2 - 1/8*f**3.
-(f - 1)**2*(f + 1)/8
Suppose -4*r + 39 = 7. Solve -14 - u**2 - r*u + 7*u**3 - u**5 + u**5 + 5*u**4 + 10 + u**5 = 0.
-2, -1, 1
Let j(u) be the first derivative of 0*u**3 + 0*u + 1/2*u**2 + 1/240*u**6 - 1/120*u**5 - 2 + 0*u**4. Let t(m) be the second derivative of j(m). Factor t(d).
d**2*(d - 1)/2
Let z(t) be the first derivative of -t**4/8 - t**3/2 - 3*t**2/4 - t/2 + 6. Factor z(o).
-(o + 1)**3/2
Let d(f) = f**3 + 2*f**2 - f + 1. Let w be d(-2). Suppose -p - 15 = -4*j, p - 5*p = -2*j - 10. Factor p*y**3 - 4*y**w - 2*y**3 + 2*y - y.
-y*(y - 1)*(y + 1)
Solve 12*r - 10*r**2 - 12 - 12*r**2 + 19*r**2 = 0.
2
Let y(f) be the third derivative of -f**8/2352 - f**7/245 - 11*f**6/840 - f**5/210 + f**4/14 + 4*f**3/21 + 6*f**2. Factor y(x).
-(x - 1)*(x + 1)*(x + 2)**3/7
Let d(w) be the second derivative of w**5/180 + 5*w**4/108 + 4*w**3/27 + 2*w**2/9 - 13*w. Let d(v) = 0. What is v?
-2, -1
Let f(c) be the second derivative of c**7/252 - c**6/60 + c**5/60 + c**4/12 + c. Let n(l) be the third derivative of f(l). Let n(o) = 0. What is o?
1/5, 1
Let d(h) = -h**2 - h + 1. Let i(k) be the second derivative of k**5/10 - 5*k**4/12 + 5*k**3/6 - k**2/2 - k. Let c(g) = -d(g) - i(g). Factor c(p).
-2*p*(p - 2)*(p - 1)
Let a(x) be the third derivative of -1/45*x**5 + 1/105*x**7 - 1/9*x**3 - 1/504*x**8 + 1/12*x**4 + 3*x**2 + 0 - 1/90*x**6 + 0*x. Factor a(z).
-2*(z - 1)**4*(z + 1)/3
Let u(m) be the second derivative of -1/2*m**2 + 1/12*m**4 + 0 + 1/6*m**3 - 1/20*m**5 - m. Factor u(t).
-(t - 1)**2*(t + 1)
Let i(x) be the first derivative of 1/96*x**4 + x**2 + 0*x**3 + 0*x + 2 + 1/240*x**5. Let u(n) be the second derivative of i(n). Find v such that u(v) = 0.
-1, 0
Let a(n) be the third derivative of 1/40*n**6 + 0*n - 1/8*n**3 + 5*n**2 + 0 - 3/40*n**5 - 1/280*n**7 + 1/8*n**4. Factor a(k).
-3*(k - 1)**4/4
Let p(s) = -9*s**2 - 24*s - 15. Let h(k) = 13*k**2 + 36*k + 23. Let w(o) = -5*h(o) - 7*p(o). Factor w(v).
-2*(v + 1)*(v + 5)
Let j be 4*1 - 7/(-7). Factor -2*g**4 + 4*g**3 - 6*g**j - g**2 + g**2.
-2*g**3*(g + 1)*(3*g - 2)
Let o(c) be the first derivative of -c**7/560 - c**6/120 - 8*c**3/3 - 3. Let b(g) be the third derivative of o(g). Let b(k) = 0. What is k?
-2, 0
Let s(b) be the first derivative of b**2 + 0*b - 2 + 1/48*b**4 - 1/24*b**3 - 1/240*b**5. Let r(z) be the second derivative of s(z). Factor r(x).
-(x - 1)**2/4
Suppose -4*x + 0*x = -8, b + 10 = 3*x. Let q(l) = l**3 + 3*l**2 - 6*l - 5. Let t be q(b). Factor 4/3*y**4 + 0*y - 2/3*y**5 - 2/3*y**t + 0*y**2 + 0.
-2*y**3*(y - 1)**2/3
Find r such that 3/7*r**3 - 6/7 - 3/7*r - 3/7*r**4 + 9/7*r**2 = 0.
-1, 1, 2
Let z(n) be the first derivative of 0*n**3 - 1/40*n**6 + 0*n - 1/30*n**5 - 2 - 1/72*n**4 - 3/2*n**2. Let l(r) be the second derivative of z(r). Factor l(s).
-s*(3*s + 1)**2/3
Suppose 2*q + 193 = 199. Find g such that 1/4 + 0*g - 1/2*g**2 + 0*g**q + 1/4*g**4 = 0.
-1, 1
Let f(p) be the third derivative of p**8/1680 - p**7/1050 - p**6/200 + p**5/300 + p**4/60 - 70*p**2. Factor f(r).
r*(r - 2)*(r - 1)*(r + 1)**2/5
Let i(j) be the third derivative of -j**5/150 + j**4/20 - 2*j**3/15 - 5*j**2. Factor i(c).
-2*(c - 2)*(c - 1)/5
Suppose -8 = -2*s + 4*z + 12, 2*s = 5*z + 25. Let l(g) be the second derivative of -1/3*g**3 + 0*g**2 + g - 1/6*g**4 + s + 1/10*g**5 + 1/15*g**6. Factor l(b).
2*b*(b - 1)*(b + 1)**2
Let d(g) be the third derivative of -g**7/945 + g**6/270 + g**5/90 + 45*g**2. Solve d(l) = 0.
-1, 0, 3
Suppose -2*r = 2*x - 14, x + 5*r - 2*r - 17 = 0. Let 0*d + 2/11*d**x + 0 = 0. Calculate d.
0
Solve 50*k**3 - 8/3*k + 66*k**2 - 62/3*k**4 - 8 - 10*k**5 = 0 for k.
-3, -1, -2/5, 1/3, 2
Let y be (-14)/(-60) - (-1)/(-5). Let a(q) be the second derivative of y*q**5 - 2/3*q**2 + 0 + 5/9*q**3 - 2/9*q**4 + q. Suppose a(z) = 0. Calculate z.
1, 2
Suppose -4*x = 1 - 9. Suppose p + 3*u = -p + 3, -x = 2*u. Factor -1/4*c**p + 1/4*c**2 + 0 + 0*c.
-c**2*(c - 1)/4
Let n(s) be the second derivative of s**6/280 - 3*s**5/140 + s**4/28 + s**2/2 + 2*s. Let j(c) be the first derivative of n(c). Factor j(m).
3*m*(m - 2)*(m - 1)/7
Let j = 49/20 - 11/5. Determine g, given that -j*g + 0 + 1/4*g**3 + 0*g**2 = 0.
-1, 0, 1
Let g(p) be the second derivative of -p**5/5 + p**4 - 2*p**3 + 2*p**2 - 35*p. Determine c so that g(c) = 0.
1
Let z(i) = 12*i**3 + 3*i**2 + 3*i + 6. Let q(m) = -23*m**3 - 6*m**2 - 5*m - 11. Let v(l) = -6*q(l) - 11*z(l). Factor v(o).
3*o*(o + 1)*(2*o - 1)
Let b(o) = -5*o**5 + 25*o**4 - 34*o**3 + 35*o**2 + o. Let u(p) = -p**5 + 5*p**4 - 7*p**3 + 7*p**2. Let c(i) = 6*b(i) - 33*u(i). Let c(k) = 0. Calculate k.
0, 1, 2
Let d(p) be the third derivative of p**6/1140 - p**4/228 - 15*p**2. Suppose d(x) = 0. What is x?
-1, 0, 1
Let h(u) = -2*u**3 - u. Let g(t) = -16*t**3 - 10*t**2 + 3*t. Let v(n) = -g(n) + h(n). Factor v(f).
2*f*(f + 1)*(7*f - 2)
Let f(v) be the first derivative of -2*v**4 + 4*v**3/3 + 2*v**2 - 42. Factor f(n).
-4*n*(n - 1)*(2*n + 1)
Let n(a) be the first derivative of -a**6/12 - a**5/10 + a**4/8 + a**3/6 + 4. Factor n(m).
-m**2*(m - 1)*(m + 1)**2/2
Let s(f) be the second derivative of f**5/30 - f**4/6 + 2*f**3/9 + 20*f. Suppose s(v) = 0. What is v?
0, 1, 2
Let y be ((-5)/3 - -1)*-3. Suppose 1 = -c + y. Let c + 0*x**2 - x**2 + 0 = 0. Calculate x.
-1, 1
Let f(k) = 7*k**3 + 7*k**2 + 3*k - 2. Let y(s) = -2*s + 1 + s**2 - 3*s**2 - 4*s**3 - 3*s**2 + s**2. Let l(c) = -6*f(c) - 10*y(c). Solve l(r) = 0.
-1, 1
Let q = 2 + 4. Let s be (4/6)/(q/18). Suppose 0*d**s + d**2 - 2*d**4 - 2*d**3 + 3*d**4 = 0. Calculate d.
0, 1
Factor -2 - 3*b**3 + 3*b**3 + b**2 + b**2 - b**3 + b.
-(b - 2)*(b - 1)*(b + 1)
Factor 0*n**4 + 1/2*n**3 + 0 - 1/2*n**5 + 0*n**2 + 0*n.
-n**3*(n - 1)*(n + 1)/2
Let n(j) be the second derivative of j**8/168 - j**7/35 + j**6/20 - j**5/30 + j**2 - j. Let b(o) be the first derivative of n(o). Factor b(g).
2*g**2*(g - 1)**3
Let n(h) be the third derivative of h**8/1848 - h**7/385 + h**6/220 - h**5/330 + 4*h**2. Factor n(i).
2*i**2*(i - 1)**3/11
Let f(o) be the first derivative of 0*o + 1 - o**4 - 2*o**2 + 8/3*o**3. Find j such that f(j) = 0.
0, 1
Let s = 14 + -11. Factor 6*b - b**s + 6*b + 3 + 13*b**3 + 3*b**4 + 18*b**2.
3*(b + 1)**4
Let t(b) be the second derivative of b**5/210 - 2*b**4/63 + b**3/21 + 37*b. Find q such that t(q) = 0.
0, 1, 3
Let k = 5 + -2. Let t = k - 1. Factor 2*w**t - w - w**2 + 0*w**2.
w*(w - 1)
Let u be 3/2*(-12)/(-6). Suppose -2*q + 2*y = -8, -u*q - 2*y + 20 = 2*q. Suppose 4*n**3 + 2*n**3 + 18 - 6 - 12*n - 9*n**2 + 2*n**q + n**4 = 0. What is n?
-2, 1
Let d(g) be the first derivative of g**4 - 4*g**3/3 - 2*g**2 + 4*g + 3. Factor d(z).
4*(z - 1)**2*(z + 1)
Let s(x) be the second derivative of -25*x**7/21 - 13*x**6/2 - 59*x**5/4 - 215*x**4/12 - 25*x**3/2 - 5*x**2 + 9*x. Determine d so that s(d) = 0.
-1, -1/2, -2/5
Determine b so that -9/5*b**2 - 48/5*b + 48/5*b**3 + 21/5*b**4 - 12/5 = 0.
-2, -1, -2/7, 1
Let s be (1*-2)/(5/(-15)). Factor 3*u**2 - 3*u + 9*u**3 + s*u - 8*u**2 - 4*u**2 - 3*u**4.
-3*u*(u - 1)**3
Suppose -4 + 0 = f + j, -4*f - 5*j - 21 = 0. Find r, given that -f + 1/2*r + 1/2*r**2 = 0.
-2, 1
Let b(c) = -c**2 - 5*c + 27. Let f be b(-8). Suppose -12 = o - 3*p, -f*p = -3*o + 2 - 14. Factor o + 2/5*r**2 - 2/5*r**4 - 2/5*r + 2/5*r**3.
-2*r*(r - 1)**2*(r + 1)/5
Let u(y) = 2*y**2 - 3*y + 1. Let r be u(2). Factor 4 - 1 - 4*w**2 - r.
-4*w**2
Let r be 11/24 - (75/24 - 3). Solve -2/3*a**2 + 1/3*a + 0*a**3 + 2/3*a**4 + 0 - r*a**5 = 0 for a.
-1, 0, 1
Factor 9/4 - 3/4*t**2 + 3/2*t.
-3*(t - 3)*(t + 1)/4
Let a be (-2)/(-3)*273/14. Suppose 2*s + 4*d - 3 + 1 = 0, a = 3*s + d. Factor 0*p - 1/5*p**s + 0 - 1/5*p**2 + 1/5*p**3 + 1/5*p**4.
-p**2*(p - 1)**2*(p + 1)/5
Let f(s) = -4*s**4 - 3*s**3 - s**2 + 3*s + 5. Let b(m) = -6*m**4 - 4*m**3 - 2*m**2 + 4*m + 8. Let w(r) = 5*b(r) - 8*f(r). Factor w(x).
2*x*(x - 1)*(x + 1)*(x + 2)
Let w(y) = -y**2 - 2*y + 3. Let f(v) = 2*v**2 + 2*v - 4. Let o(j) = -3*f(j) - 4*w(j). Factor o(n).
-2*n*(n - 1)
Let u(a) be the second derivative of a**5/210 - a**3/21 + a**2/2 + 2*a. Let w(d) be the first derivative of u(d). What is g in w(g) = 0?
-1, 1
Let c = -2/199 - -203/398. Factor 0 + c*n**2 - 1/2*n.
n*(n - 1)/2
Let u(v) be the third derivative of 1/210*v**5 + 1/42*v**4 + 0*v + 0 + 1/21*v**3 + 3*v**2. Factor u(d).
2*(d + 1)**2/7
Suppose 3*u - 6 - 3 = 0. Let q(d) be the s