 4*y - 27, m + 0*m + 5*y + 10 = 0. Factor -8*w**4 + w**2 - 4*w**m + 4*w + 6*w**2 + w**2.
-4*w*(w - 1)*(w + 1)**3
Suppose 4*n = 4*u + 5 + 15, -5 = -5*n. Let s(x) = x**2 + 4*x + 3. Let c be s(u). Factor 7*v**2 + v**c - 3*v**2 + 0*v**3 + v**3 + 2*v.
2*v*(v + 1)**2
Factor -5/3*s**3 + 5 + 5/3*s - 5*s**2.
-5*(s - 1)*(s + 1)*(s + 3)/3
Let a(f) be the first derivative of -f**7/840 - f**6/360 + f**3 + 5. Let n(u) be the third derivative of a(u). Factor n(j).
-j**2*(j + 1)
Let a(b) be the third derivative of b**8/3024 - b**6/1080 - 3*b**2. Suppose a(j) = 0. What is j?
-1, 0, 1
Let m(b) be the first derivative of b**6/420 - b**5/105 + b**4/84 + 3*b**2/2 - 3. Let k(j) be the second derivative of m(j). Suppose k(f) = 0. Calculate f.
0, 1
Suppose 0 = 3*b + b - 20. Suppose -3*r + 17 = 5*w - w, -b*r = w - 17. Factor -z**2 - w*z**2 + 2*z**2 - 1 - 2*z.
-(z + 1)**2
Let g(x) be the third derivative of -x**6/80 + x**5/10 - 5*x**4/16 + x**3/2 + 41*x**2. Find t such that g(t) = 0.
1, 2
Let c(l) be the third derivative of l**6/60 - l**5/30 + 3*l**2. Determine f so that c(f) = 0.
0, 1
Let m = -31/2 - -16. Let -3/2*b**3 + 7/2*b**2 - 5/2*b + m = 0. What is b?
1/3, 1
Let 0*b + 10 + 2*b**2 - 8*b - 4 + 2 = 0. What is b?
2
Let h = 11 + 5. Let g = h + -9. Factor -g*d - 4*d**3 + 5*d**3 + 2*d**3 + 3*d**2 + d.
3*d*(d - 1)*(d + 2)
Let q(a) be the second derivative of a**5/100 + a**4/20 - a**2/2 - 3*a. Let n(j) be the first derivative of q(j). Let n(p) = 0. What is p?
-2, 0
Let j(l) be the first derivative of 3*l**5/5 - 3*l**4/2 - l**3 + 3*l**2 + 12. Solve j(h) = 0.
-1, 0, 1, 2
Let c(o) be the third derivative of -o**8/2016 - o**7/630 + o**6/360 + o**5/15 + 5*o**2. Let r(a) be the third derivative of c(a). Factor r(h).
-2*(h + 1)*(5*h - 1)
Let i be -1*10/3 - 2*-2. Find n such that 0*n + i*n**2 + 0 + 2/3*n**3 = 0.
-1, 0
Let i(y) be the third derivative of -1/90*y**6 + 2/315*y**7 + 0*y + 0 - 2/45*y**5 + 9*y**2 + 0*y**4 + 0*y**3. Factor i(h).
4*h**2*(h - 2)*(h + 1)/3
Let o(c) = -c**3 - 8*c**2 - 7*c + 3. Let k be o(-7). Suppose p + g - 5*g = -12, -g + k = 4*p. Solve p + 1/3*a**3 + 0*a - 1/3*a**2 = 0.
0, 1
Suppose 4 - 1 = -z, -z = -c. Let t be c + ((-51)/(-5))/3. Solve 18/5*h**4 + 28/5*h**2 + t - 32/5*h**3 - 12/5*h - 4/5*h**5 = 0.
1/2, 1
Suppose -19 = -5*j + 3*f, 6*j - 3*j = -3*f - 3. Let -1 + 2 + j - 6*y + 3*y**2 = 0. What is y?
1
Let t(h) be the first derivative of -h**2 + 0*h + 1/24*h**4 + 0*h**3 + 1 + 1/60*h**5. Let m(x) be the second derivative of t(x). Factor m(r).
r*(r + 1)
Let x(i) = 3*i**3 - 15*i**2 + 9*i - 3. Let a(l) = -3*l**3 + 14*l**2 - 9*l + 3. Let p(r) = 6*a(r) + 5*x(r). Determine g so that p(g) = 0.
1
Let -10 - 10 + 12*y + 4*y**2 + 4 = 0. Calculate y.
-4, 1
Suppose q = -5*l + 8, -5*l = 4*q + 1 - 18. Suppose -3*u + 11 + l = 0. Solve u*w**2 + 2*w - 3*w**2 - w = 0 for w.
-1, 0
Suppose 10 = 6*p - 8. Find f, given that 5/3*f**3 - 5/3*f + p*f**2 - 7/3*f**4 - 2/3 = 0.
-1, -2/7, 1
Let o be (-6)/1*2/(-6). Suppose -3 + 1 - 4*s + 4*s**o + 2 = 0. What is s?
0, 1
Factor 1/10*y**5 + 9/10*y**3 + 0 - 7/10*y**2 - 1/2*y**4 + 1/5*y.
y*(y - 2)*(y - 1)**3/10
Let q(i) be the third derivative of 3*i**3 + 0 - 1/6*i**5 - 1/4*i**4 + 4*i**2 + 0*i - 1/60*i**6. Factor q(w).
-2*(w - 1)*(w + 3)**2
Suppose 0*g + 10 = 2*g. Suppose 4*f = 3*f - g*s + 4, -3*f + 12 = 5*s. Solve -n**2 - 4*n**5 + 1 - 4*n + 1 - 2*n**2 - n**2 + 8*n**3 + 2*n**f = 0.
-1, 1/2, 1
Let y(t) = t**3 + 12*t**2 + 11*t + 3. Let m be y(-11). Let i(j) be the first derivative of -2/9*j**m - 1/3*j**2 + 1 + 0*j. Factor i(z).
-2*z*(z + 1)/3
Let k be (-8)/(-4)*(-1 + 2). Let 0*c**2 + k*c + 2*c**2 - 4 + 0*c**2 = 0. What is c?
-2, 1
Let p(v) = -20*v**2 - 26*v + 1. Let k(a) = -7*a**2 - 9*a. Let m(z) = -21*k(z) + 6*p(z). What is c in m(c) = 0?
-1, -2/9
Let f = 67/192 - 1/64. Find d such that 1/3*d**2 - f*d + 1/3*d**3 + 0 - 1/3*d**4 = 0.
-1, 0, 1
Let l(j) = j**2 - 1. Let f(s) be the second derivative of s**5/20 - s**4/12 + s**3/2 + 5*s**2/2 - 2*s. Let c(v) = -f(v) - 4*l(v). Factor c(u).
-(u + 1)**3
Let c(o) = o**2 - 5*o + 7. Let k be c(4). What is w in 0*w**4 + 3*w**3 - 18*w**2 + k*w**4 - 3*w**5 + 15*w**2 = 0?
-1, 0, 1
Let v(b) = -b**4 - b**3 + b**2 - b. Let n = 13 - 12. Let y(l) = 15*l**3 - 18*l**2 + 9*l. Let h(a) = n*y(a) + 3*v(a). Factor h(d).
-3*d*(d - 2)*(d - 1)**2
Factor -3*a + 7*a - 4 + 6*a + 6*a**2 + 0*a.
2*(a + 2)*(3*a - 1)
Factor 9*l + 20*l**4 + 0*l**2 + 155*l**3 - l + 4*l**2 - 187*l**3.
4*l*(l - 1)**2*(5*l + 2)
Let a = -18 - -12. Let j(o) = -2*o**4 - 11*o**3 - 2*o**2 + 7*o + 7. Let u(k) = -2*k**4 - 10*k**3 - 2*k**2 + 6*k + 6. Let p(h) = a*j(h) + 7*u(h). Factor p(l).
-2*l**2*(l + 1)**2
Let d(k) be the second derivative of -k**7/63 + 2*k**6/45 - k**5/30 + k. Suppose d(z) = 0. Calculate z.
0, 1
Let k be (-17)/(-7) - (-6)/(-14). Factor -z**2 + 4 - z**2 - 4*z**2 - 2*z**3 + 2*z + k*z**2.
-2*(z - 1)*(z + 1)*(z + 2)
Let o(l) = l - 2. Let r be o(4). Let -4 + 9*c**r + 4 + 4 - 15*c - 1 + 27*c**3 = 0. Calculate c.
-1, 1/3
Solve -h**4 - 3*h**4 + 21*h**5 - 2*h**4 = 0.
0, 2/7
Let x = -46 - -48. Let k(m) be the first derivative of 0*m**x - 3 + 6/5*m**3 + 9/25*m**5 - 6/5*m**4 - 3/5*m. Solve k(o) = 0.
-1/3, 1
Let i(k) be the first derivative of 1/7*k**2 + 4/21*k**3 - 4/7*k - 1/14*k**4 + 3. Factor i(j).
-2*(j - 2)*(j - 1)*(j + 1)/7
Factor 126*c**2 - 49*c**3 + 2 - 60*c + 0 + 6.
-(c - 2)*(7*c - 2)**2
Let z(a) be the first derivative of -5*a**6/2 + 4*a**5 + 5*a**4/2 - 20*a**3/3 + 5*a**2/2 - 16. Let z(k) = 0. What is k?
-1, 0, 1/3, 1
Let h(p) = 2*p**2 + 20*p - 46. Let i(b) = 5*b**2 + 60*b - 139. Let v(c) = -11*h(c) + 4*i(c). Factor v(o).
-2*(o - 5)**2
What is g in -8/7*g**4 + 0*g**2 + 4/7*g**3 + 0 + 0*g + 4/7*g**5 = 0?
0, 1
Let d be (0/7)/(2/(-2)). Factor 0*b**2 + 0*b**4 - 4/11*b**3 + 2/11*b + d + 2/11*b**5.
2*b*(b - 1)**2*(b + 1)**2/11
Let p be ((-1)/6)/(2/(-6)). Let k = 0 + p. Find i, given that 0 - k*i**2 - 1/4*i = 0.
-1/2, 0
Let -26*q - 15 - 181 - 30*q - 4*q**2 = 0. Calculate q.
-7
Let l(w) be the third derivative of w**8/84 - 4*w**7/105 + 2*w**5/15 - w**4/6 - w**2. Factor l(u).
4*u*(u - 1)**3*(u + 1)
Let z(h) = 3*h + 38. Let y be z(-12). Let v(d) be the 