 - 4/5*c**5 - 1/3*c**6 + c**2 + 0*c**4. Factor d(r).
-2*r*(r - 1)*(r + 1)**3
Let k(o) be the third derivative of o**8/20160 - o**7/1890 + o**6/540 + o**4/12 - 4*o**2. Let z(p) be the second derivative of k(p). Let z(x) = 0. Calculate x.
0, 2
Solve 21/4*f**4 - 83/4*f**3 + 53/2*f**2 + 2 - 13*f = 0 for f.
2/7, 2/3, 1, 2
Factor -21/4*v + 3*v**3 - 15/4*v**2 + 3/2.
3*(v - 2)*(v + 1)*(4*v - 1)/4
Let s(g) be the first derivative of g**6/132 + g**5/110 - g**4/66 - g**2 + 3. Let q(v) be the second derivative of s(v). Factor q(u).
2*u*(u + 1)*(5*u - 2)/11
Let p(v) = 3*v**5 + 6*v**4 + 6*v**3 + 3*v + 3. Let o(k) = -k**3 - k - 1. Let x(n) = 3*o(n) + p(n). Factor x(z).
3*z**3*(z + 1)**2
Let l(a) = a**2 + 24*a - 24*a + 1. Let g(p) = 3*p**4 - 3*p**3 - 6*p**2 + 3*p - 3. Let x(f) = g(f) + 3*l(f). Factor x(s).
3*s*(s - 1)**2*(s + 1)
Let o = 92 - 92. Let a(r) be the second derivative of 2*r + o*r**2 + 0*r**3 + 0 - 1/130*r**5 + 0*r**4. Let a(p) = 0. What is p?
0
Let t be (-14)/49 + (-58)/(-7). Let r be 92/5 + t/(-20). Determine x so that -5 - 13 + r + x**2 - x**5 + x**3 - x**4 = 0.
-1, 0, 1
Let b(n) be the first derivative of -n**3/7 - 9*n**2/7 - 15. Find g, given that b(g) = 0.
-6, 0
Let v(i) = -i - 1. Let z(s) = s**2 - s - 1. Let c(f) = 5*v(f) - z(f). Solve c(a) = 0.
-2
Let m be -1*(4 + (-9)/2). Let m*p + 1/4*p**4 - 1/2*p**3 - 1/4*p**2 + 0 = 0. What is p?
-1, 0, 1, 2
What is m in 4/3*m**3 - 4/3 + 10/3*m**2 + 2/3*m = 0?
-2, -1, 1/2
Let u be (6 - 3) + 0/(-1). Suppose -4*c + y + 19 = 2*y, u*y = 2*c - 27. Let -b**4 - c*b**2 + 6*b**2 - b**3 = 0. Calculate b.
-1, 0
Let s(y) = -2*y**3 + y**2 + 3*y. Let n(i) = -i**3 + i. Let q(b) = 5*n(b) - s(b). Factor q(j).
-j*(j + 1)*(3*j - 2)
Suppose -s = 3*o + 4*s - 31, -2*o - 4*s + 24 = 0. Factor -2/3*w**2 - 4/3 - o*w.
-2*(w + 1)*(w + 2)/3
Let r(o) = -10*o**2 - 30*o. Let v(l) = -5*l**2 - 15*l. Let w(g) = -4*r(g) + 9*v(g). Find d, given that w(d) = 0.
-3, 0
Let f(w) be the second derivative of -1/24*w**4 + 0 - 1/3*w**3 - w**2 + 2*w. Factor f(g).
-(g + 2)**2/2
Let g(o) = o + 33. Let c be g(-30). Let q(v) be the second derivative of -4*v + 1/16*v**4 + 1/40*v**6 + 3/40*v**5 + 0*v**2 + 0 + 0*v**c. Factor q(r).
3*r**2*(r + 1)**2/4
Suppose -4*h - 15 = 2*z - 3, 36 = 4*z - 4*h. Factor 51*p**4 + p**3 - p**3 - 54*p**z.
-3*p**4
What is f in 27*f**2 + 9*f**2 - 20*f**3 - 28*f + 4 + 4*f**4 + 11 - 7 = 0?
1, 2
Let b(w) be the second derivative of -1/45*w**6 - 1/18*w**4 + 0*w**2 + 0 + 0*w**3 - 2*w + 1/15*w**5. Determine s so that b(s) = 0.
0, 1
Let w be (-165)/(-252) - (-21)/(-252). Factor 2/7*c + w - 2/7*c**2.
-2*(c - 2)*(c + 1)/7
Let p(c) = c - 1. Let d(n) = 2*n - 3. Let v(f) = 6*d(f) - 13*p(f). Let z be v(-6). What is w in 3/2*w - 1/2*w**2 - z = 0?
1, 2
Factor -6/5*f - 2/5*f**3 + 2*f**2 + 0 - 2/5*f**4.
-2*f*(f - 1)**2*(f + 3)/5
Let d(v) = 14*v + 7. Let q be d(4). Factor -q*t**4 + t**3 + 64*t**4 + 3*t**3 + 4*t**2.
t**2*(t + 2)**2
Let g(i) be the second derivative of i**4/108 - i**3/18 - 12*i. Factor g(s).
s*(s - 3)/9
Suppose -4*a + 8*a - 16 = 0. Let h = a + 1. Find g such that -1/4 - 5/2*g - 16*g**h + 20*g**4 - 25/4*g**2 + 5*g**3 = 0.
-1/4, 1
Let f be ((-2)/4)/(11/(-132)). Let c be 3 + (-3)/f + -2. Factor 1/2*k**3 + 0*k**2 + 0 - c*k.
k*(k - 1)*(k + 1)/2
Let x(k) be the second derivative of -3*k**7/245 + k**6/28 - k**5/30 + k**4/84 - k**2 + 4*k. Let t(h) be the first derivative of x(h). Factor t(s).
-2*s*(s - 1)*(3*s - 1)**2/7
Let l = 33 - 26. Suppose 0*q + 21 = l*q. Factor 0*t + 0 + 0*t**2 - 2/3*t**q.
-2*t**3/3
Let k(a) be the first derivative of a**4/30 - a**2/15 + 22. Let k(n) = 0. Calculate n.
-1, 0, 1
Let k(a) be the first derivative of 4 - 1/3*a - 2/3*a**2 - 1/3*a**3. Suppose k(c) = 0. What is c?
-1, -1/3
Find b, given that 4/5 - b**2 + 0*b + 1/5*b**4 + 0*b**3 = 0.
-2, -1, 1, 2
Let m(i) = 18*i**2 + 3*i - 15. Let l(s) = 4*s**2 - 5*s**2 + 2 - 1. Let y(d) = 15*l(d) + m(d). Suppose y(j) = 0. Calculate j.
-1, 0
Let x(y) = -y**2 + 3*y - 2. Let b be x(2). Let -4/5*w + 2/5*w**2 + b = 0. What is w?
0, 2
Factor 127*z**2 + 6 + 127*z**2 + 3*z - 257*z**2.
-3*(z - 2)*(z + 1)
Solve -59*l**3 + 80*l**2 + 79*l**3 - 6*l**5 + l**5 - 80 - 15*l**4 = 0 for l.
-2, 1, 2
Let n(u) be the second derivative of u**4/48 - u**3/24 - 6*u. Solve n(x) = 0.
0, 1
Let z(y) be the second derivative of y**5/300 - y**4/120 - y**3/15 + y**2 - 9*y. Let v(m) be the first derivative of z(m). Factor v(i).
(i - 2)*(i + 1)/5
Let v be (-2)/3 - (-4)/6. Suppose -16 = -v*w - 4*w. Let d**4 + 0*d**w + d**3 - d + 0*d - d**2 = 0. What is d?
-1, 0, 1
Suppose -10 - 21*r**2 + 16*r - r + 16*r**2 = 0. What is r?
1, 2
Let k(y) = -4. Let m(a) = a**2 + a + 1. Let r(d) = -k(d) - 4*m(d). Solve r(o) = 0.
-1, 0
Let v(p) be the first derivative of -2*p**5/5 + 2*p**3 + 2*p**2 + 22. Factor v(t).
-2*t*(t - 2)*(t + 1)**2
Let h be (3/280)/(-3)*(-48)/180. Let t(q) be the third derivative of -2*q**2 + 2/15*q**3 + 0 + 0*q - 1/300*q**6 + h*q**7 + 1/30*q**4 - 1/100*q**5. Factor t(w).
(w - 2)**2*(w + 1)**2/5
Let f(m) be the second derivative of m**7/14 - 13*m**6/10 + 48*m**5/5 - 37*m**4 + 80*m**3 - 96*m**2 + 51*m. Solve f(p) = 0.
1, 2, 4
Factor -16/5*s - 4/5*s**2 - 16/5.
-4*(s + 2)**2/5
Suppose 0 = 5*b - 5, 3*h + 3*b = 5*h + 13. Let j be h*((-99)/15)/1. Factor -33*z + 2*z**4 - 2*z**2 + j*z.
2*z**2*(z - 1)*(z + 1)
Let w(g) be the first derivative of -4*g**5/25 - 9*g**4/20 - 2*g**3/5 - g**2/10 - 7. Suppose w(z) = 0. What is z?
-1, -1/4, 0
Let m = -2/17 - -23/51. Let u be (-2)/(-8) + 1/12. Factor 0 + m*a + u*a**2.
a*(a + 1)/3
Let l(w) = -2*w**2 + 7*w + 3. Let q(x) = -25*x**2 + 90*x + 40. Let g(i) = -40*l(i) + 3*q(i). Factor g(a).
5*a*(a - 2)
Let m be (4/(-8))/((-5)/20). Let k(h) be the third derivative of 0*h**3 + 1/60*h**5 + 0*h + 1/24*h**4 - m*h**2 + 0. Find r such that k(r) = 0.
-1, 0
Let d(f) be the first derivative of -f**6/24 + f**4/16 - 8. Solve d(n) = 0.
-1, 0, 1
Let y = 15/76 + 1/19. Let z(m) = m**3 + 6*m**2 + m + 6. Let b be z(-6). Solve -1/4*x**2 + b*x - 1/2*x**3 + 0 - y*x**4 = 0.
-1, 0
Let t(w) = w**3 + 9*w**2 + 12*w + 34. Let b be t(-8). Suppose 3 - 2*k + 1/3*k**b = 0. What is k?
3
Determine v so that v**3 - 9/4*v**2 + 3/2*v - 1/4 = 0.
1/4, 1
Let v(c) be the third derivative of 0 + 1/18*c**4 + 5*c**2 - 1/90*c**5 + 0*c + 0*c**3. Find z, given that v(z) = 0.
0, 2
Suppose 5*h + 9 = 8*h. Suppose -2*q + h*s = 0, 0 = -3*q - s - 2*s + 15. Solve -7*y**3 + y**5 - 2*y**5 + 7*y**q = 0 for y.
0
Let v(o) be the third derivative of -o**6/480 + o**5/60 - 5*o**4/96 + o**3/12 + 40*o**2. Factor v(p).
-(p - 2)*(p - 1)**2/4
Let a = 3 + -3. Suppose 4 = -2*d - 2*k + 16, a = 3*d + 4*k - 21. Determine z, given that -1/4*z**4 + 0 - 1/4*z**2 - 1/2*z**d + 0*z = 0.
-1, 0
Find b, given that b + 12*b**2 + 2*b**2 + 10*b**3 + 3*b = 0.
-1, -2/5, 0
Let o = 11 - 7. Factor -2*w**2 + 5*w**o + 2*w - w**2 - 2*w**3 - 2*w**2.
w*(w - 1)*(w + 1)*(5*w - 2)
Let x be (-2 - 1)*12/9. Let q be x/(-10) + 36/(-315). Factor 0 + 2/7*j**3 + 2/7*j**4 + 0*j - q*j**5 - 2/7*j**2.
-2*j**2*(j - 1)**2*(j + 1)/7
Let m(i) = i**5 + 6*i**4 - 7*i**3 - 7*i**2 + 9*i + 1. Let b(a) = -8*a**5 - 42*a**4 + 50*a**3 + 50*a**2 - 64*a - 8. Let d(t) = 6*b(t) + 44*m(t). Factor d(v).
-4*(v - 1)**4*(v + 1)
Let t(r) be the second derivative of -1/24*r**3 + r + 1/8*r**2 + 1/80*r**5 - 1/48*r**4 + 0. What is s in t(s) = 0?
-1, 1
Let x(a) = -2*a**2 + 7. Suppose 0 = -5*c - 5*g, 0 = 2*c + 2*c - g - 25. Let y(f) = -2 + 1 + 0. Let b(p) = c*y(p) + x(p). Factor b(d).
-2*(d - 1)*(d + 1)
Let f(n) be the first derivative of n**3/18 - n**2/4 + n/3 - 11. Suppose f(l) = 0. What is l?
1, 2
Let b(g) be the third derivative of g**6/40 + 3*g**5/20 + g**4/4 - 6*g**2. Determine r so that b(r) = 0.
-2, -1, 0
Suppose w - 3*r = -3, 5*r - 5 = 3*w - 5*w. Suppose 4*d - d = w. Determine k so that 4*k + 0*k**2 + d*k**2 + 3*k**2 - 2*k**2 + 4 = 0.
-2
Let q be (-1*(-18)/(-24))/(30/(-16)). Suppose y + 0*y = 0. Solve y*v - 2/5 + q*v**2 = 0 for v.
-1, 1
Let a(c) be the first derivative of c**4/14 - 4*c**3/7 + 12*c**2/7 - 16*c/7 + 10. Factor a(q).
2*(q - 2)**3/7
Let s be 27/(-6)*4/(-2). Suppose -s - 3 = -3*y. Find r, given that -4/3 - 2/3*r**3 + 7*r**2 - 8/3*r - 7/3*r**y = 0.
-2, -2/7, 1
What is o in 1/2*o**3 + 0*o**2 + 1/4*o**4 + 0 + 0*o = 0?
-2, 0
Let h(s) = s**2. Let q be h(2). Factor q*f**3 - 2*f**3 + 334*f**4 - 337*f*