+ 0*r**2.
-r**3/3
Let r = -21 + 316/15. Let s(k) be the second derivative of k + 1/5*k**5 + 0*k**2 + 0*k**4 - r*k**6 + 0 + 0*k**3. Factor s(o).
-2*o**3*(o - 2)
Let m(n) be the first derivative of -2/35*n**5 + 0*n**2 - 2/7*n**3 + 0*n + 3 - 2/7*n**4. Factor m(d).
-2*d**2*(d + 1)*(d + 3)/7
Let w be 0/(-1) + -3 + 7. Let k(g) be the third derivative of 0 + 0*g + 1/48*g**w - 1/240*g**5 + g**2 + 0*g**3. Let k(y) = 0. What is y?
0, 2
Suppose 2*g + 12*g = 336. Let y(x) be the first derivative of -3/2*x**2 - 8*x**6 - g*x**5 + 3 - 10*x**3 - 99/4*x**4 + 0*x. Factor y(q).
-3*q*(q + 1)**2*(4*q + 1)**2
Let a = 21 - 11. Suppose -4*z = -6*z + a. Determine q, given that 4*q**2 - 2*q**2 + 3*q**4 - 6*q**2 - q**z = 0.
-1, 0, 2
Let o be (-2)/(-4)*1*-60. Let f = o - -33. Factor -1/3*u**5 + 1/3*u**4 + 0 + 1/3*u**f + 0*u - 1/3*u**2.
-u**2*(u - 1)**2*(u + 1)/3
Suppose -13 = k + s + 1, -4*k = 3*s + 56. Let w be 2 - k/(-16)*2. Factor 0 - 1/4*h**3 + 0*h + w*h**2.
-h**2*(h - 1)/4
Let b = 1 + -7. Let s = b + 8. Factor -1/2*r**s - 3/4*r**3 + 0 + 0*r.
-r**2*(3*r + 2)/4
Solve l**3 - 6*l + 2*l**3 + 0*l**2 + l**2 + 2*l**2 = 0.
-2, 0, 1
Suppose 0 = 3*r - 2*x - 5, 2*r = 5*r + 3*x - 30. Let s(q) be the third derivative of -3*q**2 + 1/30*q**r + 0*q - 1/12*q**4 + 0*q**3 + 0. Factor s(u).
2*u*(u - 1)
Let u(y) be the first derivative of -y**6/1620 + y**5/540 + y**4/54 + 2*y**3/3 - 2. Let h(i) be the third derivative of u(i). Factor h(a).
-2*(a - 2)*(a + 1)/9
Let g(d) be the third derivative of -49*d**6/240 + 217*d**5/120 + 17*d**4/6 + 5*d**3/3 - 14*d**2. Find q, given that g(q) = 0.
-2/7, 5
Factor -3*v**3 + 2*v**3 - 3*v + 3*v**2 - 5 + 6.
-(v - 1)**3
Let j(g) be the first derivative of 2/3*g**3 + 0*g**2 - 3/10*g**5 + 0*g + 1/12*g**6 - 4 + 0*g**4. Factor j(d).
d**2*(d - 2)**2*(d + 1)/2
Let t be ((-5)/(-3))/((-10)/(-30)). Let c = 0 - -5. Solve 2*q**3 + q**4 - 7*q**5 - q + 1 - 4*q**2 + c*q**5 + 2*q**2 + q**t = 0 for q.
-1, 1
Let j(w) be the second derivative of -w**5/70 - 2*w**4/21 - w**3/7 - 5*w. Factor j(h).
-2*h*(h + 1)*(h + 3)/7
Let k(j) be the third derivative of j**5/20 - j**4/8 - 4*j**2. Factor k(z).
3*z*(z - 1)
Let w(o) be the second derivative of -o**6/2340 + o**5/260 - o**4/78 - 2*o**3/3 - 6*o. Let x(g) be the second derivative of w(g). Suppose x(l) = 0. Calculate l.
1, 2
Suppose 5*m + 2*c - 12 = m, -c = -m. Factor 12*z + 4 - 16 - 4*z**m + z**2.
-3*(z - 2)**2
Factor 20*k - 952 + k**2 + 896 + 3*k**2.
4*(k - 2)*(k + 7)
Suppose -2*p - 18 = -2*t + 3*t, -49 = 3*p - 4*t. Let y be (p/(-55))/((-3)/(-5)). Let -y*z + 0 + 1/3*z**2 = 0. What is z?
0, 1
Factor 2/3*d - 2/3*d**5 + 0*d**3 - 4/3*d**4 + 0 + 4/3*d**2.
-2*d*(d - 1)*(d + 1)**3/3
Suppose 32/7*o + 8/7*o**3 + 1/7*o**4 + 24/7*o**2 + 16/7 = 0. What is o?
-2
Determine p so that 1/5*p**3 + 16*p + 17/5*p**2 + 64/5 = 0.
-8, -1
Find y, given that -10*y**3 + 28*y**3 + 6*y**4 + 12*y**3 + 48 + 120*y + 99*y**2 - 3*y**4 = 0.
-4, -1
Suppose b = -44*b. Find d such that b*d**2 + 1/5*d**5 + 0 - 2/5*d**3 + 0*d**4 + 1/5*d = 0.
-1, 0, 1
Let z = 24 + -24. Let k(x) be the second derivative of z + 1/8*x**3 + 1/16*x**4 + 3*x + 1/8*x**2 + 1/80*x**5. Factor k(y).
(y + 1)**3/4
Let p(t) be the second derivative of 0*t**5 - 1/27*t**4 + 0*t**3 + 7*t + 1/135*t**6 + 0 + 1/9*t**2. Factor p(i).
2*(i - 1)**2*(i + 1)**2/9
Let p be 8/4 + (-29)/12. Let v = p - -2/3. Find f such that 1/4*f**2 - 1/4*f - 1/4*f**4 + v*f**3 + 0 = 0.
-1, 0, 1
Let o(q) be the first derivative of q**4 - 2*q**2 - 7. Factor o(i).
4*i*(i - 1)*(i + 1)
Suppose 7*n - 20 = 8*n - 4*f, 3*n + 5 = f. Factor 2/13*i**2 + 0 + n*i + 2/13*i**3.
2*i**2*(i + 1)/13
Let s(f) = -f + 12. Let a = -21 - -33. Let m be s(a). Factor -1/2*z**2 + m + 1/2*z.
-z*(z - 1)/2
Let m(u) be the second derivative of -u**6/30 - u**5/15 - 3*u**2/2 + 2*u. Let b(p) be the first derivative of m(p). Suppose b(a) = 0. What is a?
-1, 0
Let q(u) = u + 0*u + 3*u**3 - 2*u**3. Let b(l) be the second derivative of l**4/4 - l**3/3 + l**2/2 + 3*l. Let d(g) = -b(g) + q(g). What is n in d(n) = 0?
1
Let p be (-3412)/(-1452) + 2 + -4. Let c = p - 2/121. Factor 2/3 - y**2 + c*y.
-(y - 1)*(3*y + 2)/3
Let f = 7/75 - -823/825. Let n = f + -86/99. Factor 4/9*m**4 + 0*m**3 - 4/9*m**2 + 0 + n*m**5 - 2/9*m.
2*m*(m - 1)*(m + 1)**3/9
Let c(l) be the first derivative of l**6/18 - l**5/5 + l**4/6 - 2. Factor c(z).
z**3*(z - 2)*(z - 1)/3
Let w(m) be the second derivative of -m**8/4704 - m**7/735 - m**6/630 + m**4/4 + 5*m. Let u(j) be the third derivative of w(j). Solve u(q) = 0 for q.
-2, -2/5, 0
What is v in -2/3*v**4 - 4/3*v**3 - 2/3*v**2 + 0*v + 0 = 0?
-1, 0
Let a(i) be the first derivative of -1/2*i**4 + 0*i + 1/6*i**6 - 3 + 0*i**5 + 0*i**3 + 1/2*i**2. Suppose a(k) = 0. What is k?
-1, 0, 1
Let d be 12/27*(-9)/(-2). Let h(y) be the first derivative of 0*y**d + 0*y + 1/3*y**6 + 0*y**3 + 1/3*y**4 - 2/3*y**5 - 2. Factor h(c).
2*c**3*(c - 1)*(3*c - 2)/3
Let w be 28/(-1) - (-3 - 1). Let a = w + 26. Factor -1/4*p**a - 1 - p.
-(p + 2)**2/4
Let z(s) be the first derivative of s**4 + 4*s**3/15 - 28*s**2/5 + 32*s/5 + 9. Suppose z(l) = 0. Calculate l.
-2, 4/5, 1
Let q(k) be the third derivative of k**6/96 - k**5/48 - 5*k**4/48 + 11*k**2. Factor q(m).
5*m*(m - 2)*(m + 1)/4
Let b(g) = -12*g - 2. Let u be b(2). Let p = u + 26. Factor p*l**4 - 1/2*l**5 + 0*l**2 + 0 + 0*l + 1/2*l**3.
-l**3*(l - 1)*(l + 1)/2
Let c(r) be the third derivative of 0*r + 0*r**6 - r**2 + 0*r**5 + 0 + 0*r**4 + 0*r**3 + 1/735*r**7. Find m such that c(m) = 0.
0
Let h(k) = k**3 + 8*k**2 - k - 3. Let i be h(-8). Suppose -23*x**2 + 84*x + i*x**3 - 8*x**2 + 3*x**3 - 18 - 19*x**2 = 0. What is x?
1/4, 3
Let w(h) be the first derivative of h**6/3 - 6*h**5/5 - h**4/2 + 2*h**3 - 4. Find m, given that w(m) = 0.
-1, 0, 1, 3
Let a = 16 + -13. Solve -6*z**2 + 6*z**3 + 3/5*z**5 - 3/5 + a*z - 3*z**4 = 0 for z.
1
Let i(p) be the first derivative of 2/3*p**6 + 3*p**4 - 3*p - 8*p**2 + 2 - 14/3*p**3 + 17/5*p**5. Solve i(s) = 0.
-3, -1, -1/4, 1
Let u(y) = y - 4. Let w be 1 + -2 + 7/1. Let f be u(w). Factor -3*m - f*m**3 + 2*m + 3*m.
-2*m*(m - 1)*(m + 1)
Let r be ((-2)/9)/(-1) + (-2 - -2). Factor r*c + 2/9*c**4 - 2/9*c**3 + 0 - 2/9*c**2.
2*c*(c - 1)**2*(c + 1)/9
Let x be 3/(-36)*3*1*0. Factor 0*h**2 + 0*h**4 - 2/3*h**3 + x*h + 2/3*h**5 + 0.
2*h**3*(h - 1)*(h + 1)/3
Let z(f) = -23*f**2 + 23*f - 14. Let n(g) = -8*g**2 + 8*g - 5. Let m = 25 + -36. Let j(t) = m*n(t) + 4*z(t). Factor j(d).
-(2*d - 1)**2
Let v = 9 - 7. Factor -1 + 3 + 3*b**v + b**2 - 6*b**2.
-2*(b - 1)*(b + 1)
Let b(v) be the second derivative of v + v**2 - 1/12*v**4 + 0 + 1/60*v**5 + 1/6*v**3. Let g(j) be the first derivative of b(j). Factor g(o).
(o - 1)**2
Suppose 0 = 103*j - 118*j. Determine d, given that 2/11*d + j + 2/11*d**2 = 0.
-1, 0
Let v(p) = 4*p**3 - 5*p**2 - 3*p - 9. Let j(a) = a**3 + a - 1. Let l(q) = 20*j(q) - 4*v(q). Factor l(t).
4*(t + 1)*(t + 2)**2
Find x such that 1/2*x**5 + 1/2*x**4 + 1/2 - x**2 - x**3 + 1/2*x = 0.
-1, 1
Let k(x) be the first derivative of -x**3/7 - 5*x**2/14 - 2*x/7 - 6. Factor k(d).
-(d + 1)*(3*d + 2)/7
Let q(x) = 20*x**3 - 12*x + 5*x**4 + 11*x**4 - 12 - 12*x**4. Let p(d) = -d**4 - d**2 + d + 1. Let h(m) = -12*p(m) - q(m). Suppose h(f) = 0. Calculate f.
0, 1, 3/2
Let u = -51/94 + 31087/470. Let m = 66 - u. Factor m*w**2 + 4/5 - 6/5*w.
2*(w - 2)*(w - 1)/5
Let v be (1 - (-4 - -5))*2/(-4). Let l = 104 + -308/3. Suppose v - l*a**2 + 0*a - 2*a**5 - 6*a**3 - 20/3*a**4 = 0. Calculate a.
-2, -1, -1/3, 0
Let p(g) be the third derivative of g**7/280 - g**6/160 - g**5/40 + 5*g**2. Factor p(d).
3*d**2*(d - 2)*(d + 1)/4
Let m(p) = 10*p**2 + 8*p - 2. Let r(w) = 11*w**2 + 8*w - 3. Let b(n) = -7*m(n) + 6*r(n). Find u such that b(u) = 0.
-1
Factor 4*s**3 + s**3 + s**3 - 2*s**3.
4*s**3
Let f = -867 - -870. Factor 1/3*b**f - 1/3*b + 0 - 1/3*b**4 + 1/3*b**2.
-b*(b - 1)**2*(b + 1)/3
Let c(t) = 4*t**3 - 5*t**2 - 2*t. Let x(w) = 12*w**3 - 14*w**2 - 6*w. Let z(i) = -21*c(i) + 6*x(i). Determine r so that z(r) = 0.
-1/4, 0, 2
Let f(k) = 21*k**2 + 24*k. Let n(y) = 19*y**2 + 14*y - 7. Let i(s) = -10*s**2 - 7*s + 4. Let h(j) = -7*i(j) - 4*n(j). Let t(d) = 5*f(d) + 18*h(d). Factor t(w).
-3*w*(w + 2)
Let z(g) be the second derivative of -1/84*g**4 - g**2 + 0*g**3 + 1/105*g**5 + 0 - 2*g. Let j(f) be the first derivative of z(f). Determine n so that j(n) 