- -64. Let f be l - (-2 + -2)/8 - 2. Factor -1/4 - f*i - 1/4*i**2.
-(i + 1)**2/4
Suppose 4*d - 8*d - 5*m = 26, -d - 2 = -m. Let a be (d/(16/6))/(-2 - 1). Find o such that 3/2*o + 0*o**2 - 1 - a*o**3 = 0.
-2, 1
Suppose 0 = -5*u, o + 4*o - 15 = -4*u. Suppose -d = -o*f + 6, 6*f + 3 = 4*f + 3*d. Factor -2/7*k**f + 4/7*k**4 + 0 + 0*k + 0*k**2 - 2/7*k**5.
-2*k**3*(k - 1)**2/7
Let d(w) be the first derivative of w**4/14 + 4*w**3/21 - 11*w**2/7 - 24*w/7 - 362. Factor d(q).
2*(q - 3)*(q + 1)*(q + 4)/7
Let g(f) be the third derivative of f**5/270 - f**4/36 + 2*f**3/27 - 175*f**2. Solve g(b) = 0 for b.
1, 2
Suppose -3/5*d**2 + 27/5*d + 0 = 0. What is d?
0, 9
Let k(s) be the third derivative of 1/180*s**5 + 6*s**2 + 0*s**3 + 0 - 1/24*s**4 + 0*s. Factor k(u).
u*(u - 3)/3
Let r be (4 - (-1)/(-1))/1. Let 4 + 5*d**3 - 12*d + 12*d**2 - 6*d**3 - r*d**3 = 0. Calculate d.
1
Suppose 12*u - 16*u + 32 = 0. Suppose -3 - 6*c**2 - 5 + 3*c**3 + u = 0. What is c?
0, 2
Let z(w) be the third derivative of -1/3*w**4 + 0*w + 13*w**2 + 0 - 1/60*w**5 - 8/3*w**3. Factor z(j).
-(j + 4)**2
Suppose 9*g - 7 = 74. Factor -2*q + 5*q - 12*q**3 + g*q + 4 - 4*q**2.
-4*(q - 1)*(q + 1)*(3*q + 1)
Let h(o) be the first derivative of -o**4/8 + 3*o**2/4 - o + 383. Factor h(i).
-(i - 1)**2*(i + 2)/2
Let -48 - 12*f**2 + 58*f - 14*f - f + 37*f = 0. Calculate f.
2/3, 6
Suppose 0 = -6*a + 12*a. Suppose 5*l + 3*h + 5 = 0, -l + a*l = -2*h - 12. Factor -54*k**l + 24*k - 8/3.
-2*(9*k - 2)**2/3
Let h(x) be the second derivative of -x**9/1512 - x**8/448 - x**7/504 + 3*x**4/4 + 6*x. Let m(s) be the third derivative of h(s). Find l such that m(l) = 0.
-1, -1/2, 0
Let m(p) be the first derivative of 169*p**3/5 - 1638*p**2/5 + 5292*p/5 + 115. Factor m(u).
3*(13*u - 42)**2/5
Let i be -1 - 3 - -14*(-14)/7. Let y = i + 41. Factor 27/2 + 3/2*a**2 + y*a.
3*(a + 3)**2/2
Suppose 0 = -2*i - 3*c + 10 - 1, -i = -c + 3. Suppose i = -5*r - 3 + 3. What is v in 1/4*v**5 - 1/4*v + r*v**3 + 1/2*v**2 - 1/2*v**4 + 0 = 0?
-1, 0, 1
Let d(p) be the first derivative of -2*p**3/3 + 11*p**2 - 29. Suppose d(l) = 0. Calculate l.
0, 11
Let u(m) = -12*m - 2. Let z be u(-5). Let a be z/7 - (-10)/(-35). Factor -3 + 2*r**5 + 3 + 16*r**2 - 4*r**4 - 4*r**5 + a*r**3.
-2*r**2*(r - 2)*(r + 2)**2
Solve 700*p**2 - 360*p**3 - 9*p**4 + 29*p**4 - 480*p + 41*p**4 + 14*p**4 - 5*p**5 = 0 for p.
0, 2, 3, 8
Let r(a) be the first derivative of 2*a**3/15 + 14*a**2 + 138*a/5 - 299. Factor r(z).
2*(z + 1)*(z + 69)/5
Let a(y) be the second derivative of 4*y**5/3 + y**4/6 - 2*y**3/3 + 9*y**2/2 + 21*y. Let x(i) be the first derivative of a(i). Factor x(h).
4*(4*h + 1)*(5*h - 1)
Let x be ((-255)/170)/(0 + -1). Factor -6 - x*k**2 - 15/2*k.
-3*(k + 1)*(k + 4)/2
Let t(z) be the second derivative of z**6/6 + 9*z**5/4 + 25*z**4/4 + 35*z**3/6 + 69*z + 1. Factor t(j).
5*j*(j + 1)**2*(j + 7)
Find m such that -1281*m**3 - 4794*m**2 + 33*m**4 + 17727*m**2 + 1008 - 3174 + 4595*m - 14114*m = 0.
-2/11, 1, 19
Let 5/2*h**2 + 1/2*h**4 + 0 - 3*h**3 + 0*h = 0. Calculate h.
0, 1, 5
Suppose p + 4 = -3*c, 5*p - 2 = 3*c + 14. Suppose 0*j - 2*j = 0. Solve -2/3*h**3 + 2/3*h + 2/3*h**p - 2/3*h**4 + j = 0 for h.
-1, 0, 1
Let z(i) be the third derivative of -i**6/14 - 41*i**5/140 - 11*i**4/28 - i**3/14 - 103*i**2. Factor z(m).
-3*(m + 1)**2*(20*m + 1)/7
Let u(n) = 0*n**3 + 8*n**2 - 2*n**3 - 556*n + 547*n + n**3 + 14. Let b be u(7). Factor 0 - 1/3*h**3 + 0*h + b*h**2.
-h**3/3
Factor 33*u**2 - 17*u + 22 - 17*u**2 - 13*u**2 - 2.
(u - 4)*(3*u - 5)
Let w = 11127/5 + -2225. Factor 4/5*v**5 + 0*v + 4/5*v**4 + w*v**2 - 7/5*v**3 + 0.
v**2*(v + 2)*(2*v - 1)**2/5
Let f(i) be the second derivative of i**8/1344 - i**7/280 + i**6/160 - i**5/240 + 6*i**2 - 25*i. Let b(a) be the first derivative of f(a). Factor b(l).
l**2*(l - 1)**3/4
Let g(z) = 3*z**2 + 23*z - 56. Let i(b) = -12*b**2 - 93*b + 225. Let l(v) = 9*g(v) + 2*i(v). Factor l(x).
3*(x - 2)*(x + 9)
Suppose -2*x = -x + 23. Let o = x - -27. Suppose -o*w**4 - 10*w**3 + 2 + 6*w**3 + w**5 - 2*w**2 + 3*w + 4*w**4 = 0. What is w?
-1, 1, 2
Suppose 3*o + 2*t - 5 = 0, -30 = -o - o + 4*t. Factor 15 - 13 + r - 3*r**2 - o + 5*r.
-3*(r - 1)**2
Let j be (54/(-33))/((-92)/253). Let i(p) be the first derivative of 12*p + j*p**2 + 8 - p**3. Factor i(q).
-3*(q - 4)*(q + 1)
Factor 69*l**2 - 84/5 + 12/5*l**3 + 249/5*l.
3*(l + 1)*(l + 28)*(4*l - 1)/5
Let o(c) be the third derivative of -c**6/360 - c**5/180 + c**4/36 + 141*c**2. Factor o(b).
-b*(b - 1)*(b + 2)/3
Solve -2/15*c**2 - 2/5 + 2/3*c - 2/15*c**3 = 0 for c.
-3, 1
Let i(d) be the third derivative of d**5/15 - d**4/6 - 44*d**2. Find r such that i(r) = 0.
0, 1
Factor 36*a**2 + 61*a**2 - 117*a**2 + 55*a - 35.
-5*(a - 1)*(4*a - 7)
Let t(u) be the second derivative of -u**6/195 + 3*u**5/65 - 4*u**4/39 - 2*u**3/13 + 9*u**2/13 + 129*u. Solve t(k) = 0 for k.
-1, 1, 3
Suppose -z = -4*g - 11, -z = -8*g + 9*g - 1. Factor -1442 + 2*a + 4*a**z + 1438 - 12*a**2 + 10*a.
4*(a - 1)**3
Let v(j) = -j**2 - 5*j + 11. Let u be v(-6). Let k be 24/(-30) + 14/u. Factor k*i**2 + 2/3 + 2*i + 2/3*i**3.
2*(i + 1)**3/3
Let q = -65 - -57. Let w = q - -41/5. Factor 1/5*u - 1/5 + w*u**2 - 1/5*u**3.
-(u - 1)**2*(u + 1)/5
Let q(i) be the first derivative of i**3/8 + 81*i**2/16 - 214. Determine t so that q(t) = 0.
-27, 0
Let p = -4532/3 - -1511. Suppose 1/3*h - p*h**2 + 2/3 = 0. Calculate h.
-1, 2
Let n = -37 + 17. Let a be ((-10)/(-24))/(n*(-1)/8). Let 1/6*l**2 + 1/6*l - 1/6 - a*l**3 = 0. What is l?
-1, 1
Suppose 153*a**2 - 77*a - 443/4*a**3 + 21/2*a**4 + 12 + 49/4*a**5 = 0. Calculate a.
-4, 2/7, 6/7, 1
Suppose 0 + 2/9*l**5 + 4/9*l**4 + 0*l + 0*l**2 + 2/9*l**3 = 0. What is l?
-1, 0
Let y(v) be the first derivative of 5*v**6/12 + 3*v**5 + 55*v**4/8 + 5*v**3/3 - 15*v**2 - 20*v + 8. Factor y(i).
5*(i - 1)*(i + 1)*(i + 2)**3/2
Let r(q) = 2*q**2 - 16*q - 12. Let b be r(9). Suppose h = -4*v + 18, 3*v + 0 = 3*h + b. Solve 2/3*g**3 + 0*g**h + 0*g + 0 - 2/3*g**4 = 0.
0, 1
Let y = -28 - -22. Let t(k) = -10*k - 57. Let w be t(y). Factor -3/2*n**w + 0*n + 0 + 0*n**2.
-3*n**3/2
Let p(s) be the second derivative of s**4/24 + s**3/4 - s**2 + 146*s. Factor p(j).
(j - 1)*(j + 4)/2
Let x(n) = -n**3 - 6*n**2 + 19*n - 8. Let a(t) = 5*t**3 + 35*t**2 - 115*t + 50. Let u(p) = -4*a(p) - 25*x(p). Solve u(b) = 0 for b.
-3, 0, 1
Find c such that -6/5 + 2/5*c**3 + 6/5*c**2 - 2/5*c = 0.
-3, -1, 1
Let f(t) = t**3 + t**2 + t - 1. Let k(o) = 10*o**2 + 8*o**3 + 5*o + 3*o - 2*o + 2*o - 6. Let c(r) = 6*f(r) - k(r). Find m such that c(m) = 0.
-1, 0
Let u(h) be the first derivative of 2*h**3/3 + 16*h**2 + 128*h + 13. Factor u(g).
2*(g + 8)**2
Let c(u) be the second derivative of 2*u**6/15 - u**5/5 - 2*u**4 + 8*u**3/3 + 16*u**2 - 26*u. Factor c(l).
4*(l - 2)**2*(l + 1)*(l + 2)
Suppose 0 = 255*j - 133*j - 176*j + 648. Suppose j + 32/3*l - 4/3*l**2 = 0. What is l?
-1, 9
Let p(u) be the second derivative of -u**4/6 + 25*u**3/9 + 6*u**2 + 144*u. Determine a so that p(a) = 0.
-2/3, 9
Find z, given that 0 + 6*z**2 - 20/3*z + 2/3*z**3 = 0.
-10, 0, 1
Let g(w) = -w**3 + 1. Let c(n) = 8*n**2 + 16*n + 1. Let d(a) = -3*c(a) + 3*g(a). Let d(o) = 0. What is o?
-4, 0
Let k(z) be the third derivative of -5*z**8/672 + z**7/60 + 43*z**6/240 + 37*z**5/120 - z**4/24 - 2*z**3/3 + z**2 - 39. Determine t, given that k(t) = 0.
-1, 2/5, 4
Let n(a) be the second derivative of a**6/2 - 13*a**5/20 - a**4/6 + 12*a. Factor n(z).
z**2*(z - 1)*(15*z + 2)
Factor -27*u - 60*u**2 + 20*u**3 - 59*u + 11*u - 20.
5*(u - 4)*(2*u + 1)**2
Factor 1/8*v**3 - 1/8*v - 1/4 - 1/8*v**4 + 3/8*v**2.
-(v - 2)*(v - 1)*(v + 1)**2/8
Find a such that 7/3 + 88/3*a**4 + 167/3*a**3 - 16/3*a**5 + 13/3*a**2 - 43/3*a = 0.
-1, 1/4, 7
Suppose 607*r - 3150 = -443*r. Solve 1/3*x**2 + 1/6*x**r + 0 - 1/2*x = 0.
-3, 0, 1
Let j = 29/120 + 11/120. Suppose -1/3*f**3 - 1/3*f**2 + 1/3 + j*f = 0. Calculate f.
-1, 1
Factor -2 - 3 - 696*b + 4 - 15138*b**2 - 7.
-2*(87*b + 2)**2
Let w = 967 - 967. Let b(m) be the third derivative of 0*m**4 + 0*m + 1/140*m**7 + 8*m**2 + 0*m**3 + 0*m**6 + w - 1/40*m**5. Solve b(q) = 0 for q.
-1, 0, 1
Let x(d) be the second derivative of d**7/98 + d**6/30 - 17*d**5/70 - 11*d**4/7 - 68*d**3/21 - 16*d**2/7 + 267*d. Factor x(h).
(h - 4)*(h + 2)**3*(3*h + 1)/7
Let n = 73/300 - 4/25. Let b(z) be the first derivative of -4/15*z**