ivative of c(r). Factor k(d).
d*(d + 1)*(5*d - 1)
Suppose -t + 4*a = -2, -3*a = -2*a + 2. Let o be (t/8)/(161/28 + -6). Suppose -3/2*f + 3/2*f**3 + o - 3*f**2 = 0. What is f?
-1, 1, 2
Let m(p) be the third derivative of -p**6/360 - p**5/180 + p**4/18 + 2*p**3/9 - 96*p**2. Factor m(o).
-(o - 2)*(o + 1)*(o + 2)/3
Factor 928/7*y**3 + 12487168/7*y + 161472/7*y**2 + 362127872/7 + 2/7*y**4.
2*(y + 116)**4/7
Let d(g) = 3*g**2 + 3*g - 2. Let l be d(1). Factor -5*w**3 - 19*w + 24*w + 5*w**2 - 17*w**l + 12*w**4.
-5*w*(w - 1)*(w + 1)**2
Let g(x) = x**3 - 9*x**2 + x - 7. Suppose 0 = -18*h + 15*h + 27. Let f be g(h). Factor 8*j - 9 + 5 - f*j**2 - 2*j**2.
-4*(j - 1)**2
Let k(n) be the third derivative of n**5/12 - 5*n**4/6 + 10*n**3/3 + 22*n**2. Factor k(q).
5*(q - 2)**2
Let p be -3*1 - (230/(-15) - -12). Let k(n) be the second derivative of p*n**3 + 0 + 0*n**2 + 1/6*n**4 + 6*n. Find y, given that k(y) = 0.
-1, 0
Let r(k) be the third derivative of -k**6/600 - 3*k**5/50 + 122*k**2. Suppose r(o) = 0. What is o?
-18, 0
Suppose 5*t + 5 = 0, -5*c - 5*t = 27 - 22. What is x in c + 1/4*x + x**2 = 0?
-1/4, 0
Let b = 1365631/735 - 1858. Let r(v) be the third derivative of 1/21*v**3 + 0*v - b*v**7 - 5*v**2 + 0 + 0*v**5 - 1/210*v**6 + 1/42*v**4. Factor r(c).
-2*(c - 1)*(c + 1)**3/7
Let u = 171/98 - 313/1078. Factor 2/11*d**4 + 0*d**2 + u*d**3 + 0 + 0*d.
2*d**3*(d + 8)/11
Let p(i) = 5*i**3 - 31*i**2 + 20*i - 6. Let z(f) = -5*f**3 + 30*f**2 - 20*f + 5. Let y(h) = -5*p(h) - 6*z(h). Suppose y(m) = 0. Calculate m.
0, 1, 4
Let t(r) be the first derivative of 3*r**4/8 - r**3/2 - 39*r**2/2 - 36*r + 283. Find b, given that t(b) = 0.
-4, -1, 6
Let h(v) be the first derivative of v**6/18 + 17*v**5/30 + v**4 + 10*v**3/3 + 4. Let r(q) be the third derivative of h(q). Factor r(w).
4*(w + 3)*(5*w + 2)
Factor 0 + 3/5*s**4 - 66/5*s - 3/5*s**2 + 66/5*s**3.
3*s*(s - 1)*(s + 1)*(s + 22)/5
Suppose 0 = -5*g + 3*y + 84, 2*g - 4*y + 5*y = 16. Find s such that 3/4*s**3 + 6*s**2 + g*s + 0 = 0.
-4, 0
Let w be 1 - 2*(-4 - (-88)/20). Let d(b) be the first derivative of -7 + 6/5*b**2 + w*b**4 + 0*b + 16/15*b**3. Solve d(l) = 0.
-3, -1, 0
Suppose 0 = 7*b + 11*b - 18. Let c(f) = -f**3 + f + 1. Let q(t) = 4*t**3 - 10*t - 7. Let m(g) = b*c(g) + q(g). Factor m(l).
3*(l - 2)*(l + 1)**2
Let b be 90/(-15)*6/(-900). Let v(h) be the second derivative of -8*h + 0 + 0*h**2 - 2/15*h**3 - 2/15*h**4 - b*h**5. What is a in v(a) = 0?
-1, 0
Let c(b) be the first derivative of -b**4 + 40*b**3 - 600*b**2 + 4000*b + 6. Factor c(o).
-4*(o - 10)**3
Let x(i) be the second derivative of i**4/54 + 10*i**3/27 + i**2 - 339*i. Suppose x(k) = 0. What is k?
-9, -1
Let m(j) be the third derivative of -j**5/20 + 7*j**4/4 - 13*j**3/2 + 431*j**2. Factor m(p).
-3*(p - 13)*(p - 1)
Let n be (-3)/21*(3 + (-851 - 1)). Let m = -121 + n. Factor -2/7 + 2/7*v**5 + 4/7*v**2 + m*v - 2/7*v**4 - 4/7*v**3.
2*(v - 1)**3*(v + 1)**2/7
Let b(m) be the second derivative of 2*m**7/21 + 28*m**6/15 + 36*m**5/5 + 34*m**4/3 + 22*m**3/3 + 831*m. Determine a so that b(a) = 0.
-11, -1, 0
Let a(u) = 10*u**2 - 34*u - 44. Suppose -3*l - 54 = -0*l - 3*x, -5*x = -20. Let h(n) = 2*n**2 - 7*n - 9. Let d(c) = l*h(c) + 3*a(c). Factor d(b).
2*(b - 3)*(b + 1)
Let c = -218 - -676/3. Let h = c + -98/15. Let -h*w**2 + 16/5*w - 16/5 = 0. Calculate w.
2
Let p be 44/(-20)*(0 + -5). Let b(i) = -i**3 + 12*i**2 - 12*i + 11. Let t be b(p). Factor 3/4*s**3 + t*s + 0*s**4 - 1/4*s**5 + 0 + 1/2*s**2.
-s**2*(s - 2)*(s + 1)**2/4
Let j(h) be the third derivative of -1/20*h**5 + 1/336*h**8 + 1/70*h**7 - 1/12*h**4 + 0*h**3 + 0*h + 1/120*h**6 + 0 + 26*h**2. Determine u so that j(u) = 0.
-2, -1, 0, 1
Let x(f) = f**2 - 9*f + 4. Let i(m) = 3*m - 9. Let p be i(6). Let d be x(p). Factor 2*y + 11*y**3 - d*y**2 + 7*y**2 - 3 - 8*y**3 - 5*y.
3*(y - 1)*(y + 1)**2
Let f = -3496 + 24506/7. Solve -6/7*o**5 + 2/7*o**4 + 0 + 12/7*o + 38/7*o**2 + f*o**3 = 0.
-1, -2/3, 0, 3
Let -39*q**3 - 36*q + 31*q**2 - 86*q**2 - 53*q**2 - 132*q**2 = 0. What is q?
-6, -2/13, 0
Let u(z) = 7*z + 86. Let b be u(-12). Let k be -4 - -2 - 64/(-26). Factor -8/13*i - 16/13 - k*i**3 + 20/13*i**b.
-2*(i - 2)**2*(3*i + 2)/13
Factor 44/5*y + 46/5 - 2/5*y**2.
-2*(y - 23)*(y + 1)/5
Determine r so that -3598 + 450*r - 18847 + 220*r - 19*r**2 + 14*r**2 = 0.
67
Let t(n) be the second derivative of -n**6/30 + 7*n**5/20 - 13*n**4/12 - n**3/2 + 9*n**2 + 4*n - 13. Let t(b) = 0. What is b?
-1, 2, 3
Let m(n) be the first derivative of 10*n - 25/3*n**3 - 15/2*n**2 + 13. Factor m(d).
-5*(d + 1)*(5*d - 2)
Let l(v) = -15*v**2 + 410*v - 373. Let u(i) = 4*i**2 - 103*i + 93. Let f(g) = 6*l(g) + 22*u(g). Factor f(s).
-2*(s - 96)*(s - 1)
Let t(i) be the third derivative of -i**5/150 + i**4/60 + i**2 + 87*i. Solve t(u) = 0.
0, 1
Let t = 83035/42 - 1977. Let q(w) be the third derivative of 1/105*w**5 + 0*w + 0*w**3 - t*w**4 + 0 - w**2. Factor q(y).
4*y*(y - 1)/7
Let u be -2 + ((-120)/(-14))/2. Let j(f) = -10*f - 248. Let i be j(-25). Factor 2/7*z**3 + 24/7*z + 12/7*z**i + u.
2*(z + 2)**3/7
Let y be (1077 + -1081)*(-1 + 0). Determine w so that -75/4*w**2 - 9/4*w**3 + 3/2*w**5 - 69/4*w - 9/2 + 21/4*w**y = 0.
-3, -1, -1/2, 2
Let n(d) be the second derivative of -d**6/1620 + d**4/108 + 13*d**3/3 + 26*d. Let j(r) be the second derivative of n(r). Factor j(a).
-2*(a - 1)*(a + 1)/9
Suppose 2*f = -h, -5 = 4*f + 5*h + 7. Suppose 30*m**3 + 2*m**f + 5*m**5 + 10*m - 22*m**2 - 5*m - 20*m**4 = 0. What is m?
0, 1
Let l(t) = 2*t - 12. Let x(o) = -o**2 + 9*o. Let v be x(8). Let z be l(v). Factor z*r + 0 - r**2 - 1 + 4 - 6.
-(r - 3)*(r - 1)
Let z(y) = -y**2 - 5*y + 4. Let a be z(-5). Suppose a*c - 8*c + 28 = 0. Factor -10*k**2 - 3 - 6 + 12*k + 0 + c*k**2.
-3*(k - 3)*(k - 1)
Let d = 46 + -40. Factor m**4 - 20*m**3 + m**4 - 36*m**2 - 16 - 4*m**4 - 40*m + d*m**3.
-2*(m + 1)*(m + 2)**3
Let f(p) = -p**3 - p. Let h be f(2). Let q be (-2)/(-4) - 45/h. Suppose -9/5*n**4 + 0*n**2 + 0 + 7/5*n**q + 0*n + 2/5*n**3 = 0. What is n?
0, 2/7, 1
Factor 4/5 - 2/5*c**3 + 2/5*c - 4/5*c**2.
-2*(c - 1)*(c + 1)*(c + 2)/5
Let r(v) be the second derivative of v**4/12 + 8*v**3/3 + 32*v**2 + 56*v. Solve r(w) = 0 for w.
-8
What is n in 12 + 24 + 10320*n - 4*n**2 - 10288*n = 0?
-1, 9
Suppose -78*q = -70*q - 36*q + 56. Factor 0 - 2/3*r + 1/3*r**q.
r*(r - 2)/3
Let x(v) = -2*v**3 - v**2 - 19*v - 18. Let m be x(-1). Find d such that 0 - 8/5*d + 2/5*d**m = 0.
0, 4
Let p(v) be the third derivative of -1/260*v**6 - 36*v**2 + 0*v + 0 + 1/2184*v**8 + 0*v**3 + 1/39*v**4 + 2/195*v**5 - 2/1365*v**7. Find b such that p(b) = 0.
-1, 0, 2
Suppose 7*x + 8 = 2*q + 5*x, -4*q - 5*x + 7 = 0. Suppose 2/9 + 2/9*m - 2/9*m**2 - 2/9*m**q = 0. Calculate m.
-1, 1
Let c be (-3)/1*(-17)/68. Let n = 12 - 12. Solve 0*u**3 + 3/4*u**2 - c*u**4 + n + 0*u = 0.
-1, 0, 1
Let g be (4/(-22))/(1/(-11)). Factor 35*c**4 + 37*c**4 - c**3 - g*c**2 - 71*c**4.
c**2*(c - 2)*(c + 1)
Let r = 9377/3 + -3125. Factor 0*u - r + 2/3*u**2.
2*(u - 1)*(u + 1)/3
Let h(k) be the first derivative of k**6/900 + k**5/75 + k**4/20 + 28*k**3/3 + 16. Let w(s) be the third derivative of h(s). Factor w(f).
2*(f + 1)*(f + 3)/5
Let f(h) be the second derivative of -h**6/210 - h**5/70 + 5*h**4/84 + h**3/7 - h + 14. Factor f(u).
-u*(u - 2)*(u + 1)*(u + 3)/7
Let p = -3817 - -19424/5. Let o = -66 + p. Factor -3/5*w**2 + 3/5*w**5 + o*w**3 - 9/5*w**4 + 0 + 0*w.
3*w**2*(w - 1)**3/5
Factor 0*d - 3/8*d**2 + 0 - 1/8*d**4 - 1/8*d**5 + 5/8*d**3.
-d**2*(d - 1)**2*(d + 3)/8
Let y be 0/((9/(-3))/3). Let c(k) be the second derivative of 0*k**2 - 9/100*k**5 + 2*k - 3/70*k**7 + 1/5*k**3 + y - 7/50*k**6 + 3/20*k**4. Solve c(o) = 0.
-1, 0, 2/3
Let h(c) = c**3 + 11*c**2 + 12*c + 22. Let v be h(-10). Factor -4*a**2 - 3*a - 3*a**2 - 2 + 11*a**2 + a**v.
(a - 1)*(5*a + 2)
Suppose -4*y + 1 + 11 = -4*a, 5*a = -3*y - 15. Suppose 3*s - s - 4 = y. Find d, given that -d**2 + s*d**3 - d**4 - 8 + 8 = 0.
0, 1
Let q(w) = -4*w**2 + 54*w - 113. Let b(y) = -2*y**2 + 28*y - 57. Let x(u) = -7*b(u) + 3*q(u). Solve x(m) = 0.
2, 15
Let v(a) be the third derivative of -5*a**6/84 - a**5/7 - 3*a**4/28 - a**2 + 22. Factor v(r).
-2*r*(5*r + 3)**2/7
Let p be (-12 - 913/(-77)) + 17/21. What is v in -p*v - 1/6*v**2 - 2/3 = 0?
-2
Let o be 7 - 3*(28/12 + -1). Let v(t) = 25*t**2 + 380*t + 2515. Let m(a) = -8*a**2 - 