9*p - 17. Let u(l) = -3*d(l) + r(l). Factor u(t).
(t - 20)*(t + 1)
Let j be 33 + -30 + 0/(-6). Factor 4*w**j + 8/3*w**2 + 10/9*w**4 - 16/9*w + 0.
2*w*(w + 2)**2*(5*w - 2)/9
Suppose -2/7*h**4 + 0*h - 8/7 + 10/7*h**2 + 0*h**3 = 0. Calculate h.
-2, -1, 1, 2
Let x(w) = -w**2 + 11*w + 7. Let q(m) = -m + 18. Let i be q(7). Let j be x(i). Suppose -j*c - 4*c - c**2 + 11*c = 0. What is c?
0
Suppose 0 = 12*s - s. Let f(i) be the first derivative of 0*i**2 + s*i + 1/12*i**3 + 1/8*i**4 - 1 + 1/20*i**5. Factor f(d).
d**2*(d + 1)**2/4
Let h(m) be the third derivative of 0*m - 1/2856*m**8 + 0 + 0*m**3 + 1/357*m**7 - 1/102*m**4 - 3/340*m**6 + 7/510*m**5 - 3*m**2. Solve h(w) = 0.
0, 1, 2
Suppose 5*t - 35 = 5*r, 9 + 0 = 3*t + r. Let l(p) be the first derivative of -1/12*p**3 - p**2 - t*p - 3. Factor l(s).
-(s + 4)**2/4
Let q(s) be the second derivative of -s**4/24 + 41*s**3/6 - 1681*s**2/4 - 9*s + 7. Factor q(n).
-(n - 41)**2/2
Let y = 116 - 113. Let k be (-2)/8*((-24)/y - 1). Solve k*c - 1/2 + c**2 - 1/2*c**4 + 9/4*c**5 - 9/2*c**3 = 0 for c.
-1, 2/9, 1
Let r(x) = -x**2 - x + 1. Suppose 14 = 7*l - 14. Let g(b) = 14*b**2 - b - 9. Let p(i) = l*r(i) + g(i). Factor p(y).
5*(y - 1)*(2*y + 1)
Find w, given that 18 - 1/3*w**3 - 28/3*w**2 - 25/3*w = 0.
-27, -2, 1
Suppose 4*l - 5 - 10 = 3*z, 25 = -5*z. Let f(u) be the third derivative of 1/9*u**3 + 0*u - 1/90*u**5 + 0*u**4 + 4*u**2 + l. Factor f(o).
-2*(o - 1)*(o + 1)/3
Let x(c) be the first derivative of c**6/180 + c**2/2 + c - 3. Let h(j) be the first derivative of x(j). Let n(d) be the first derivative of h(d). Factor n(z).
2*z**3/3
Let d(r) be the first derivative of 54*r**6 - 1512*r**5/5 + 648*r**4 - 704*r**3 + 416*r**2 - 128*r - 64. Let d(t) = 0. What is t?
2/3, 2
Suppose 15*k**2 - 5/2*k**4 + 0*k - 25/2*k**3 + 0 = 0. Calculate k.
-6, 0, 1
Let y(u) = -3*u**4 - 13*u**3 + 11*u**2 + 13*u. Let k(z) = z**4 + z**3 - z**2 - z - 2. Let v(h) = -20*k(h) - 5*y(h). Let v(m) = 0. Calculate m.
-1, 1, 8
Let d(o) be the second derivative of -o**5/60 + o**4/8 + 2*o**3/3 - 37*o**2/2 + 51*o. Let p(w) be the first derivative of d(w). Factor p(b).
-(b - 4)*(b + 1)
Let h(k) be the first derivative of 8*k**6/15 + 28*k**5/5 + 99*k**4/5 + 388*k**3/15 + 34*k**2/5 - 48*k/5 - 73. Solve h(s) = 0 for s.
-4, -3, -1, 1/4
Let u(n) be the third derivative of -n**8/4200 - n**7/350 - n**6/100 - n**5/75 - 29*n**3/6 + 24*n**2. Let p(o) be the first derivative of u(o). Factor p(l).
-2*l*(l + 1)**2*(l + 4)/5
Let l = -12057 + 84407/7. Let -4*m**4 - l*m**2 + 8*m**3 + 4/7*m**5 + 36/7 - 60/7*m = 0. Calculate m.
-1, 1, 3
Let j(m) = 61*m + 307. Let d be j(-5). Factor 2/7*r**d + 0 - 2/7*r**3 + 0*r.
-2*r**2*(r - 1)/7
Factor -4*d**3 + 5244 + 28*d**2 + 49*d - 5244 + 23*d.
-4*d*(d - 9)*(d + 2)
Suppose 4*z + 12 = 10*z. Suppose 0 = z*m + 2*m - 8*m. Solve 1/7*d - 2/7*d**2 + 1/7*d**3 + m = 0.
0, 1
Factor 459*i + 3*i**2 + 625*i + 5043 + 329*i - 1659*i.
3*(i - 41)**2
Let q = -19041 - -19045. Find u such that 4/3*u**3 - q - 4/3*u**2 - 20/3*u = 0.
-1, 3
Suppose -w + 4*p + 5 + 7 = 0, 3*w = p + 14. Let y be w/(-7) - (-72)/126. Factor -12/5*o**3 - 3/5*o**4 - 12/5*o**2 + 0*o + y.
-3*o**2*(o + 2)**2/5
Factor 22*s - 24 + 2*s**3 + 21*s - 6*s - 6*s**3 - 9*s.
-4*(s - 2)*(s - 1)*(s + 3)
Let b(h) be the second derivative of -h**4/18 + 4*h**3/9 + 5*h**2/3 + 7*h. Factor b(p).
-2*(p - 5)*(p + 1)/3
Let m(q) = q**3 - q - 3. Let h be m(2). Let o(f) be the first derivative of 0*f - 3/4*f**4 + 2*f**h + 1 - 3/2*f**2. Solve o(t) = 0 for t.
0, 1
Let n be 2/(-6) + (-646)/(-1254). Factor -4/11*r + 2/11*r**2 + n.
2*(r - 1)**2/11
Let b(o) = 7*o**3 - 7245*o**2 + 1166445*o - 62599231. Let c(p) = -5*p**3 + 4830*p**2 - 777630*p + 41732820. Let n(q) = 5*b(q) + 8*c(q). Solve n(s) = 0 for s.
161
Let p(x) be the third derivative of -x**5/240 + 5*x**4/24 - 3*x**3/2 + 204*x**2. Factor p(m).
-(m - 18)*(m - 2)/4
Let f(s) be the third derivative of -s**6/40 + 17*s**5/20 + 37*s**2. Factor f(h).
-3*h**2*(h - 17)
Suppose 65 = -15*h + 28*h. What is z in -4*z**4 + 7*z**5 + 10*z + 4*z**2 - 9*z**h - 8*z = 0?
-1, 0, 1
Let s(i) be the second derivative of i**7/126 + 2*i**6/45 - 2*i**5/15 - i**4/2 + 9*i. Let y(r) be the third derivative of s(r). Solve y(a) = 0.
-2, 2/5
Let a(q) be the second derivative of -7*q**6/120 + 19*q**5/80 - 5*q**4/16 + q**3/24 + q**2/4 - 89*q + 2. Suppose a(v) = 0. What is v?
-2/7, 1
Let 3*t**3 - 117*t + 66 - 7*t + 51*t**2 + 54 - 50*t = 0. What is t?
-20, 1, 2
Let 2/3 - 1/3*r**2 + 1/3*r = 0. Calculate r.
-1, 2
Let j(p) be the second derivative of -p**6/6 + 7*p**5 - 245*p**4/2 + 3430*p**3/3 - 12005*p**2/2 - 70*p + 2. Factor j(s).
-5*(s - 7)**4
Suppose 8*y - 9*y = -4. Find r such that -2*r**y - 2*r**2 - 4*r**3 - 565 + 565 = 0.
-1, 0
Let u(v) = -30654935*v**3 - 847598*v**2 - 7816*v - 24. Let h(j) = -j**3 - j**2 + j. Let z(y) = 4*h(y) + u(y). Factor z(q).
-3*(217*q + 2)**3
Suppose -8 = 5*t + 4*a, 0*a - 3*a = -2*t + 6. Let d be (-68)/(-8) - (t + 4). Solve -3/2*b**2 + d*b - 3 = 0 for b.
1, 2
Suppose z = -3*g + 5*g + 4, -4*z + 4 = -2*g. Suppose z = -3*u + 2*o + 2, 0 = 5*u - o - 4*o. Solve -4*n**2 - u*n**4 - 2*n - 2/5*n**5 - 4*n**3 - 2/5 = 0.
-1
Let x(y) be the second derivative of y**7/252 + y**6/120 - y**5/30 - 7*y**4/6 + 4*y. Let t(z) be the third derivative of x(z). Find i, given that t(i) = 0.
-1, 2/5
Let b(w) be the first derivative of -2/5*w**5 - 10/3*w**3 - 2*w**2 + 0*w + 33 - 2*w**4. Find f such that b(f) = 0.
-2, -1, 0
Let b = -439 + 445. Let l(r) = r**3 + 7*r**2 - 2*r - 10. Let v be l(-7). Let -3*w**5 - 11*w**3 + b*w**v + 11*w**3 = 0. Calculate w.
0, 2
Let q be 16/248 + (-115)/(-620). What is f in 0 - 5/4*f**3 + 1/4*f**5 + q*f**4 + 0*f + 3/4*f**2 = 0?
-3, 0, 1
Let i be -16 + 360/32 - -5. Factor -i*h**4 - 1/4*h + 0 - 3/4*h**3 - 3/4*h**2.
-h*(h + 1)**3/4
Let 3*a**2 - 8*a**2 + 9*a - 2135 - 33*a - 176*a + 135 = 0. What is a?
-20
Suppose 70*a = 18*a. Let p(t) be the third derivative of 0*t - 1/90*t**5 + 2/9*t**4 + a - 7*t**2 - 16/9*t**3. Factor p(m).
-2*(m - 4)**2/3
Suppose -2*d = -8 + 2. Solve -16*t**3 + 8*t**3 - t**d + 33*t - 15*t**2 - 9 = 0.
-3, 1/3, 1
Let m(d) = -10*d + 290. Let h be m(29). Let v(y) be the second derivative of -4*y + 1/24*y**4 - 1/6*y**3 + 1/4*y**2 + h. Solve v(t) = 0 for t.
1
Let s = -7/5 - -3/2. Let w(c) be the second derivative of 0 + s*c**6 + 1/42*c**7 - 1/2*c**2 - 5*c - 1/2*c**3 + 1/10*c**5 - 1/6*c**4. Let w(u) = 0. What is u?
-1, 1
Let n(k) be the third derivative of -27/2*k**3 - 1/60*k**5 + 0*k - 38*k**2 + 3/4*k**4 + 0. Factor n(x).
-(x - 9)**2
Suppose -7*k - 2 = -9. Let l(y) = -2*y**2 + 8*y + 5. Let r(m) = 1. Let n(q) = k*l(q) + 5*r(q). Factor n(x).
-2*(x - 5)*(x + 1)
Determine w so that -12*w - 3*w**4 + 39/4*w**3 + 3 - 9/4*w**2 = 0.
-1, 1/4, 2
Factor -4*v**2 - 43 - 100*v - 57 + 4.
-4*(v + 1)*(v + 24)
Let r(c) be the first derivative of 4*c**5/5 + 6*c**4 + 16*c**3 + 16*c**2 + 697. What is k in r(k) = 0?
-2, 0
Suppose 4*h - 18 = -2*h. Suppose -z - h = 0, -8*z + 3*z - 24 = -3*n. Factor -2/7 + 4/7*y**n + 4/7*y**2 - 2/7*y**5 - 2/7*y**4 - 2/7*y.
-2*(y - 1)**2*(y + 1)**3/7
Let w(m) be the second derivative of 28*m - 3/40*m**5 - 1/40*m**6 + 1/16*m**4 + 1/4*m**3 + 0*m**2 + 0. Factor w(j).
-3*j*(j - 1)*(j + 1)*(j + 2)/4
Let u(f) be the third derivative of f**6/24 - f**5/3 - 35*f**4/24 + 25*f**3/3 + f**2 + 56. Factor u(p).
5*(p - 5)*(p - 1)*(p + 2)
Let h(q) = 24*q**3 + q**2 - q. Let f be h(1). Let z be (15/(-12))/((-3)/f). Solve -2*l**4 - z*l**2 + 6*l**3 + 4*l - 4*l**3 + 6*l**3 = 0.
0, 1, 2
Let 93*t**3 + 14*t**4 - 21*t**4 + 82*t**2 + 5*t**4 - 13*t**3 = 0. Calculate t.
-1, 0, 41
Suppose 0 = -5*q + 4964 - 924. Let w be (q/(-168) + 5)*(-6)/(-4). Factor 0*h**3 + 4/7*h**2 + 2/7*h**5 - 4/7*h**4 - w*h + 0.
2*h*(h - 1)**3*(h + 1)/7
Suppose -4*b = -5*m + 137 + 1, 0 = -5*b + 5*m - 170. Let r = b + 34. Factor -3 - 10*q**r - 1 + 4 - 4*q.
-2*q*(5*q + 2)
Suppose -7*x + 25 = -17. Factor 2*t**2 + t + 2 + x*t + 0*t - 3*t.
2*(t + 1)**2
Let r = 27/140 + 2/35. Let l(b) be the first derivative of 0*b**2 + 0*b + 1/3*b**3 + r*b**4 - 5. Suppose l(a) = 0. Calculate a.
-1, 0
Let y(c) = 2*c**4 + 8*c**3 - 16*c**2 - 52*c - 2. Let g(j) = -2*j**4 - 9*j**3 + 15*j**2 + 51*j + 3. Let w(z) = 4*g(z) + 6*y(z). Let w(m) = 0. What is m?
-3, 0, 3
Let d(j) = j**3 + 2*j**2 - 5*j - 3. Let k be d(-3). Let m = -1045/26