18*k**2 - 36*k**2 + 14*k**2 + 50*k**3.
2*k*(5*k - 2)**2
Let d(g) be the second derivative of 2*g + 1/75*g**6 + 4/15*g**3 - 4/5*g**2 + 0 - 2/25*g**5 + 1/10*g**4. Find v, given that d(v) = 0.
-1, 1, 2
Let r be -4 - ((-1344)/49)/6. Factor 6/7*m + 2/7*m**2 + r.
2*(m + 1)*(m + 2)/7
Let k be 3/(-110)*(-580)/(-15). Let a = 16/11 + k. Find y, given that 4/5 - a*y**2 + 2/5*y = 0.
-1, 2
Let i(h) be the third derivative of 1/30*h**5 + 1/60*h**6 + 0*h**3 + 0 + 0*h**4 - 3*h**2 + 0*h - 2/35*h**7. Factor i(q).
-2*q**2*(2*q - 1)*(3*q + 1)
Let h be 2/(-45)*(-3)/126. Let g(k) be the third derivative of -h*k**7 - 1/90*k**5 + 0*k**3 - 1/108*k**4 - 1/180*k**6 - 2*k**2 + 0*k + 0. What is r in g(r) = 0?
-1, 0
Let i = -17 - -10. Let p = i - -9. Factor 4*q**3 + 1/4*q + 0 - p*q**2.
q*(4*q - 1)**2/4
Let k(w) be the second derivative of -2*w**5/55 - 3*w**4/22 - 2*w**3/33 + 7*w. Factor k(z).
-2*z*(z + 2)*(4*z + 1)/11
Suppose 15 = 5*r + 3*c, -2*c - c = 0. Suppose r*t + 3 = -0*t + 3*g, -g = 4*t - 11. Solve 0 - 10/3*u**t + 14/3*u**3 - 4/3*u = 0 for u.
-2/7, 0, 1
Let f = 4 - 19/5. Solve 2/5 - 1/5*k**2 - f*k = 0 for k.
-2, 1
Determine s so that -5/3*s**4 + 4/3 - 7/3*s**3 - 1/3*s**5 + 1/3*s**2 + 8/3*s = 0.
-2, -1, 1
Find c, given that -16*c**3 - 6 - 4*c**4 + 12*c**2 - 4*c**4 + 16*c + 2*c**4 = 0.
-3, -1, 1/3, 1
Let r(q) be the second derivative of -q**4/12 - q**3/3 - 3*q. Let o be r(0). Suppose o - 1/6*n**3 + 0*n - 1/6*n**2 = 0. What is n?
-1, 0
Let m(i) be the first derivative of -i**4 - 16*i**3/3 - 10*i**2 - 8*i + 6. Factor m(w).
-4*(w + 1)**2*(w + 2)
Let v(m) = 5*m**2 + 4*m + 9. Let g(q) = -6*q**2 - 5*q - 10. Let t(c) = 6*g(c) + 7*v(c). Suppose t(h) = 0. What is h?
-3, 1
Let g be 0/((-16)/(-10) - (-2)/5). Let b(n) be the third derivative of n**2 + 8/3*n**3 + n**4 + 1/60*n**6 + 1/5*n**5 + g + 0*n. Find z such that b(z) = 0.
-2
Let r(n) be the first derivative of 1/2*n**2 - 3 - 5/6*n**3 + 0*n + 3/8*n**4. Factor r(h).
h*(h - 1)*(3*h - 2)/2
Let d = 16 - 14. Factor 1/2*y**5 - 4*y**d + 13/3*y**3 - 1/3 - 7/3*y**4 + 11/6*y.
(y - 1)**4*(3*y - 2)/6
Let s(f) be the first derivative of f**5/20 - f**4/8 + 3*f**2/2 - 3. Let c(d) be the second derivative of s(d). Factor c(v).
3*v*(v - 1)
Let h(v) = -v**3 - 11*v**2 - 9*v + 12. Let q be h(-10). Find w, given that q*w**2 + 18 - 18 = 0.
0
Suppose 0 + 1/4*f**2 + 2*f**3 - 1/4*f**4 - 2*f = 0. What is f?
-1, 0, 1, 8
Let -8*m**3 + 6*m - 36 + 8*m**2 - 8*m**3 + 14*m**3 = 0. What is m?
-2, 3
Let j(b) = b**2 + 6*b - 4. Let l be j(-7). Suppose l*v - 8*v = 0. Factor -4*p**2 - 1 + 2*p + 3*p**2 + v.
-(p - 1)**2
Let f(m) = m**3 - m + 1. Let c(g) = 12*g**3 + 12*g**2 - 14*g + 5. Let x(v) = -c(v) + 3*f(v). Factor x(h).
-(h + 2)*(3*h - 1)**2
Let s = 2/31 - -25/93. Suppose 1/3*j**5 + 0 + 0*j + 1/3*j**2 - s*j**3 - 1/3*j**4 = 0. Calculate j.
-1, 0, 1
Let n(j) = -27*j**5 + 12*j**4 - 12*j**3 + 33*j - 24. Let x(y) = y**5 + y**4 - y**3 - y + 1. Let k(w) = -n(w) - 18*x(w). Factor k(a).
3*(a - 1)**4*(3*a + 2)
Let f(g) be the first derivative of 0*g**2 + 0*g**3 + 1 - 2/5*g**5 + 0*g + 1/4*g**4 + 1/6*g**6. Let f(q) = 0. What is q?
0, 1
Let f = -4 + 6. Factor -9*n - 6*n**2 + 0*n + 6*n**3 + 3*n**5 + 0*n + 0*n**f + 9*n**4 - 3.
3*(n - 1)*(n + 1)**4
Let l be ((-8)/(-6)*-6)/1. Let r = l - -14. Factor 21*t + 14*t**2 - 11*t**2 + 12*t**2 + r.
3*(t + 1)*(5*t + 2)
Let v(z) = z**3 + 7*z**2 + 7*z + 8. Let j be v(-6). Factor 4*y**2 - 4*y - 4*y + 4*y**2 - j*y**3 + 0*y**2.
-2*y*(y - 2)**2
Suppose 0 = -3*b + n - 14, -2*b - 2*b = n + 28. Let k = 8 + b. Find v such that -2*v**2 + 2 + v**k + 2*v**3 - v**2 - 2*v + 0*v**2 = 0.
-1, 1
Let j(f) = f**2 - f + 1. Let b(t) = t**3 - 4*t**2 + 4*t - 4. Let l(a) = b(a) + 4*j(a). Determine i, given that l(i) = 0.
0
Let k be (18/(-8))/3*-4. Let y be 1 + k + 33/(-12). Factor y*h**2 + 0 - 1/2*h.
h*(5*h - 2)/4
Let k(z) be the second derivative of -z**4/3 + 4*z**3/3 + 6*z. Determine n so that k(n) = 0.
0, 2
Find g such that 3 + 1 - 11*g - 9*g**2 + 6*g**2 = 0.
-4, 1/3
Let g(x) be the second derivative of 0 + 1/21*x**3 + 0*x**2 - 4*x - 1/35*x**5 + 1/42*x**4. Determine o so that g(o) = 0.
-1/2, 0, 1
Determine d, given that 1/2*d**2 + 0 - 1/2*d = 0.
0, 1
What is y in -1/3*y + 0 - 1/6*y**3 - 1/2*y**2 = 0?
-2, -1, 0
Let l(r) be the second derivative of -r**5/60 + r**4/36 + r**3/9 - 3*r. Factor l(g).
-g*(g - 2)*(g + 1)/3
Let p(s) be the first derivative of -s**7/105 + 2*s**6/75 + 2*s**5/75 + 3*s**2/2 - 2. Let w(x) be the second derivative of p(x). Factor w(c).
-2*c**2*(c - 2)*(5*c + 2)/5
Let p(k) = -5*k**2 + 8*k + 3. Let j(w) = -4*w**2 + 7*w + 2. Let o(i) = 6*j(i) - 5*p(i). Let n be o(-3). Factor 0*d**2 + 2/9*d + n - 2/9*d**3.
-2*d*(d - 1)*(d + 1)/9
Let v(m) be the third derivative of -27*m**6/220 - 3*m**5/5 - 19*m**4/33 - 8*m**3/33 + 12*m**2. Suppose v(k) = 0. What is k?
-2, -2/9
Suppose 2*l - 6 = 6. Let v be 9/(1/(l/63)). Factor -4/7*a - v*a**4 - 2*a**2 + 0 - 16/7*a**3.
-2*a*(a + 1)**2*(3*a + 2)/7
Let h = -12 + 12. Let y(u) be the first derivative of 1/2*u**2 + 2 - 1/6*u**6 + 2/5*u**5 + h*u - 2/3*u**3 + 0*u**4. Factor y(l).
-l*(l - 1)**3*(l + 1)
Let j(b) be the first derivative of -b**7/21 + b**5/10 - 2*b + 5. Let d(t) be the first derivative of j(t). Factor d(g).
-2*g**3*(g - 1)*(g + 1)
Let s(a) be the second derivative of a**6/40 - 3*a**5/20 + a**4/4 + 2*a**2 - 7*a. Let y(h) be the first derivative of s(h). Factor y(o).
3*o*(o - 2)*(o - 1)
Suppose 3*h - 20 = -h. Let o = h - 1. What is f in 5*f**2 + 2 - o - 3*f**2 = 0?
-1, 1
Let w(g) = -10*g**2 - 45*g + 5. Let n(k) = 15*k**2 + 67*k - 7. Let s(a) = 5*n(a) + 7*w(a). Determine f so that s(f) = 0.
-4, 0
Let l(q) be the first derivative of -21*q**4/16 + 9*q**3/4 - 3*q**2/4 + 2. Factor l(s).
-3*s*(s - 1)*(7*s - 2)/4
Let n(t) be the second derivative of t**7/840 + t**6/90 + t**5/30 - t**3/3 + t. Let d(j) be the second derivative of n(j). Let d(p) = 0. Calculate p.
-2, 0
Let r(s) = -78*s - 15. Let a be r(-12). Let c = a - 4589/5. Factor 2/5*q - 14/5*q**2 + c*q**3 + 32/5*q**4 + 0.
2*q*(q + 1)*(4*q - 1)**2/5
Let q(n) = -5*n**2 + 5*n - 11. Let w(z) = -3*z**2 + 3*z - 6. Let x(c) = -4*q(c) + 7*w(c). Factor x(a).
-(a - 2)*(a + 1)
Factor -4*i - 8*i - 2*i**4 + 5*i**4 - 40*i**3 + 49*i**3.
3*i*(i - 1)*(i + 2)**2
Factor -6/5*o**2 + 6 + 24/5*o.
-6*(o - 5)*(o + 1)/5
Let b(t) be the second derivative of -t**8/56 - 2*t**7/21 - t**6/20 - 5*t**2/2 - 4*t. Let v(m) be the first derivative of b(m). Let v(h) = 0. Calculate h.
-3, -1/3, 0
Let d(k) be the second derivative of 1/8*k**4 + 5*k + 0 - 1/6*k**3 + 0*k**2. Factor d(p).
p*(3*p - 2)/2
What is g in 3/2*g**2 + 75/2 + 15*g = 0?
-5
Suppose -5*g - 10 = -10*g. Let j(c) be the third derivative of 0 + 1/30*c**5 - 2/3*c**3 + g*c**2 + 0*c - 1/12*c**4. Factor j(o).
2*(o - 2)*(o + 1)
Let z(w) be the second derivative of -3*w**5/50 + w**4/15 - 3*w. Determine p, given that z(p) = 0.
0, 2/3
Let i(c) be the first derivative of -1/2*c**3 + 3/10*c**5 + 0*c + 3 + 3/4*c**2 - 3/8*c**4. Suppose i(a) = 0. Calculate a.
-1, 0, 1
Let h(k) be the second derivative of -k**6/42 - 3*k**5/140 + k**4/42 + 6*k. Solve h(v) = 0 for v.
-1, 0, 2/5
Let j(w) = 8*w + 66. Let n be j(-8). Let 2/3 - 1/3*l - 1/3*l**n = 0. Calculate l.
-2, 1
Suppose 2*i - 3*i = 0. Suppose -5*t - 2*c = -i*c, 0 = 2*t + 4*c + 16. Solve -2*n + n**2 - 5*n**t + 2*n**2 = 0 for n.
-1, 0
Let a(v) be the third derivative of v**8/336 - v**7/42 + 7*v**6/120 + v**5/60 - v**4/3 + 2*v**3/3 - v**2. Let a(b) = 0. Calculate b.
-1, 1, 2
Let v(m) be the second derivative of m**7/1260 + m**6/180 + m**5/60 - m**4/4 - 3*m. Let j(h) be the third derivative of v(h). Suppose j(p) = 0. Calculate p.
-1
Let b(c) = 4*c**2. Let n(f) = -8*f**2. Let k(y) = -3*y**2. Let i(g) = 11*k(g) - 4*n(g). Let d(r) = -b(r) - 3*i(r). Factor d(a).
-a**2
Let j(r) = -r**2 + 1. Let x be -1*2/(-4)*0. Let h(g) = x*g - 3 + 3*g - 5*g**2 + 5. Let u(t) = -h(t) + 3*j(t). Suppose u(d) = 0. Calculate d.
1/2, 1
Let r(q) be the third derivative of -q**6/60 - 2*q**5/15 - q**4/4 - 9*q**2. Suppose r(u) = 0. Calculate u.
-3, -1, 0
Let h(s) = 4*s - 21. Let d be h(6). Factor 6/5*n**2 + 2/5*n**4 + 0 - 6/5*n**d - 2/5*n.
2*n*(n - 1)**3/5
Let -107*f**2 + 117*f**2 + 6*f + f**4 - 9*f**4 - 6*f**3 - 2 = 0. Calculate f.
-1, 1/4, 1
Let q(v) be the second derivative of v**4/24 + v**3/6 - 2*v. Factor q(c).
c*(c + 2)/2
Let z