. Let j = m - -133. Suppose -2/3*u - 10/3*u**3 + 16/3*u**2 - j = 0. What is u?
-2/5, 1
Factor -3/2*k**3 - 1/2*k**2 + 1 - 1/2*k**4 + 3/2*k.
-(k - 1)*(k + 1)**2*(k + 2)/2
Let u = 8 + -5. Let r(k) = u*k**3 + k**3 + 2*k + 4*k**2 + 2*k. Let m(y) = 5*y**3 + 4*y**2 + 5*y. Let x(t) = -6*m(t) + 7*r(t). Factor x(b).
-2*b*(b - 1)**2
Let k = -78 + 82. Let v be (-1 + -2)/(60/(-8)). Let -4/5*h**3 - v + h - 2/5*h**2 + 4/5*h**k - 1/5*h**5 = 0. Calculate h.
-1, 1, 2
Suppose 3/7*j**2 - 15/7*j + 3/7*j**3 + 9/7 = 0. What is j?
-3, 1
Factor -2*p**3 - 38/7*p**2 + 12/7*p + 0.
-2*p*(p + 3)*(7*p - 2)/7
Let n(d) be the third derivative of -d**8/1680 - d**7/210 - 3*d**6/200 - 7*d**5/300 - d**4/60 + 3*d**2. Factor n(i).
-i*(i + 1)**3*(i + 2)/5
Let t(q) = q**3 - 4*q**2 - 4*q - 3. Let y be t(5). Solve -10*s**y + 3 - 3 - 4*s - 8*s**3 - 2*s**4 = 0 for s.
-2, -1, 0
Let q(f) be the second derivative of -f**4/96 - 5*f**3/8 - 225*f**2/16 - 2*f - 15. Factor q(n).
-(n + 15)**2/8
Let p(u) = 2*u**4 + 2*u**3 - 3*u**2 - 3. Let f(i) = 3*i**4 + 4*i**3 - 5*i**2 - 5. Let s = -6 - 4. Let j(q) = s*p(q) + 6*f(q). Suppose j(l) = 0. What is l?
0, 2
Suppose 10 = 3*v + 2*v. Let b(j) be the first derivative of 2/5*j**5 + j**2 + v*j + 2 - 4/3*j**3 - j**4 + 1/3*j**6. Factor b(c).
2*(c - 1)**2*(c + 1)**3
Let j = 5 - 5. Let i**3 + j*i**3 + 3*i**3 - 2*i**2 = 0. What is i?
0, 1/2
Let i be 32/10 + 3 + -6. Factor 0 - i*a**4 - 2/5*a**3 + 0*a - 1/5*a**2.
-a**2*(a + 1)**2/5
Solve -3/2*d**2 + 9/2*d + 0 = 0 for d.
0, 3
Let d(q) be the first derivative of q**5/35 - q**4/28 - q**3/21 + q**2/14 - 19. Suppose d(b) = 0. What is b?
-1, 0, 1
Factor 3 + 1/2*p**2 - 7/2*p.
(p - 6)*(p - 1)/2
Factor -1/4*m + 1/4 - 5/4*m**2 - 3/4*m**3.
-(m + 1)**2*(3*m - 1)/4
Let f be (-315)/54*15/(-70). Let 3/2 + 17/4*u + f*u**2 = 0. Calculate u.
-3, -2/5
Let s be (0/3)/(12/(-6)). Find j such that 4/3 - 3*j**2 + s*j = 0.
-2/3, 2/3
Let p(c) be the first derivative of 2*c**3/3 - 4*c**2 + 8*c - 2. Suppose p(m) = 0. What is m?
2
Let r(a) be the third derivative of a**7/252 + a**6/240 - 7*a**5/360 - a**4/48 + a**3/18 + 3*a**2. Factor r(b).
(b - 1)*(b + 1)**2*(5*b - 2)/6
Let t(x) be the first derivative of 2*x**5/25 + x**4/5 - 2*x**3/15 - 2*x**2/5 + 24. Factor t(w).
2*w*(w - 1)*(w + 1)*(w + 2)/5
Find i such that i - 7/2*i**4 + 4*i**2 - 1/2 - 2*i**5 + i**3 = 0.
-1, 1/4, 1
Let n(q) be the second derivative of q**10/136080 + q**9/34020 + q**8/30240 - 5*q**4/12 - 5*q. Let w(d) be the third derivative of n(d). What is g in w(g) = 0?
-1, 0
Let w(k) = 3*k - 1. Let f be w(1). Suppose -5 = -r - 3. Factor -f*j**2 - r*j + 0*j**2 + 4*j**2.
2*j*(j - 1)
Let b be (0 - -2)*(-1 + 9). Let g be (10/(-25))/(b/(-10)). Factor 0 + 0*i**2 - 1/4*i**4 + 0*i - g*i**3.
-i**3*(i + 1)/4
Let b(q) be the first derivative of -q**5/45 - q**4/18 + q**3/9 + 4*q**2/9 + 4*q/9 + 20. Factor b(n).
-(n - 2)*(n + 1)**2*(n + 2)/9
Let a(w) be the second derivative of 0 + 0*w**2 + 2/9*w**3 - 9*w + 4/9*w**4 - 7/90*w**6 + 1/12*w**5. Factor a(u).
-u*(u - 2)*(u + 1)*(7*u + 2)/3
Let u(k) be the first derivative of -k**4/22 + 10*k**3/33 - 8*k**2/11 + 8*k/11 - 1. Factor u(a).
-2*(a - 2)**2*(a - 1)/11
Let l(a) be the third derivative of -a**6/660 - 2*a**5/165 - a**4/44 + 7*a**2. Factor l(g).
-2*g*(g + 1)*(g + 3)/11
Let u(m) be the second derivative of -m**6/180 - m**5/60 - m**3/2 + 4*m. Let r(d) be the second derivative of u(d). Suppose r(i) = 0. What is i?
-1, 0
Let f(w) = -w**3 - 14*w**2 - 13*w. Let i = 5 - 18. Let h be f(i). Solve 2/11*q**3 + 0 + h*q**2 + 0*q = 0.
0
Let h = -3 + 3. Let -2/9*k**4 + 0*k - 2/9*k**2 - 4/9*k**3 + h = 0. Calculate k.
-1, 0
Let d be (-4)/(-26) - (-22)/(-143). Let r(x) be the first derivative of 0*x**4 - 4/15*x**3 + 2/5*x + 2/25*x**5 + d*x**2 + 1. Factor r(s).
2*(s - 1)**2*(s + 1)**2/5
Let x(h) be the first derivative of -h**4/78 + 2*h**3/39 - h**2/13 - 2*h - 2. Let k(z) be the first derivative of x(z). Factor k(s).
-2*(s - 1)**2/13
Find m such that -1/3*m**3 - 4/3 - 5/3*m**2 - 8/3*m = 0.
-2, -1
Let i(f) be the third derivative of -f**7/420 - f**6/180 - f**3/3 + 2*f**2. Let u(j) be the first derivative of i(j). Let u(k) = 0. What is k?
-1, 0
Let i = 107/3 - 35. Let k be ((-2)/(-5))/((-1)/(-5)). Let 0 + 0*t**k + 0*t**4 - 1/3*t - 1/3*t**5 + i*t**3 = 0. What is t?
-1, 0, 1
Let x = 359 + -3227/9. Let n be (-1 + 0)*(350/(-45))/5. Factor -10/9*s + x - n*s**2.
-2*(s + 1)*(7*s - 2)/9
Let i(l) be the third derivative of -l**8/1176 - l**7/147 - l**6/140 + l**5/42 + l**4/21 + 5*l**2. Find p such that i(p) = 0.
-4, -1, 0, 1
Let v be (-1)/(-5) - 376/(-120) - 2. Find b such that 2/3*b**2 + 2/3 + v*b = 0.
-1
Let q(s) be the second derivative of s**4/6 - 4*s**3/3 + 3*s**2 + 4*s. Factor q(b).
2*(b - 3)*(b - 1)
Factor -14*a**2 - a**5 + a**4 + a**4 + 3*a**5 - 4*a + 4*a**2 - 6*a**3.
2*a*(a - 2)*(a + 1)**3
Let m(l) be the third derivative of 0 + 1/105*l**7 + 4*l**2 + 0*l**3 + 1/35*l**6 + 0*l - 1/42*l**4 + 1/70*l**5. Find o, given that m(o) = 0.
-1, 0, 2/7
Let b**2 - 20 + 5*b - 26 + 32 = 0. What is b?
-7, 2
Let u = -3 - -3. Factor u*b - b + 3*b + 2*b**2.
2*b*(b + 1)
Let a(v) = 3*v - 6. Let f be a(6). Suppose 4*b + 0*b - f = 0, -4*p + 17 = -b. Solve -10*c - c**2 - c**3 + c**4 + 10*c + c**p = 0.
-1, 0, 1
Let k(f) be the first derivative of -3*f**5/20 + f**4/4 + f**3/2 - 3*f**2/2 - 6*f - 1. Let g(s) be the first derivative of k(s). Factor g(j).
-3*(j - 1)**2*(j + 1)
Let x be (9/((-9)/(-2)))/((-20)/(-15)). Factor 1/4*k**5 + 7/2*k**3 - x*k**4 + 9/4*k - 4*k**2 - 1/2.
(k - 2)*(k - 1)**4/4
Let k be 4/12 - 0/2. Determine d so that 0 - 1/3*d**2 - 1/3*d**3 + k*d + 1/3*d**4 = 0.
-1, 0, 1
Let l = 238 + -1186/5. Determine x so that l*x + 2/5 + 2/5*x**2 = 0.
-1
Solve -l**4 + 2*l + 3*l**3 + 1 - 7*l**3 + 2*l**3 = 0.
-1, 1
Suppose -7 = -2*d + 1. Suppose -2 - z**4 - 5*z - 4*z**4 + 2*z**2 + 8*z**d + 5*z**3 - 3*z**2 = 0. What is z?
-1, -2/3, 1
Let d be 1138/(-30) + (-6)/15. Let y = -38 - d. Let y*i**4 - 1/3*i + 0 + 1/3*i**3 - 1/3*i**2 = 0. What is i?
-1, 0, 1
Let t = 0 + -3. Let f be (-45)/(-21) + 2 + t. Factor -f*s + 24/7*s**2 - 18/7*s**3 + 0.
-2*s*(3*s - 2)**2/7
Let j = 1 - -11. Suppose 2*i - 3*u + 7 = -4, -i - 2*u = -j. Find y, given that 0*y**2 + y**2 + 2*y**i - 3*y = 0.
0, 1
Let b(y) be the third derivative of 5*y**2 + 0*y - 1/60*y**6 + 1/5*y**5 - y**4 + 0 + 8/3*y**3. Determine f, given that b(f) = 0.
2
Let n(x) be the first derivative of x**6/15 - 4*x**5/25 - x**4/5 + 8*x**3/15 + x**2/5 - 4*x/5 - 1. Find a, given that n(a) = 0.
-1, 1, 2
Factor 15*g**3 - 8*g**3 + 14*g**2 + 4*g + 4*g**4 + 7*g**3 + 0*g**4.
2*g*(g + 1)*(g + 2)*(2*g + 1)
Let h be (9/27)/((-1)/(-9)). Let f(m) be the first derivative of -1 + 0*m + 0*m**2 - 2/27*m**h. Find l such that f(l) = 0.
0
Let y(i) = -i. Let w be y(-4). Determine u so that -u**5 - 2*u**2 - 6*u**3 - 4*u**4 - 2*u**w - u**5 = 0.
-1, 0
Let k = 12 - 7. Suppose 2*p + 20 = k*y, y + p - 4*p - 17 = 0. Factor -4*r**3 - r**4 - 3*r**2 + y*r - 3*r + r**3.
-r*(r + 1)**3
Let t be 4 + ((-24)/(-6) - 5/4). Let c(f) be the first derivative of 2*f**3 + 0*f + 21/5*f**5 - 3 + 0*f**2 - t*f**4. Determine y, given that c(y) = 0.
0, 2/7, 1
Let t = -8 + 8. Suppose t = -5*g + 10 + 5. Find c, given that -2/3*c**g + 2/3 - 2/3*c**2 + 2/3*c = 0.
-1, 1
Let u be 3*(75/(-27) - -3). Suppose -5*d + 2*q - 10 = -3*q, -d + 2*q - 6 = 0. Find v such that -1/3*v**d + 1/3*v + u = 0.
-1, 2
Suppose -2*j - 2 = 2*k - 4, k - j = 3. What is z in -3 - 3 - z**2 + k*z + 5 = 0?
1
Factor -u**3 + 2*u**2 + 0*u**2 - 2*u**3 - u**3 + 2*u**4.
2*u**2*(u - 1)**2
Factor -c**4 + 0*c**3 + 1/2*c**5 + 0 - 1/2*c + c**2.
c*(c - 1)**3*(c + 1)/2
Let l(r) = r**3 - 3*r**2 + 3*r - 1. Let z be l(2). Let h be 5/z + 1 + -4. Factor -f**2 - f - f**h - f.
-2*f*(f + 1)
Let m(b) be the first derivative of 2*b**7/105 - b**6/20 - b**5/30 + b**4/4 - b**3/3 - b**2/2 - 1. Let u(j) be the second derivative of m(j). Factor u(v).
2*(v - 1)**2*(v + 1)*(2*v - 1)
Let p(h) = 6*h**2 + 4*h + 2. Let q be p(-1). Suppose 0*l**3 + 3/5*l**2 + 0*l - 3/5*l**q + 0 = 0. Calculate l.
-1, 0, 1
Factor 0 - 1/3*n**3 - 1/3*n + 2/3*n**2.
-n*(n - 1)**2/3
Let v(m) be the first derivative of 4*m**3/15 + 11*m**2/10 - 3*m/5 + 37. Determine a, given that v(a) = 0.
-3, 1/4
Suppose 3*u = 41*u - 152. What is o in 4/3 - 1/3*o**u - 4/3*o**3 - o**2 + 4/3*o = 0?
-2, -1, 1
Let l(v) = -v - 6.