*v**3 - 6*v**2 - l*v.
-(v + 2)**2*(5*v - 2)/3
Let s(f) be the second derivative of -f**7/126 + 2*f**6/45 - f**5/30 - f**4/9 + f**3/6 - 11*f. Solve s(u) = 0 for u.
-1, 0, 1, 3
Let k = 297/5 - 14251/240. Let d(w) be the second derivative of -1/12*w**3 - 3*w + 1/8*w**2 + 0 + k*w**4. Solve d(l) = 0 for l.
1
Let i(s) be the second derivative of s**6/30 - s**5/20 - s**4/6 + 2*s. Solve i(n) = 0.
-1, 0, 2
Factor -2*i**2 - 10*i - 7 + 23 - 3*i**2 - 1.
-5*(i - 1)*(i + 3)
Let p(j) be the second derivative of 0*j**4 - 3*j - 1/3*j**3 + 0 + 1/10*j**5 + 0*j**2. Suppose p(h) = 0. Calculate h.
-1, 0, 1
Let d(c) be the first derivative of -10*c**6/3 - 3*c**5 + 5*c**4/4 + 11. Factor d(u).
-5*u**3*(u + 1)*(4*u - 1)
Let o(b) = -b**2 - 6*b - 6. Let r be o(-4). Let w be r/(-3) - (-32)/36. What is x in 0 + 2/9*x + w*x**2 = 0?
-1, 0
Factor 0 - 2/5*f**2 + 0*f + 0*f**3 + 2/5*f**4.
2*f**2*(f - 1)*(f + 1)/5
Let d = -111/2 + 1015/18. Let s = -6542/9 + 728. Suppose s*r - 4/9 + 2/9*r**3 - d*r**2 = 0. What is r?
1, 2
Let s = 1297/288 - 1/288. Factor -3/2*h**4 - 3/2*h**3 + 3 + 15/2*h + s*h**2.
-3*(h - 2)*(h + 1)**3/2
Let s(m) be the second derivative of 5*m**7/273 + 7*m**6/195 + m**5/65 - 5*m. Factor s(i).
2*i**3*(i + 1)*(5*i + 2)/13
Let b(f) = 4*f**3 - 2*f**2 - 13*f - 7. Let y(a) = 7 - 3*a**3 + 1 - 3*a**2 + 6*a**2 + 12*a - 2. Let t(p) = 6*b(p) + 7*y(p). Factor t(r).
3*r*(r + 1)*(r + 2)
Suppose 0 - f + 1/2*f**2 - 1/2*f**4 + f**3 = 0. Calculate f.
-1, 0, 1, 2
Suppose -22 = 9*z - 20*z. Factor -2/13*l**z + 4/13*l + 0 - 6/13*l**3.
-2*l*(l + 1)*(3*l - 2)/13
Suppose -2*p = -6, 2*p + 17 - 71 = -4*w. Suppose -10*l - 4 = -w*l. Factor -1/2*s**l - 1/4*s**5 + 0 + 1/2*s**4 + 1/4*s + 0*s**3.
-s*(s - 1)**3*(s + 1)/4
Let l be -2*(1 - 0)*-2. Let f(p) = -p**3 + 3*p**2 + 4*p + 3. Let q be f(l). What is v in 3*v**4 - 30 + 30 - 3*v**q = 0?
0, 1
Let l(d) be the third derivative of -d**8/336 - d**7/70 - d**6/120 + d**5/20 + d**4/12 + 7*d**2. Factor l(j).
-j*(j - 1)*(j + 1)**2*(j + 2)
Solve 2*l**3 - 5/6*l**4 + 1/3*l + 0 - 3/2*l**2 = 0.
0, 2/5, 1
Factor -33/10*s + 1/2*s**2 - 7/5.
(s - 7)*(5*s + 2)/10
Let l(f) = -f + 13. Let o be l(7). Factor 4*p**5 + p**3 + 4*p**4 - p**2 + p**3 - o*p**3 - 3*p**2.
4*p**2*(p - 1)*(p + 1)**2
Let t(l) = -l**3 - 5*l**2 - 3*l + 7. Let n be t(-4). Suppose 5*m**2 - 2*m**2 + 3*m**n - 8*m - 3*m**4 + 5*m = 0. What is m?
-1, 0, 1
Let t(h) be the third derivative of -h**6/240 + h**4/48 - 21*h**2. Determine f so that t(f) = 0.
-1, 0, 1
Let s(u) be the first derivative of -7*u**6/30 + 2*u**5/25 + 7*u**4/20 - 2*u**3/15 + 45. Determine g, given that s(g) = 0.
-1, 0, 2/7, 1
Let n(g) be the second derivative of g**5/60 - g**4/18 - g**3/18 + g**2/3 - 5*g. Determine a so that n(a) = 0.
-1, 1, 2
Let f(g) be the second derivative of -g**5/8 - 5*g**4/12 + 5*g**3/3 + 10*g**2 - 11*g. Factor f(s).
-5*(s - 2)*(s + 2)**2/2
Let f(y) be the first derivative of 4*y**3/3 + 10*y**2 + 16*y - 9. Factor f(a).
4*(a + 1)*(a + 4)
Let j(l) = l**3 + 3*l**2 + l + 5. Let r be j(-3). Let i(v) be the first derivative of -2 - 1/6*v**4 + 1/15*v**5 + 0*v + 0*v**r + 1/9*v**3. Factor i(g).
g**2*(g - 1)**2/3
Let j be (-14)/7*1/(-3). Determine d so that -2/3 + 0*d + j*d**2 = 0.
-1, 1
Let h(m) be the third derivative of m**6/360 - m**5/36 + 7*m**4/72 - m**3/6 - m**2. Factor h(n).
(n - 3)*(n - 1)**2/3
Let m(a) = -3*a**2 + 60*a - 55. Let v be m(19). Find b such that 4/3*b**v + 2/3*b - 4/3*b**4 - 2/3*b**3 + 0 = 0.
-1, -1/2, 0, 1
Let 0*o**2 - 11*o**2 + 6 + o**2 + 7*o**2 + 3*o = 0. What is o?
-1, 2
Let j(y) be the second derivative of y**5/20 - 5*y**4/12 + 7*y**3/6 - 3*y**2/2 - 2*y. Factor j(p).
(p - 3)*(p - 1)**2
Let m(t) be the third derivative of t**6/180 + t**5/90 - t**4/18 - 5*t**2. Determine l so that m(l) = 0.
-2, 0, 1
Let p(k) be the second derivative of k**5/40 + 3*k**4/8 + 2*k**3/3 + 58*k. Factor p(l).
l*(l + 1)*(l + 8)/2
Suppose -4*j + 12 + 0 = 0. Factor 1/2*v + 0 + 1/2*v**j - v**2.
v*(v - 1)**2/2
Determine q, given that 49*q + 10*q**3 - 27*q - 27*q - 5*q**5 = 0.
-1, 0, 1
Suppose 2*h = 3*g, h = -4*h - 4*g. Let r(z) be the second derivative of z + 0*z**3 + h*z**2 + 0 + 0*z**4 + 1/90*z**5. What is s in r(s) = 0?
0
Let n(m) = -m**3 + 7*m**2 - 5*m + 2. Let p be n(4). Suppose d + p = 6*d. Factor -d*a**2 + 2*a + a**2 - a**2.
-2*a*(3*a - 1)
Let b(d) = -d**3 + 4*d**4 - 5*d**2 - 7*d + 8*d**3 - 3*d**2 + 4*d**2. Let t(v) = -2*v**4 - 4*v**3 + 2*v**2 + 4*v. Let s(h) = -4*b(h) - 7*t(h). Factor s(p).
-2*p**2*(p - 1)*(p + 1)
Let l(w) be the first derivative of w**6/75 + w**5/25 - 2*w**3/15 - w**2/5 + 3*w - 5. Let x(c) be the first derivative of l(c). Find v such that x(v) = 0.
-1, 1
Suppose -5*i = 3*t - 6, 10 = 4*i - t - 5. Let b be (-10)/(-85) - 66/(-17). Factor -2*s**5 + i*s**b - 2*s**4 - 2*s**5 + 5*s**5.
s**4*(s + 1)
Suppose 2*h = -2*t - 16, t = -4*t - 4*h - 36. Let s be 6/2 - (t + 3). Determine p, given that 0*p**4 + 3*p**4 - s*p**2 - p**4 - 2*p**2 + 4*p = 0.
-2, 0, 1
Let r(o) be the second derivative of o**5/110 + o**4/22 + 2*o**3/33 + o. Factor r(i).
2*i*(i + 1)*(i + 2)/11
Let o(x) be the first derivative of -x**3/5 + 12*x/5 - 7. Find r, given that o(r) = 0.
-2, 2
Let m be (2/(-10))/(-1)*(-190)/(-57). Determine z, given that 1/3*z**2 - 1 - m*z = 0.
-1, 3
Let a(c) = -44*c**3 + 104*c**2 - 60*c - 28. Let f(w) = 8*w**3 - 19*w**2 + 11*w + 5. Let d(j) = 5*a(j) + 28*f(j). Factor d(u).
4*u*(u - 2)*(u - 1)
Let j be (-4)/(-420)*5*1. Let p(b) be the second derivative of -1/42*b**4 + j*b**3 + 0*b**2 + 0 - b. Suppose p(w) = 0. Calculate w.
0, 1
Let m be ((-2)/3)/((-5)/15). Let l be (-104)/(-20) - m/10. Solve 6*i**4 - 4*i**l + i**5 - 4*i**4 + 4*i**5 + i**3 = 0.
-1, 0
Let i(t) be the first derivative of -1/10*t**2 - 2/5*t - 1 + 1/15*t**3. Let i(n) = 0. What is n?
-1, 2
Factor -8/3 + 4/3*p**4 - 4*p**3 + 4/3*p**2 + 4*p.
4*(p - 2)*(p - 1)**2*(p + 1)/3
Factor -11*f**4 - 84*f**3 - 116*f**2 - 35*f - 2*f**4 - 3*f**4 + 11*f.
-4*f*(f + 2)*(f + 3)*(4*f + 1)
Let x(o) = -6*o + 5*o**3 + 6*o - 2*o**3 + o. Let m(f) = f**3. Let d(v) = -4*m(v) + x(v). Factor d(i).
-i*(i - 1)*(i + 1)
Let n be -2 + -3 + (8 - 3). Let d(o) be the second derivative of -2*o + 1/12*o**3 + 0 + 1/12*o**4 + n*o**2. Let d(c) = 0. What is c?
-1/2, 0
Let s(a) be the second derivative of -1/24*a**4 + 0 + a + 1/6*a**3 + 0*a**2. Factor s(m).
-m*(m - 2)/2
Suppose 0 = 5*f + 2*y - 20, -2*f + 0*f - 5*y + 29 = 0. Suppose -5*d + v + 4 = 2*v, -8 = 2*d - f*v. Let 0*p**2 + 1/3*p + d - 1/3*p**3 = 0. Calculate p.
-1, 0, 1
Let l(u) = u**2 + u + 2. Let o be l(0). Suppose -6 = 3*r - 3*q, -1 = -4*r + 7*r - o*q. Factor -1/2*z**r + 1/2*z**2 + 0*z + 0.
-z**2*(z - 1)/2
Factor 1/3*w**3 + 0*w - 3/2*w**4 + 0 + 0*w**2 + 7/6*w**5.
w**3*(w - 1)*(7*w - 2)/6
Let l(m) = 3*m**3 - 11*m**2 + 13*m - 5. Let j(f) = -16*f**3 + 60*f**2 - 72*f + 28. Let w(i) = 5*j(i) + 28*l(i). Determine x, given that w(x) = 0.
0, 1
Let t(m) be the second derivative of 3/20*m**5 - 1/2*m**4 + 8*m + 3*m**2 + 0 - 1/2*m**3. Let t(i) = 0. What is i?
-1, 1, 2
Let c(l) = l**4 - l**3 - l**2 - l - 1. Let j = -2 - -1. Let f(k) = -k**4 - k**3 + k**2 - k - 1. Let g(u) = j*f(u) + c(u). Factor g(r).
2*r**2*(r - 1)*(r + 1)
Determine m so that 3/4*m**2 + 3/2 + 9/4*m = 0.
-2, -1
Let k = -124 + 127. Let i(a) be the first derivative of 4*a + k*a**2 - 10/3*a**3 - 3. Determine u, given that i(u) = 0.
-2/5, 1
Let r be 18/36*(-8)/(-6). Factor -r + 2/3*a**2 - a + 0*a**4 + 4/3*a**3 - 1/3*a**5.
-(a - 2)*(a - 1)*(a + 1)**3/3
Let c(y) be the third derivative of 0 - 1/60*y**6 + 0*y**5 + 1/6*y**3 - 1/210*y**7 + 0*y + 1/12*y**4 + 4*y**2. Factor c(b).
-(b - 1)*(b + 1)**3
Let k(b) be the first derivative of 5*b**3/3 + 35*b**2 - 75*b + 56. Solve k(r) = 0 for r.
-15, 1
Let h(p) be the first derivative of p**3/9 + p**2/2 - 10*p/3 - 50. Let h(j) = 0. Calculate j.
-5, 2
Let w = 146 + -145. Let q(i) be the first derivative of 0*i + 3*i**2 - 9*i**3 - 5*i**6 + 27/5*i**5 + 6*i**4 - w. Suppose q(k) = 0. Calculate k.
-1, 0, 2/5, 1/2, 1
Let z(d) be the third derivative of 0*d + 0 - 3*d**2 + 3*d**3 - 17/8*d**4 + 1/4*d**5. Solve z(h) = 0.
2/5, 3
Let h(y) be the second derivative of y**6/105 + 3*y**5/70 + y**4/14 + y**3/21 + 4*y. Solve h(n) = 0.
-1, 0
Let u(w) = -42*w**4 + 35*w**3 + 45*w**2 - 21*w + 4. Let m(b) = -2 + 45*b**2 - 7*b**3 + 6 + 41*b**3 - 22*b - 43*b**4. Let i(n) = 7*m(n) 