lve l(a) = 0.
0, 1
Let f = -1/3 + 2/3. Let l(s) be the second derivative of -2/3*s**2 + 0 + s - f*s**3 - 1/18*s**4. Factor l(y).
-2*(y + 1)*(y + 2)/3
Suppose -28*w + 8 = -24*w. Let l(y) be the second derivative of 1/4*y**4 - 1/2*y**2 - w*y - 1/3*y**3 + 0. What is o in l(o) = 0?
-1/3, 1
Let k(b) = -3*b**3 + 45*b**2 - 60*b. Let h(f) = -f**3 + 13*f**2 - 17*f. Let o(p) = -18*h(p) + 5*k(p). Determine t, given that o(t) = 0.
0, 1, 2
Factor 21*i + 7*i - 98 + 80*i**2 - 82*i**2.
-2*(i - 7)**2
Let a(x) be the second derivative of x**5/30 + x**4/18 - 2*x**3/9 + 6*x. Factor a(i).
2*i*(i - 1)*(i + 2)/3
Determine o, given that 12/11*o**2 + 16/11 + 30/11*o - 2/11*o**3 = 0.
-1, 8
Let l be -1 + (-1)/(-3)*3. Suppose f + 0*f = l. Let 0*x**4 - x**5 + x**2 - x**4 + x**3 + f*x**5 = 0. Calculate x.
-1, 0, 1
Let h = 22197/4 - 5515. Let j = -34 + h. Factor 0 + 0*a - j*a**2.
-a**2/4
Suppose -k + 10 = 4*k. Let b(o) be the first derivative of 6/5*o**5 - 2*o**3 + 0*o - o**k + 1/2*o**4 - 2. Determine n, given that b(n) = 0.
-1, -1/3, 0, 1
Let l = 577/5 - 115. Factor -2/5*x + 0 - l*x**3 + 4/5*x**2.
-2*x*(x - 1)**2/5
Suppose -2 = b + b. Let u be (-1 + -3)/(b*2). Suppose u*v**2 + 0*v + 3*v - 5*v = 0. Calculate v.
0, 1
Let f(l) be the second derivative of -2*l**6/15 - 6*l**5/5 - 4*l**4 - 20*l**3/3 - 6*l**2 + 16*l. Find n, given that f(n) = 0.
-3, -1
Let d = 195 + -1363/7. Find i, given that -4/7*i - 2/7 - d*i**2 = 0.
-1
Let i = -131/78 + 24/13. Let z(j) be the second derivative of j**2 + 2*j + 0 - i*j**4 + 0*j**3. Factor z(o).
-2*(o - 1)*(o + 1)
Let u be -1 + 52/5 - 2. Let l = u - 249/35. Let 0*h + 0 - l*h**2 = 0. Calculate h.
0
Suppose 0 = -4*q - 2*c - 6, -c = -5*q + 2 + 1. Suppose 0*i**3 + 0 + 0*i - 2/5*i**4 + q*i**2 = 0. Calculate i.
0
Factor -1/3*w**3 + 0 + 0*w - 2/3*w**2.
-w**2*(w + 2)/3
Let w(p) = -p**2 - 14*p - 11. Let f be w(-13). Let t(v) be the second derivative of -1/90*v**5 + 2*v + 0 + 0*v**f - 1/27*v**3 + 1/27*v**4. Factor t(c).
-2*c*(c - 1)**2/9
Let b be (-29)/(-1) + (-4)/2. Let v = b + -13. Factor -v*z + 1 + 10*z**2 - 5 + 8.
2*(z - 1)*(5*z - 2)
Let m(r) be the third derivative of -1/12*r**5 + 0 - r**2 + 0*r**3 + 0*r + 1/12*r**4 - 3/20*r**6. Let m(h) = 0. What is h?
-1/2, 0, 2/9
Let d(o) be the third derivative of 1/96*o**4 - 1/6*o**3 + 1/1440*o**6 + 0 + 0*o + o**2 + 1/240*o**5. Let h(a) be the first derivative of d(a). Factor h(z).
(z + 1)**2/4
Let d(u) be the third derivative of u**7/560 + 7*u**6/720 + u**5/48 + u**4/48 - u**3/6 + 2*u**2. Let t(z) be the first derivative of d(z). Factor t(w).
(w + 1)**2*(3*w + 1)/2
Let h(o) be the first derivative of -o**4/4 + o**3 - o**2/2 + o - 8. Let c be h(2). Suppose -6/11*j**2 + 2/11*j**c - 2/11 + 6/11*j = 0. Calculate j.
1
Let x(d) be the second derivative of d**8/3360 - 13*d**7/5040 + 11*d**6/1440 - d**5/120 - d**4/4 + 3*d. Let u(b) be the third derivative of x(b). Factor u(j).
(j - 2)*(j - 1)*(4*j - 1)/2
Let l(v) be the third derivative of v**7/630 - v**6/360 - 2*v**5/45 + v**4/6 + 10*v**2. Factor l(c).
c*(c - 2)**2*(c + 3)/3
Suppose 0 = 3*d + q - 1 - 2, 0 = -5*d + 3*q - 9. Factor -v**3 + v + v**2 - 2*v + d*v - 3*v**2.
-v*(v + 1)**2
Factor 5 - 8*b + 6 + 2*b**2 + 5 - b**2.
(b - 4)**2
Suppose -w**3 + 3*w**3 + 304*w - 4*w**2 - 310*w = 0. What is w?
-1, 0, 3
Let m(h) be the second derivative of h**6/105 - h**5/70 - h**4/42 + h**3/21 + 8*h. Factor m(w).
2*w*(w - 1)**2*(w + 1)/7
Let h(b) = -b + 4. Let c be h(5). Let s be 2 + ((-18)/10 - c). Solve 4/5*a + 2*a**2 + 0 + s*a**3 = 0 for a.
-1, -2/3, 0
Let f(w) be the second derivative of -w**10/50400 + w**9/25200 + w**8/11200 - w**7/4200 + w**4/4 - 4*w. Let g(p) be the third derivative of f(p). Factor g(s).
-3*s**2*(s - 1)**2*(s + 1)/5
Let i(k) be the third derivative of k**7/21 + k**6/8 - k**5/6 - 37*k**2. Determine v so that i(v) = 0.
-2, 0, 1/2
Suppose -4*k + 4*z = -24, -k - z = 3*k - 9. Let o(p) be the first derivative of 1/6*p**k + 0*p + 1/4*p**2 - 1. Factor o(x).
x*(x + 1)/2
Let a be 1/(2 - 4 - -1). Let o be a - (-2)/(-36)*-22. Factor -o*d**3 - 2/9*d**2 + 2/9*d + 2/9.
-2*(d - 1)*(d + 1)**2/9
Let a(g) be the second derivative of g - 1/24*g**4 + 1/8*g**2 + 0 + 0*g**3 + 0*g**5 + 1/120*g**6. Factor a(s).
(s - 1)**2*(s + 1)**2/4
Let w be (-6)/4 + (-205)/(-70). Solve 0 - w*d**3 - 2/7*d - 4/7*d**4 - 8/7*d**2 = 0 for d.
-1, -1/2, 0
Suppose 5*n = 9 + 26. Let r(j) = n - 3 - 5 + j**2. Let x(m) = -6*m**2 + 6. Let u(l) = -22*r(l) - 4*x(l). Determine z so that u(z) = 0.
-1, 1
Let n be (-2)/6 + 80/348. Let g = n + 149/319. Factor 0*f**2 + 0 + 0*f + 2/11*f**4 - g*f**3.
2*f**3*(f - 2)/11
Let m(b) be the second derivative of -2*b + 1/50*b**5 + 2/15*b**4 + 0*b**2 + 0 + 4/15*b**3. Factor m(o).
2*o*(o + 2)**2/5
Let u(o) = o**4 - o**3 + o**2 + 1. Let c(f) = -7*f**4 + 3*f**3 - 8*f**2 - 6. Let d(n) = c(n) + 6*u(n). Solve d(y) = 0 for y.
-2, -1, 0
Suppose -414 = -4*f - 414. What is v in 12/5*v**3 + 0*v + 8/5*v**2 + f + 4/5*v**4 = 0?
-2, -1, 0
Let s(m) = m**5 + m**3 + m**2 - m. Let n(v) = 3*v**5 + 4*v**4 + 8*v**3 + 6*v**2 - v. Let j(k) = -n(k) + 2*s(k). Determine y so that j(y) = 0.
-1, 0
Let z(c) be the first derivative of 2*c**5/5 - 2*c**4 + 10*c**3/3 - 2*c**2 + 10. Determine a, given that z(a) = 0.
0, 1, 2
Suppose 16*p**2 + 16*p**3 - 88*p + 176*p - 84*p = 0. What is p?
-1/2, 0
Let m(u) be the third derivative of 1/9*u**3 - u**2 - 1/18*u**4 + 1/90*u**5 + 0 + 0*u. Factor m(i).
2*(i - 1)**2/3
Let q = -143/5 - -31. Factor 18/5*h**2 + 3/5*h**4 - 12/5*h - q*h**3 + 3/5.
3*(h - 1)**4/5
Let z = 4 - 2. Let b = 55/3 - 17. Find v such that -b*v - 1/3*v**z - 4/3 = 0.
-2
Let x(a) be the second derivative of 4/25*a**5 + 0 - 1/5*a**4 - 1/25*a**6 + 0*a**3 + 1/5*a**2 - 3*a. Factor x(m).
-2*(m - 1)**3*(3*m + 1)/5
Factor -4*g**3 - 480*g + 400 + 61*g**2 - 21*g**2 + 44*g**2.
-4*(g - 10)**2*(g - 1)
Let q = -121 - -124. Let f(a) be the first derivative of 2 + 0*a + 2/15*a**q + 1/5*a**2. Factor f(h).
2*h*(h + 1)/5
Let t(c) be the third derivative of -c**8/2880 - c**7/2520 + c**5/30 - 2*c**2. Let r(j) be the third derivative of t(j). Factor r(m).
-m*(7*m + 2)
Let z(d) be the third derivative of -2/5*d**3 + 0*d - 1/75*d**5 + 2/15*d**4 + 0 - 5*d**2. Solve z(m) = 0.
1, 3
Let x(y) be the second derivative of 3/8*y**5 - 4*y - 3/4*y**3 - 1/6*y**4 - 1/2*y**2 + 0. Factor x(k).
(k - 1)*(3*k + 1)*(5*k + 2)/2
Let b = 0 - -3. Suppose 7 = b*s - 2. Find m such that -3*m**s + 2 - 2 - 3*m**2 + 6*m = 0.
-2, 0, 1
Let t(p) be the third derivative of -4*p**5/15 + 11*p**4/24 - 2*p**2. Let s(j) = 8*j**2 - 6*j. Let r(d) = -7*s(d) - 4*t(d). Solve r(c) = 0 for c.
0, 1/4
Let o(k) = 2*k**4 - 4*k**2 - 7*k + 2. Let p(q) = q**4 - q**3 - q**2. Let n(i) = -2*o(i) + 14*p(i). What is r in n(r) = 0?
-1, 2/5, 1
Let o(r) be the second derivative of -11/15*r**3 + 2*r - 4/75*r**6 + 2/5*r**4 + 0 + 1/50*r**5 + 2/5*r**2. Solve o(j) = 0 for j.
-2, 1/4, 1
Let o(s) = s**3 - 4*s**2 - 5*s. Let i be o(5). Let c(z) be the first derivative of -2/21*z**3 + 0*z**2 - 1/14*z**4 + i*z + 2. What is g in c(g) = 0?
-1, 0
Let m(i) = i**3 + i. Let v(s) = -2*s**2 - 6*s. Let q(t) = 2*m(t) + v(t). Factor q(g).
2*g*(g - 2)*(g + 1)
Let r(m) be the first derivative of 5*m**6/6 - 5*m**4/2 + 5*m**2/2 + 17. Factor r(o).
5*o*(o - 1)**2*(o + 1)**2
Let d(s) = -s**2 + 5*s + 6. Let t(g) = -2*g**2 + 15*g + 17. Let r(l) = -11*d(l) + 4*t(l). Determine n, given that r(n) = 0.
-1, -2/3
Let c = 4250156/111 - 38288. Let a = -1/37 + c. Factor a*b**2 + 0 - 2/3*b.
b*(5*b - 2)/3
Factor 1/2*c**3 - 1/4*c + 0 - 1/4*c**5 + 0*c**4 + 0*c**2.
-c*(c - 1)**2*(c + 1)**2/4
Factor -24/11*y - 16/11 - 2/11*y**3 - 12/11*y**2.
-2*(y + 2)**3/11
Suppose 2*x - 166 = d + 4*d, 0 = -5*x - 2*d + 386. Let k be (-4)/6*x/(-4). Suppose -17*o - 45*o**2 - 40*o**3 + k*o**3 + 21*o**4 - 2 + 6*o**4 = 0. Calculate o.
-1/3, 2
Let 2*h**5 - 9*h**4 - 15*h**4 - 7*h**4 + 37*h**4 = 0. What is h?
-3, 0
Let d(j) be the first derivative of j**4/3 - 20*j**3 + 450*j**2 - 4500*j + 37. Factor d(w).
4*(w - 15)**3/3
Determine l, given that 1/2*l**5 + 1/2*l**4 - l - 3/2*l**3 + 0 - 5/2*l**2 = 0.
-1, 0, 2
Suppose 3*k - 8 = 88. Let -6*d**2 + 1 + 19*d**3 + k*d**4 + 13*d**3 - 2*d - 3*d = 0. Calculate d.
-1, -1/2, 1/4
Let n(c) = -139*c**4 - 184*c**3 + 240*c**2 + 80*c - 76. Let d(x) = 277*x**4 + 367*x**3 - 480*x**2 - 160*x + 153. Let i(g) = 4*d(g) + 7*n(g).