
2*(u - 2)*(u + 2)/9
Let c(f) = f**4 - f**3 + f**2 + f + 1. Let n(q) = -5*q**3 - 5*q**2 - 3*q. Let b(i) = c(i) - n(i). Find v such that b(v) = 0.
-1
Let l(a) be the first derivative of -a**6/40 + 2*a**2 - 4. Let g(x) be the second derivative of l(x). Factor g(f).
-3*f**3
Let q be (-6)/9*-3 - -4. Determine y so that -6*y - 3*y**2 + 9 + 6 - q = 0.
-3, 1
Let z be (-1)/4 + 5/20. Let w(u) be the third derivative of 0 - 2/15*u**5 + z*u**3 + 1/3*u**4 + 1/60*u**6 + 2*u**2 + 0*u. Let w(f) = 0. Calculate f.
0, 2
Let p(b) be the third derivative of -3*b**8/56 + b**7/7 + b**6/12 - b**5/2 + 4*b**3/3 - 7*b**2. Factor p(k).
-2*(k - 1)**3*(3*k + 2)**2
Let g(s) be the first derivative of -s**6/180 + 2*s**5/45 - 5*s**4/36 + 2*s**3/9 - 2*s**2 + 3. Let c(l) be the second derivative of g(l). Factor c(h).
-2*(h - 2)*(h - 1)**2/3
Let j = -1 - -9. Factor -j + 6*x + 8 + 3*x**2.
3*x*(x + 2)
Let b(n) = n**2 - 87*n - 359. Let o be b(-4). Factor -2/7*k**4 + 2/7*k**2 + 0 + 1/7*k - 1/7*k**o + 0*k**3.
-k*(k - 1)*(k + 1)**3/7
Let z(l) be the second derivative of l**7/840 + l**6/360 - l**3/2 + l. Let h(m) be the second derivative of z(m). Factor h(a).
a**2*(a + 1)
Let m(f) be the second derivative of 0 - 4/27*f**4 - 2/9*f**2 + 13/27*f**3 - 8/15*f**5 + f. Factor m(y).
-2*(3*y + 2)*(4*y - 1)**2/9
Let g(t) be the third derivative of 5*t**8/2352 - 2*t**7/245 + 3*t**6/280 - t**5/210 + 10*t**2. Let g(q) = 0. What is q?
0, 2/5, 1
Let t(j) be the third derivative of j**11/55440 + j**10/16800 - j**8/6720 - j**5/10 + 4*j**2. Let i(a) be the third derivative of t(a). Factor i(c).
3*c**2*(c + 1)**2*(2*c - 1)
Let j(x) = 25*x**3 + 20. Let h(f) = -f**3 - f**2 + f - 1. Let l(a) = -20*h(a) - j(a). Solve l(i) = 0.
0, 2
Let q(z) be the second derivative of z**6/360 - z**5/60 + z**4/24 + 7*z**3/6 - 6*z. Let j(l) be the second derivative of q(l). Solve j(a) = 0 for a.
1
Let v(c) be the third derivative of 0*c + 0 + 0*c**4 - 1/504*c**8 - 1/105*c**7 - 1/60*c**6 - 1/90*c**5 - 5*c**2 + 0*c**3. Factor v(w).
-2*w**2*(w + 1)**3/3
Let r be 0*(25/(-50))/((-6)/4). Suppose r + 2/5*d**3 + 4/5*d + 6/5*d**2 = 0. What is d?
-2, -1, 0
Let j(h) be the first derivative of -h**6/160 - h**5/24 - 3*h**4/32 - h**3/12 - h**2/2 - 2. Let f(b) be the second derivative of j(b). Factor f(r).
-(r + 1)*(r + 2)*(3*r + 1)/4
Let n = 11 - 5. Let l be 4 + 1/(-2)*2. Let 4*s**4 + l*s + n*s**2 - 2*s**4 + 6*s**3 - s = 0. What is s?
-1, 0
Suppose 7*t = 14*t + 22*t. Find s such that -8/3*s**3 + 8/3*s + 4/3 - 4/3*s**4 + t*s**2 = 0.
-1, 1
Let z(h) = h**2 - h - 2. Let x = -8 - -6. Let i be z(x). Factor -6*l**2 + 7*l + 0*l**2 - l**2 + i + 5*l.
-(l - 2)*(7*l + 2)
Suppose 6*b - 3*b - 9 = 0. Let p be 2/12*4 + 0. Determine v, given that 2/3*v - 2/3*v**2 + 0 + p*v**4 - 2/3*v**b = 0.
-1, 0, 1
Factor 0*j + 0 + 5/6*j**2 + 1/6*j**4 + j**3.
j**2*(j + 1)*(j + 5)/6
Suppose -3/8*j**2 + 15/4 - 27/8*j = 0. What is j?
-10, 1
Factor -4/7*p**4 + 16/7*p**2 + 0 - 8/7*p**3 + 2/7*p**5 + 0*p.
2*p**2*(p - 2)**2*(p + 2)/7
Let b(z) be the first derivative of 4*z**3/3 - 32*z**2 + 60*z - 4. Factor b(i).
4*(i - 15)*(i - 1)
Suppose 9*m**3 + 11*m**3 - 5*m**3 + 10*m**2 + 5*m**4 = 0. Calculate m.
-2, -1, 0
Suppose 15*n = 27 + 3. Suppose 3/2*k**4 - 15/2*k - 3 - 9/2*k**n + 3/2*k**3 = 0. Calculate k.
-1, 2
Let a(l) be the third derivative of -l**7/350 - l**6/150 + l**5/60 + l**4/60 + 12*l**2. What is b in a(b) = 0?
-2, -1/3, 0, 1
Let j(o) be the third derivative of -o**6/180 - o**5/90 + o**4/36 + o**3/9 - 6*o**2. Solve j(i) = 0 for i.
-1, 1
Let b(p) be the second derivative of 5*p**7/42 + 5*p**6/6 + 2*p**5 + 5*p**4/3 + 11*p. Find d, given that b(d) = 0.
-2, -1, 0
Let m be ((-18)/(-8) - 3 - -1)*8. Let -4/3 + 4/3*y**m + 2/3*y - 2/3*y**3 = 0. What is y?
-1, 1, 2
Find i, given that -3/2*i**4 + 0 + 0*i - 1/2*i**5 - 3/2*i**3 - 1/2*i**2 = 0.
-1, 0
Let s(b) = 406*b**3 + 440*b**2 - 15*b - 96. Let y(h) = -811*h**3 - 880*h**2 + 30*h + 191. Let i(m) = -11*s(m) - 6*y(m). What is u in i(u) = 0?
-3/4, 2/5
Suppose 0 = 5*j - 2 - 3. Let c be j + (3 - (-78)/(-21)). Factor -c*h**3 + 2/7 + 6/7*h**2 - 6/7*h.
-2*(h - 1)**3/7
Let d(q) = -q**3 + 7*q**2 + 2. Let y be d(7). Let s be 18/5 + y/5. Let 3*t - 4*t**3 - 2 - 2*t**s - t + 4*t**2 + 2*t**5 + 0*t**5 = 0. What is t?
-1, 1
Let w(t) be the second derivative of 0*t**3 + 3*t + 0 - 1/45*t**6 + 0*t**4 + 0*t**2 + 0*t**5. Factor w(u).
-2*u**4/3
Suppose -3*l - 315 = 4*l. Let b be (-9)/(l/(-20)) - -6. Factor 4/5*n**4 + 0*n**3 - 4/5*n**b + 2/5*n**5 - 2/5*n + 0.
2*n*(n - 1)*(n + 1)**3/5
Let -2/7*f**2 + 12/7 - 2/7*f = 0. Calculate f.
-3, 2
Let d be (-4 + 3)/3 - 19/(-21). What is w in 20/7*w**2 + 4*w + d*w**3 + 12/7 = 0?
-3, -1
Let q(o) be the first derivative of o**4 - 8*o**3/3 + 1. Let q(n) = 0. Calculate n.
0, 2
Let j(y) = y**3 + 19*y**2 + 17*y - 15. Let k be j(-18). Suppose 1/2*h**k + 1/2*h + h**2 + 0 = 0. Calculate h.
-1, 0
Let g(c) be the second derivative of 2/3*c**2 - 2/9*c**4 - 2*c + 0 - 7/9*c**3. Factor g(k).
-2*(k + 2)*(4*k - 1)/3
Suppose 3*a - 6 = -0*a. Let 0*n**2 - 3*n**2 - 2*n**2 + 4*n**a + 2*n = 0. What is n?
0, 2
Let f(d) be the first derivative of -d**5/15 - d**4/12 + d**3/3 + d**2/6 - 2*d/3 + 8. Suppose f(t) = 0. What is t?
-2, -1, 1
Let n be (-4)/20 - 33/(-15). Factor 6/5*f + 3/5 - 6/5*f**3 - 3/5*f**4 + 0*f**n.
-3*(f - 1)*(f + 1)**3/5
Suppose -5*o = 3*s + 15, 4 = -3*s - 11. Let k(m) be the first derivative of 1/7*m**2 - 1 + o*m + 2/21*m**3. Determine w, given that k(w) = 0.
-1, 0
Let s = -1 - -4. Find k such that -s*k**2 + 3*k**2 + 5*k**3 - 3*k**3 - 2*k**5 = 0.
-1, 0, 1
Factor -2/9 - 2/9*t**2 - 4/9*t.
-2*(t + 1)**2/9
Let v(x) be the second derivative of -5*x**7/6 - 8*x**6/3 + 3*x**5/4 + 20*x**4/3 + 10*x**3/3 - 34*x. Find u, given that v(u) = 0.
-2, -1, -2/7, 0, 1
Determine o so that 0 + 2/7*o**2 - 2/7*o**4 - 5/7*o**3 + 5/7*o**5 + 0*o = 0.
-1, 0, 2/5, 1
Suppose 3*l = -2*l + 25. Suppose l*j = 3*j + 4. Factor -4 + o**2 - 4*o - 6*o**j + 4*o**2.
-(o + 2)**2
Suppose -3*w = -0*w - 21. Suppose -4*j = -w*j + 6. Factor -5*s**2 + 3*s**2 - s**4 + j*s**4 + 1.
(s - 1)**2*(s + 1)**2
Let m(f) be the second derivative of f**5/180 + f**4/72 - f**3/9 + f**2 + 2*f. Let t(a) be the first derivative of m(a). Solve t(x) = 0.
-2, 1
Let w(i) be the third derivative of -7*i**6/300 - 2*i**5/25 + i**4/15 + 12*i**2. Determine m so that w(m) = 0.
-2, 0, 2/7
Let j(x) be the third derivative of -x**6/30 - 4*x**5/15 - 2*x**4/3 + 3*x**2 - 7. Find s, given that j(s) = 0.
-2, 0
Let b(l) = 10*l**2 + 16*l - 1. Suppose 3*o + 3*i + 0*i = 27, 1 = -o - 3*i. Let g(j) = -3*j**2 - 5*j. Let v(r) = o*g(r) + 4*b(r). Solve v(c) = 0 for c.
-2, -1
Solve -3/4*y**3 - 1/4*y**4 + 0*y**2 + 0 + y = 0 for y.
-2, 0, 1
Let i = -4279/20 - -756/5. Let z = -62 - i. Factor z*t - 1/4*t**2 - 1/2.
-(t - 2)*(t - 1)/4
Let j(d) be the first derivative of d**3/9 + d**2/3 - 14. Factor j(c).
c*(c + 2)/3
Let u be 0/3*(1 + -2). Factor u*a + 4*a - a**3 - 4*a + 2*a**2.
-a**2*(a - 2)
Let v(w) be the second derivative of -w**7/84 + 3*w**5/40 - w**4/12 - 6*w. What is u in v(u) = 0?
-2, 0, 1
Let t(n) be the third derivative of n**5/20 + 3*n**4/40 - 10*n**2. Factor t(g).
3*g*(5*g + 3)/5
Let j be (-6)/1 - -13 - 7. Suppose 2/7*y**5 + 2/7*y**2 - 2/7*y**4 + j*y - 2/7*y**3 + 0 = 0. What is y?
-1, 0, 1
Let b(v) be the third derivative of 0*v + 0 - 1/3*v**5 - 1/3*v**3 + 1/168*v**8 + v**2 + 5/12*v**4 - 1/21*v**7 + 1/6*v**6. Let b(d) = 0. What is d?
1
Let h(q) be the third derivative of -q**5/390 + q**4/78 + q**3/13 + q**2. Solve h(a) = 0 for a.
-1, 3
Factor a**4 - 85*a**2 + 9*a**3 + 91*a**2 + 2*a**4.
3*a**2*(a + 1)*(a + 2)
Let p(s) be the first derivative of -18*s**5/35 - 33*s**4/14 - 74*s**3/21 - 15*s**2/7 - 4*s/7 - 16. Find m such that p(m) = 0.
-2, -1, -1/3
Suppose -13*p**2 + 8*p**2 + 5*p**2 - 4*p**5 + 4*p**3 = 0. What is p?
-1, 0, 1
Determine k so that 24/7 + 375/7*k**3 - 150/7*k**2 - 60/7*k = 0.
-2/5, 2/5
Let z be (-852)/5*10/14. Let t = z + 122. What is g in 4/7*g - t*g**2 - 2/7 = 0?
1
Let r(k) be the second derivative of k**5/30 - k**2 - 2*k. Let x(b) be the first derivative of r(b). Factor x(s).
2*s**2
Let x(y) be the second derivative of y**4/4 - 3*y**2/2 + 8*y. Let x(v) = 0. Calculate v.
-1, 1
Let k(d) be the second derivative of 7/36*d**3 - 1/24*d**4 - d - 7/120*d**5 - 1/6*d**2 + 0 + 1/36*d**6. Solve k(h) = 0 for h.
