40*o - 38. Find l, given that m(l) = 0.
-5, -2
Suppose -5*n + d - 366 = 5*d, 372 = -5*n + 2*d. Let q = -145/2 - n. Suppose c**2 + 0 - 1/2*c**3 + 0*c - q*c**4 = 0. Calculate c.
-1, 0, 2/3
Let g(r) = -r**3 - r + 1. Let s(i) = 3*i**3 - 15*i**2 - 3*i + 9. Let h(z) = 6*g(z) - s(z). Suppose h(w) = 0. What is w?
-1/3, 1
Let g(a) = 2*a**5 + 3*a**4 - 8*a**3 + 4*a**2 + 6*a - 4. Let b(p) = p**4. Let i(d) = -6*b(d) + 2*g(d). Factor i(t).
4*(t - 1)**3*(t + 1)*(t + 2)
Let d(v) be the third derivative of v**5/150 + v**4/30 + v**3/15 + 3*v**2. Factor d(g).
2*(g + 1)**2/5
Let o(j) = j**3 - 1. Let t(w) = -w**4 - 6*w**3 - w**2 + 3*w + 5. Let q(a) = -15*o(a) - 5*t(a). Let q(u) = 0. Calculate u.
-2, -1, 1
Let q be (2 - -6) + (-4)/1. Let k(p) be the second derivative of 0*p**2 + 1/6*p**3 - 1/12*p**q + 0 - p. Factor k(l).
-l*(l - 1)
Let h(l) be the third derivative of 3*l**2 + 0*l**4 + 0*l + 0*l**3 + 0 - 1/216*l**8 + 1/135*l**5 + 16/945*l**7 - 11/540*l**6. Let h(u) = 0. Calculate u.
0, 2/7, 1
Factor -12*w + 8 + 3*w**2 + w**2 + 0.
4*(w - 2)*(w - 1)
Suppose a = 4*b + 20, 2*a + 3*b + 3 + 12 = 0. Factor 0 + a*c**2 + 2/7*c**4 + 0*c**3 + 0*c.
2*c**4/7
Let 3/5*r**3 - 1/5*r**2 + 1/5*r**5 - 3/5*r**4 + 0*r + 0 = 0. What is r?
0, 1
Let b(z) be the third derivative of z**5/420 + z**4/84 + z**3/42 - z**2. Factor b(v).
(v + 1)**2/7
Factor -3 + 1/2*h**2 + 1/2*h.
(h - 2)*(h + 3)/2
Let y(c) = -20*c - 38. Let t be y(-2). Factor 0 - 2/5*j**t + 2/5*j**4 + 2/5*j - 2/5*j**3.
2*j*(j - 1)**2*(j + 1)/5
Let d(f) be the third derivative of -1/240*f**5 + 0*f + 1/12*f**3 + 1/96*f**4 + 0 + 3*f**2. Factor d(y).
-(y - 2)*(y + 1)/4
Let v(x) be the first derivative of -x**4/48 + 3*x - 2. Let w(o) be the first derivative of v(o). Factor w(i).
-i**2/4
Let f(v) = 2*v**5 - 9*v**4 - 11*v**3 + 11*v**2 + 9*v - 9. Let m(o) = 2*o**5 - 8*o**4 - 10*o**3 + 10*o**2 + 8*o - 8. Let p(n) = -6*f(n) + 7*m(n). Factor p(z).
2*(z - 1)**3*(z + 1)**2
Find b such that 4*b**4 - 7*b**2 - 3*b**4 + 2*b**2 + 4*b**4 = 0.
-1, 0, 1
Let f(v) be the first derivative of -v**5/5 - 7*v**4/12 - v**3/3 + v**2/2 + v - 2. Let x(l) be the first derivative of f(l). Determine u, given that x(u) = 0.
-1, 1/4
Suppose -14 + 0 = -3*b + m, 7 = -b - 2*m. Let l(z) be the second derivative of z + 1/6*z**b + 0 + 1/6*z**4 + 0*z**2. Factor l(d).
d*(2*d + 1)
Factor 4 - s**2 - 3 + 3 - 3.
-(s - 1)*(s + 1)
Suppose 6*j - 3*j = -5*w - 40, -j + 2*w - 28 = 0. Let d be (-4)/j - (-3)/60. Factor -1/4*g + d*g**4 + 1/4 - 1/2*g**2 - 1/4*g**5 + 1/2*g**3.
-(g - 1)**3*(g + 1)**2/4
Let u be 1/((-54)/(-336)) - 6. Factor -2/9*q**3 + 2/9*q**4 + 2/9*q - u*q**2 + 0.
2*q*(q - 1)**2*(q + 1)/9
Let f(j) = -j**3 + 26*j**2 - 24*j - 23. Let v be f(25). Factor 1/3*t**v + 2/3*t + 1/3.
(t + 1)**2/3
Suppose 4*b + 5*n + 8 = 0, 16 = 18*n - 22*n. Solve 0*f**2 - 1/2*f**4 + 0*f + 0 - 1/2*f**b = 0 for f.
-1, 0
Determine t so that 0*t - 2*t**3 + 0 - 2/3*t**2 - 2/3*t**5 - 2*t**4 = 0.
-1, 0
Let q(a) be the second derivative of -a**5/150 + a**4/60 - a**2 + 3*a. Let u(z) be the first derivative of q(z). Factor u(m).
-2*m*(m - 1)/5
Let y be 162/39 - 5*(-6)/(-195). Let 0*i**3 + 1/2 - i**2 + 1/2*i**y + 0*i = 0. What is i?
-1, 1
Factor 11*t**2 - 27*t**2 + 8*t**2 + 7*t**2 + 3 - 2*t.
-(t - 1)*(t + 3)
Let s(p) be the first derivative of -2/55*p**5 + 2/33*p**3 + 7 + 0*p**2 + 1/22*p**4 + 0*p - 1/33*p**6. Find c, given that s(c) = 0.
-1, 0, 1
Let q be (8/20)/(7/10). Let f be (4*1)/(19 - 5). Determine x so that -q*x - 2/7 - f*x**2 = 0.
-1
Suppose 0 = f - 1, 5 = 4*n + 13*f - 16*f. Factor 1 - 1/3*l**4 - 8/3*l + 0*l**3 + n*l**2.
-(l - 1)**3*(l + 3)/3
Let j(b) be the first derivative of b**7/840 - b**6/120 + b**4/6 + 4*b**3/3 - 5. Let l(v) be the third derivative of j(v). Solve l(d) = 0.
-1, 2
Let b = 1136 - 1134. Factor -4/9*z + 2/9*z**b + 2/9.
2*(z - 1)**2/9
Factor -2/7*t**3 + 2/7*t**2 + 0 + 2/7*t - 2/7*t**4.
-2*t*(t - 1)*(t + 1)**2/7
Determine v, given that 40/17*v + 12/17*v**2 - 18/17*v**3 + 16/17 = 0.
-2/3, 2
Let x(o) = 4*o - 24. Let j be x(6). Let j + 2/3*h + 2/3*h**3 + 4/3*h**2 = 0. What is h?
-1, 0
Let g(l) = 6*l**5 - 18*l**4 + 6*l**3 + 13*l**2 - 17*l + 5. Let j(q) = 3*q**5 - 9*q**4 + 3*q**3 + 6*q**2 - 9*q + 3. Let f(x) = -3*g(x) + 5*j(x). Solve f(d) = 0.
-1, 0, 1, 2
Let p(m) be the first derivative of -m**3/24 - m**2/16 + 9. Solve p(i) = 0.
-1, 0
Let j(u) be the third derivative of -u**8/1680 + 2*u**7/525 - u**6/200 + 10*u**2 - u. Factor j(i).
-i**3*(i - 3)*(i - 1)/5
Let m(d) = 6*d**4 - 14*d**3 + 8*d**2 - 2*d + 2. Let k(w) = 24*w**4 - 55*w**3 + 32*w**2 - 9*w + 9. Let x(z) = -2*k(z) + 9*m(z). Determine u, given that x(u) = 0.
0, 2/3, 2
Let b(a) = -a**2 + 14*a + 19. Let p be b(15). Find l, given that 4*l**5 + l**4 - l**3 - 5*l**5 - l**4 + 2*l**p = 0.
0, 1
Let n(w) be the first derivative of -7*w**6/90 - w**5/12 + w**4/18 - 3*w - 4. Let k(v) be the first derivative of n(v). Factor k(o).
-o**2*(o + 1)*(7*o - 2)/3
Suppose -4*v - 25 = v. Let d = v + 8. Factor -m**2 + 1 - 3*m + d*m.
-(m - 1)*(m + 1)
Let j be (-1)/8*-26 + 57/76. Determine l, given that 1/2*l**j + 3/2*l**2 - 1/2*l + 0 - 3/2*l**3 = 0.
0, 1
Let p(a) be the third derivative of 1/24*a**4 - 1/15*a**3 + 2*a**2 + 0*a + 0 + 1/100*a**5. Factor p(x).
(x + 2)*(3*x - 1)/5
Let v(s) be the second derivative of -7*s**5/200 + 3*s**4/40 - s**3/30 + 36*s. Factor v(c).
-c*(c - 1)*(7*c - 2)/10
Let d be 1*2/(-2)*(3 + -5). Solve 1/5*s**d + 0*s - 1/5 = 0.
-1, 1
Let q(j) = -j**2 - 8*j - 3. Let f be q(-5). Solve 11*o - f*o**2 - 4*o + 7*o**2 - 2 = 0.
2/5, 1
Suppose 4*z + 0*z = -3*q + 5, 2*q + z = 5. Let a be 8/(-6)*(-4)/8. Factor 2/3*r**2 - a*r - 2/3 + 2/3*r**q.
2*(r - 1)*(r + 1)**2/3
Suppose -m = -d + 1, -5*m + 4*d = 2 - 0. Find k such that 1/4*k**4 + 0*k**m + 1/4*k**3 + 0*k + 0 = 0.
-1, 0
Let n(t) = 3*t**2 + 8*t. Let a = -8 - -17. Let g(v) = 6*v**2 + 15*v. Let z(w) = a*n(w) - 5*g(w). Factor z(b).
-3*b*(b + 1)
Let o(i) = -i**2 - i - 1. Let p(c) = 2*c**3 + 20*c**2 + 18*c + 12. Let n(r) = 12*o(r) + p(r). Let n(v) = 0. What is v?
-3, -1, 0
Let q(x) be the second derivative of 4*x**5/5 - 7*x**4/3 - 28*x**3/3 - 6*x**2 + 2*x - 3. Let q(g) = 0. Calculate g.
-1, -1/4, 3
Factor -16/5 - 1/5*g**2 - 8/5*g.
-(g + 4)**2/5
Let o be ((-12)/16)/((-3)/8). Suppose 5*h + 0*g - 4*g + 2 = 0, g = -o*h + 7. Factor -3/2*p - 1/2*p**3 + 3/2*p**h + 1/2.
-(p - 1)**3/2
Let a be (-55)/11*2/(-5). Suppose 0*b + b - 2*b**a + 3*b = 0. Calculate b.
0, 2
Solve 1/6 - 1/6*t**2 + 1/6*t - 1/6*t**3 = 0.
-1, 1
Let l = 2/15 - -46/105. Factor 8/7*q + 6/7*q**2 - l*q**3 - 2/7*q**4 - 8/7.
-2*(q - 1)**2*(q + 2)**2/7
Let c(z) be the third derivative of 6*z**7/385 - 7*z**6/220 - z**5/330 + 5*z**4/132 - z**3/33 + 11*z**2. What is q in c(q) = 0?
-1/2, 1/3, 1
Suppose -2*h = 3*r - 15, -r - 2*r = -2*h - 3. Suppose 3*u + 6*u**r - u - u - 7*u**3 = 0. Calculate u.
-1, 0, 1
Let y(t) = t - 10. Let x be y(10). Factor 3*r**4 - 4*r**4 + x*r**4.
-r**4
Let v be (0 - 1)*-3*(-15)/(-135). Factor 1/3*d**4 - 1/3*d**2 - 1/3*d + v*d**3 + 0.
d*(d - 1)*(d + 1)**2/3
Let d(c) = 27*c**2 + 42*c - 132. Let h(u) = -2*u**2 - 1. Let b(a) = -d(a) - 15*h(a). Let b(k) = 0. Calculate k.
7
Let z(r) be the second derivative of 1/12*r**3 + 1/24*r**4 + 0*r**2 + 0 - 3*r. Suppose z(b) = 0. What is b?
-1, 0
Let n = 1 + 1. Factor -15*l + l**2 - 4*l**n - 8*l - 27 + 5*l.
-3*(l + 3)**2
Let n = -75/43 - -5491/2236. Let s = -6/13 + n. Factor 0 + s*l + 3/4*l**3 - 3/4*l**2 - 1/4*l**4.
-l*(l - 1)**3/4
Let a(c) be the third derivative of -c**8/1848 + c**7/1155 + c**6/660 - c**5/330 + 20*c**2. What is o in a(o) = 0?
-1, 0, 1
Suppose 2 - 4 = 2*c, -5*c = -3*q + 17. Determine j, given that 0*j**4 + 2 - 6*j**2 - q*j**3 - 4*j - j**4 - 3 = 0.
-1
Suppose -b + 3*l = 4*b - 1695, -3*b = 2*l - 998. Let -145*r**4 + b*r**3 - 115*r**4 + 67*r**2 - 3 + 39*r - 247*r**2 + 68*r**4 = 0. What is r?
1/4, 1
Let s be -1 + 1 + (-25)/(-15). Suppose -2 = 5*h - 4*y - 30, 2*y = 4*h - 20. Factor s*p**3 - 2/3*p**h + 1/3*p - 4/3*p**2 + 0.
-p*(p - 1)**2*(2*p - 1)/3
Let n(f) = -f**3 + 12*f**2 - 11*f. Let q be n(11). Let p(g) be the second derivative of 1/3*g**3 - 2*g**2 + q + 1/6*g**4 - 2*g. Factor p(m).
2*(m - 1)*(m + 2)
Let s(w) be the first derivative of w**3 + 3*w**2 + 7. Let s(z) = 0. Calculate z.
-2, 0
Factor -3/7*m**2 + 3/7*m - 3/7*m**3 + 3/7.
-3*(m - 1)*(m + 1)**2/7
Let l = 7 - 7. Let s(v) be 