e first derivative of 5*y**4 + 55*y**3 + 180*y**2 + 80*y + 53. Suppose b(i) = 0. What is i?
-4, -1/4
Suppose -5 = 4*w - 13. Let b be ((-18)/(-15))/(w/5). Let a - 3*a**3 - 5*a - 1 + 5*a**2 + b*a = 0. Calculate a.
-1/3, 1
Determine k, given that 0 - 4/3*k - 8*k**3 + 8/3*k**5 - 2/3*k**4 + 22/3*k**2 = 0.
-2, 0, 1/4, 1
Let i(o) be the first derivative of o**5/5 + o**4/4 - o**3/3 - o**2/2 + 7. Determine w so that i(w) = 0.
-1, 0, 1
Let m(s) be the second derivative of s**8/2800 - s**7/1400 - s**6/600 + s**5/200 + 2*s**3/3 + 5*s. Let v(h) be the second derivative of m(h). Factor v(r).
3*r*(r - 1)**2*(r + 1)/5
Let o be (-3)/2*-1*2. Factor 6*x**3 + 10*x**2 - o*x**3 + 8 - 5*x**3 - 16*x.
-2*(x - 2)**2*(x - 1)
Let h(k) be the third derivative of -1/900*k**6 + 1/450*k**5 + 0*k + 0 + 1/180*k**4 - 1/45*k**3 + 4*k**2. Find u, given that h(u) = 0.
-1, 1
Let t(p) = -p**3 - p**2 - p. Let b(y) = -y**5 + 11*y**3 + 6*y**2 + 8*y. Let j(f) = 3*b(f) + 24*t(f). Factor j(r).
-3*r**2*(r - 1)**2*(r + 2)
Factor -2*b**3 - 1/4 + 7/4*b**4 + 1/2*b**2 - 1/2*b**5 + 1/2*b.
-(b - 1)**4*(2*b + 1)/4
Let v be 1 - 1*(4 - 5). Let g(p) be the first derivative of 1/5*p**v + 2/15*p**3 - 2 + 0*p. Factor g(o).
2*o*(o + 1)/5
Let x(a) = 2*a**2 - 4*a - 2. Let u(k) = -6*k**2 + 13*k + 7. Let t(z) = z**3 + 8*z**2 + 8*z + 5. Let y be t(-7). Let c(d) = y*u(d) - 7*x(d). Factor c(i).
-2*i*(i - 1)
Let d be (-12)/54 + (-143)/45 + 4. Factor 2/5 - d*s - s**2.
-(s + 1)*(5*s - 2)/5
Let x be (2/(-2))/(-1 + (-2)/(-4)). Find g, given that -1/4*g**x + 1/2 + 1/4*g = 0.
-1, 2
Find k, given that -k**2 - 3*k**3 - k**4 - k**5 - 4*k**4 + 2*k**4 = 0.
-1, 0
Let h(b) = -8*b + 43. Let g be h(5). Solve 0 + 0*l**g + l**4 - l**2 + 1/2*l**5 - 1/2*l = 0.
-1, 0, 1
Suppose 1/3 + 1/3*g**3 + g + g**2 = 0. What is g?
-1
Solve -1/2*f**2 - 3/4 + 3/2*f**3 + 1/4*f**5 + 5/4*f**4 - 7/4*f = 0.
-3, -1, 1
Let w(g) = -g**2 + 4*g + 195. Let b be w(-12). Suppose -h + 2*h = 0. What is o in 0 + 0*o**4 + h*o**2 + 0*o + 1/2*o**5 - 1/2*o**b = 0?
-1, 0, 1
Let c(g) be the third derivative of g**5/60 - g**4/2 + 6*g**3 - 22*g**2. Factor c(d).
(d - 6)**2
Let d(h) = 5*h**3 - 5*h**2 + h + 2. Let v(n) = n. Let m be v(2). Let l(y) = -y - m + 1 - 1 - y - 6*y**3 + 6*y**2. Let z(b) = -4*d(b) - 3*l(b). Factor z(p).
-2*(p - 1)**2*(p + 1)
Let j be 8/3*3/4. Let a(t) be the second derivative of 2*t + 0*t**j + 0 + 1/12*t**4 + 1/6*t**3. Solve a(q) = 0 for q.
-1, 0
Let y(q) be the third derivative of q**6/300 - q**5/300 + 5*q**2. Factor y(l).
l**2*(2*l - 1)/5
Suppose 0 = -3*y, 0 = 5*r + 3*y - 0 - 10. Factor -5/2*d**2 + r*d**3 + 0 + d - 1/2*d**4.
-d*(d - 2)*(d - 1)**2/2
Factor 2 + 3*a**2 - 5*a**3 + 11*a + 4 + a - 2.
-(a - 2)*(a + 1)*(5*a + 2)
Let z(i) be the second derivative of -i**5/12 + 5*i**4/18 + 5*i**3/18 - 5*i**2/3 + 3*i. Factor z(t).
-5*(t - 2)*(t - 1)*(t + 1)/3
Let s(y) = 12*y**2 - 13*y - 4. Let a(p) = 6*p**2 - 6*p - 7. Let g(u) = 6*u**2 - 6*u - 6. Let c(j) = -4*a(j) + 5*g(j). Let d(o) = -5*c(o) + 2*s(o). Factor d(m).
-2*(m - 1)*(3*m + 1)
Let b(u) be the third derivative of -u**6/24 - u**5/20 + u**4/12 + 6*u**2. Find w such that b(w) = 0.
-1, 0, 2/5
Let q(a) = 2*a**2 - 2*a + 2. Suppose 4*c = 6*c - 4. Let h(o) = 7*o - 3. Let s be h(c). Let i(n) = -4*n**2 + 4*n - 3. Let j(x) = s*q(x) + 6*i(x). Factor j(m).
-2*(m - 2)*(m + 1)
Let n be ((3392/(-60))/(-8))/4. Let d = n + -4/15. What is q in -5/2*q + 1/2 + 7/2*q**2 - d*q**3 = 0?
1/3, 1
Let o be 2 - (2 - (1 - -1)). Suppose -o*y = 2*y. Determine w, given that -2/5*w**4 + y*w + 0 + 0*w**3 + 0*w**2 = 0.
0
Let l = -5 - -8. Let h(z) be the third derivative of 1/48*z**4 - 1/120*z**5 + 0*z - 1/240*z**6 + 1/12*z**3 + l*z**2 + 0. Determine x, given that h(x) = 0.
-1, 1
Let v = -7 - -3. Let q be 0*((-1)/v)/1. Factor 9/2*l**4 + 3/2*l**5 + 0 + 3/2*l**2 + q*l + 9/2*l**3.
3*l**2*(l + 1)**3/2
Let 6*c - 1 - c**2 + 6 - 14 = 0. Calculate c.
3
Let k = 45 + -15. Suppose -5*o + k = 5*d, 3*o - 8 = o. Suppose -2/3 - 2/3*g**d - 4/3*g = 0. Calculate g.
-1
Let l(d) be the second derivative of -d**5/10 + d**4/3 + d**3/3 - 2*d**2 + 4*d. Factor l(q).
-2*(q - 2)*(q - 1)*(q + 1)
Suppose y = c, 2*y = y + 5*c - 12. Let q(g) be the third derivative of 1/48*g**4 - 1/120*g**5 + 0*g + 0*g**y + 2*g**2 + 0. Factor q(d).
-d*(d - 1)/2
Suppose -4*l - 8 = -2*l. Let o be 15/(-10)*l/3. Factor 2*n**3 + 2*n**2 - 4*n**3 - 1 - n**4 + o*n**3.
-(n - 1)**2*(n + 1)**2
Factor 4/19 - 10/19*a - 2/19*a**3 + 8/19*a**2.
-2*(a - 2)*(a - 1)**2/19
Let k(g) be the first derivative of g**4/7 + 8*g**3/21 + 2*g**2/7 - 4. Suppose k(q) = 0. Calculate q.
-1, 0
Suppose 52*f = 48*f. Suppose 4*h - 8 = 2*o, -3*o + o - 6 = -3*h. Let 0*k - 5/3*k**5 - k**4 + 2/3*k**3 + 0*k**h + f = 0. What is k?
-1, 0, 2/5
Let o(z) = -z**3 + 26*z + 8. Let v be o(-5). Let -4/5*a**2 - 2/5*a**v + 0 - 2/5*a = 0. Calculate a.
-1, 0
Suppose -22*x = -23*x. Let t(d) be the first derivative of 0*d + 3 + 1/6*d**3 + 1/24*d**6 - 1/8*d**2 + x*d**4 - 1/10*d**5. Find o, given that t(o) = 0.
-1, 0, 1
Let i(j) = 6*j**4 - 2*j**3 - 4*j**2 - 2. Let m be -3*(-20)/(-12)*2. Let l(u) = 12*u**4 - 3*u**3 - 9*u**2 - 5. Let v(a) = m*i(a) + 4*l(a). Factor v(p).
-4*p**2*(p - 1)*(3*p + 1)
Suppose -35 = 3*p + 31. Let l be (-1 + 1)*11/p. Determine k so that -2/3*k**4 + 0*k + 2/3*k**2 + l*k**3 + 0 = 0.
-1, 0, 1
Factor -3 + 3 + 3*a**3 - 7*a + 4*a.
3*a*(a - 1)*(a + 1)
Let u be 10/25*(1/(-16) + 1). Let a(b) be the first derivative of 0*b**3 + u*b**2 - 1/16*b**4 - 3 - 1/2*b. Factor a(z).
-(z - 1)**2*(z + 2)/4
Let m = 5/8 + -1/40. Factor -2/5 - 1/5*b**2 + m*b.
-(b - 2)*(b - 1)/5
Suppose 0*n + 2*n = 10. Suppose -3*w + 10 = 2*w. Factor n*d**2 - w*d**2 + 1 + 2*d - d**2 - d**2.
(d + 1)**2
Let c be (-315)/(-65) - 6/(-39). Let s(g) be the third derivative of 0*g**3 + 0*g**c + 1/12*g**4 - 1/60*g**6 + 0*g - g**2 + 0. Factor s(o).
-2*o*(o - 1)*(o + 1)
Let 9*t**2 + t**4 - 5*t**2 - 5*t**4 = 0. Calculate t.
-1, 0, 1
Let l = 23 + -23. Let t(d) be the third derivative of l - 5/84*d**4 - 2/105*d**5 - 1/420*d**6 - 2/21*d**3 + 0*d + 3*d**2. Suppose t(z) = 0. Calculate z.
-2, -1
Let k(u) = u**2 + 1. Let f be k(1). Let j be (-1 - -1) + 1/4. Factor 1/4*c**f + j - 1/2*c.
(c - 1)**2/4
Let u(t) be the first derivative of t**4 - 1 - 2*t**3 + 0*t - 2*t**2 + 6/5*t**5. Factor u(n).
2*n*(n - 1)*(n + 1)*(3*n + 2)
Let y = -10 - -12. Suppose 0*i - i + y = 0. Suppose -2/3*c**4 + 0 + 0*c + 8/3*c**3 - 8/3*c**i = 0. Calculate c.
0, 2
Let h be 6 - 2 - 12/(-12). Let m(r) be the second derivative of -1/70*r**h + 0*r**4 + 0 + 0*r**2 + 0*r**3 + 3*r. Determine g so that m(g) = 0.
0
Let 2*y + 1/3*y**2 + 3 = 0. Calculate y.
-3
Let d(l) = -l**3 - 7*l**2 - 7*l - 4. Let b be d(-6). Let k be (-2)/(-2 - -3 - b). Determine r, given that -2*r + 2*r + k*r + r**2 = 0.
-2, 0
Suppose -n - 6 = -3*n. Suppose -n*u + 8 = u. Suppose -7*k + 9*k**2 - 3*k**3 - 4 - u*k**3 + k**4 + 6 = 0. Calculate k.
1, 2
Factor -4*c + c**2 + 7*c**2 - 6*c**2.
2*c*(c - 2)
Suppose 7 = -6*t + 1. Let r be t/4 - (-26)/8. Find z such that 6/5*z**2 + 3/5 + 3/5*z**5 - 9/5*z + 6/5*z**r - 9/5*z**4 = 0.
-1, 1
Suppose 5*s - 103 = -93. Let t(y) be the first derivative of 3/16*y**4 - s + 0*y**3 + 0*y - 3/8*y**2. Factor t(g).
3*g*(g - 1)*(g + 1)/4
Let u(y) be the third derivative of 0*y**4 + 0 + y**2 + 1/6*y**3 + 0*y - 1/60*y**5. Factor u(z).
-(z - 1)*(z + 1)
Let b(w) be the first derivative of -w + w**2 + 1/12*w**4 + 1/2*w**3 - 2. Let o(c) be the first derivative of b(c). Factor o(k).
(k + 1)*(k + 2)
Find r such that 18*r**2 - 23*r + 42*r**2 + 3 - 4*r = 0.
1/5, 1/4
Let j = -3 - -7. Let p be (-1)/(-3) - j/12. Determine k so that 2/3*k**2 - 1/3*k + k**3 + p = 0.
-1, 0, 1/3
Suppose 4*d - 4 = -68. Let k be 0 - (d/2 - -1). Factor 2*h + h**2 + 5*h - k*h.
h**2
Factor 1/3*i**4 + 0*i**3 - 2/3*i - i**2 + 0.
i*(i - 2)*(i + 1)**2/3
Let k(x) be the first derivative of 2*x**3/9 - 2*x**2/3 + 2*x/3 + 1. Suppose k(g) = 0. What is g?
1
Let j(c) = 3*c**5 + 12*c**3 + 15*c. Let r(a) = a**5 + 3*a**3 + 4*a. Let g(o) = -4*j(o) + 15*r(o). Factor g(m).
3*m**3*(m - 1)*(m + 1)
Let d(n) be the first derivative of n**3/9 + n**2/3 + n/3 + 6. Factor d(s).
(s + 1)**2/3
Let i be (6 - 3 - 8)*4. Let d be (-5)/i + 14/8. Factor -2/7*b**3 + 0*b - 2/7*b**d + 0.
-2*b**2*(b + 1)/7
Let z(r) = r**5 - 5*r**4 + r**3 - 2*r**2 + 8*r + 7. Let m(c) = -c**4 + c**3 + c + 1. Let o(x)