r 6*v - 5*v**3 + 2*v**3 - 3*v**x + 4*v**3 + 4.
-2*(v - 2)*(v + 1)**2
Let d(g) be the third derivative of -121*g**6/90 - 286*g**5/45 - 46*g**4/9 - 16*g**3/9 + 48*g**2 - 1. Suppose d(x) = 0. Calculate x.
-2, -2/11
Let f be 0*(-2 + 1) - (-1600)/6090. Let b = 2/87 + f. Suppose 2/7*x**3 + 0 + b*x**4 - 2/7*x - 2/7*x**2 = 0. What is x?
-1, 0, 1
Suppose 121*v + 156 = 125*v. Suppose 0 = 11*o + v - 61. Factor -3/7*l**o + 12/7*l - 9/7.
-3*(l - 3)*(l - 1)/7
Solve -52/9*n**2 - 14/9*n**3 - 40/9*n + 16/9 = 0 for n.
-2, 2/7
Let z(r) be the second derivative of 17*r**6/70 - 27*r**5/35 + r**4/7 - 43*r - 1. Factor z(m).
3*m**2*(m - 2)*(17*m - 2)/7
What is p in 4*p**2 - 12/5 + 2/5*p + 0*p**3 - 2/5*p**5 - 8/5*p**4 = 0?
-3, -2, -1, 1
Factor -35*j - 18*j**2 - j - 64*j**2 - 166*j**2 + 49*j**4 - 413*j**3.
j*(j - 9)*(7*j + 2)**2
Let k(g) be the first derivative of g**6/18 + 4*g**5/15 - 2*g**4/3 - 14*g**3/3 - 3*g**2/2 + 18*g - 492. Determine j so that k(j) = 0.
-3, -2, 1, 3
Let u(p) be the third derivative of p**6/72 - p**5/4 + 5*p**4/3 + p**3/3 - 28*p**2. Let v(s) be the first derivative of u(s). What is o in v(o) = 0?
2, 4
Let l(s) be the third derivative of -1/2*s**3 + 1/14*s**7 + 9*s**2 - 3/4*s**4 - 1/5*s**5 + 0 + 3/20*s**6 + 0*s. Factor l(j).
3*(j - 1)*(j + 1)**2*(5*j + 1)
Let 20/9*c**4 + 14*c - 44/9*c**3 + 12 - 16/3*c**2 - 2/9*c**5 = 0. Calculate c.
-1, 3, 6
Suppose 13 = -4*f + 25. Factor -63*v**4 + v**5 + 63*v**4 - v**f.
v**3*(v - 1)*(v + 1)
Let s = 3588/5 + -717. Let p(t) be the first derivative of 9 + s*t**2 - 8/15*t**3 + 2/5*t. Determine u, given that p(u) = 0.
-1/4, 1
Let r(d) = 11*d**3 - 5. Let c(u) = -6*u**3 + 3. Let n(x) = -x**2 + 5*x + 17. Let f be n(-2). Let g(s) = f*r(s) + 5*c(s). Factor g(a).
3*a**3
Let q(x) be the third derivative of 1/5*x**3 + 0 - 10*x**2 + 1/8*x**4 + 0*x + 1/25*x**5 + 1/200*x**6. Factor q(m).
3*(m + 1)**2*(m + 2)/5
Let a(h) be the second derivative of 0 + 9*h + 1/84*h**4 + 1/140*h**5 - 2/21*h**3 - 2/7*h**2. Solve a(s) = 0 for s.
-2, -1, 2
Suppose -6*o - 12 = -9*o. Factor 41*v**3 - 37*v**3 - 4*v**4 + 2*v**2 - 8 + 10*v**2 - o*v.
-4*(v - 2)*(v - 1)*(v + 1)**2
Let p be 2 + -6 + 4 + 3. Factor -p*a - 3*a**3 + 0*a**3 + 0*a**3 + 6*a**2.
-3*a*(a - 1)**2
Let n be -4 - 6*6/(-9). Let -3*o + n*o**2 + 4*o**3 - 5*o + 2*o**2 - 6*o**2 = 0. What is o?
-1, 0, 2
Let x(f) = 7*f**3 - 99*f**2 + 15*f - 9. Let z be x(14). Factor 0*t**2 - 2/3*t**z + 0*t**4 - 2/3*t + 0 + 4/3*t**3.
-2*t*(t - 1)**2*(t + 1)**2/3
Let l be (-1*3)/(-56 + 56 + (2 - 3)). Suppose 2*t**4 - 192/7*t + 20*t**2 - 64/7 + 102/7*t**l = 0. Calculate t.
-4, -2/7, 1
Let r(q) be the third derivative of 0 + 0*q + 0*q**3 - 1/24*q**4 + 1/20*q**6 - 12*q**2 - 1/60*q**7 - 1/40*q**5. Factor r(d).
-d*(d - 1)**2*(7*d + 2)/2
Let o(y) = -3*y**4 - 81*y**3 - 21*y**2 + 45*y + 60. Let i(v) = v**4 + 23*v**3 + 6*v**2 - 13*v - 17. Let z(x) = 18*i(x) + 5*o(x). Determine h so that z(h) = 0.
-2, -1, 1
Determine h so that 0*h - 9/4*h**3 + 27/4*h**2 - 3/4*h**4 + 0 + 1/4*h**5 = 0.
-3, 0, 3
Let a(c) = c**5 - 2*c**2 - 1. Let r(f) = -20*f**5 - 246*f**4 - 134*f**3 + 298*f**2 + 96*f - 102. Let u(j) = -2*a(j) - r(j). Let u(p) = 0. Calculate p.
-13, -1, 2/3
Let b(p) be the first derivative of -7*p**6/12 - 5*p**5/4 + p**4/2 + 25*p**3/12 + 3*p**2/4 - 396. Suppose b(v) = 0. What is v?
-3/2, -1, -2/7, 0, 1
Suppose 48 - 2/3*w**2 + 14*w = 0. Calculate w.
-3, 24
Let w = 575 - 4023/7. Factor 4/7 + w*i**3 - 2/7*i - 4/7*i**2.
2*(i - 2)*(i - 1)*(i + 1)/7
Let s = 0 + 4. Suppose -2*a - 28 = -b + 21, -132 = -3*b + a. Factor 2*k**3 + 2*k**3 + s*k - 49*k**2 - k**4 - 1 + b*k**2.
-(k - 1)**4
Let v be 3*(7/(-3) - 1). Let f = v + 16. Solve -3*y - f*y + 3*y**2 + 10 - 4 = 0.
1, 2
Let h(t) = 2*t. Let l be h(1). Let z be 4 + 0*l/(-4). Factor b**5 + 3*b**4 - 6*b**z + 0*b**5 + 2*b**4.
b**4*(b - 1)
Let h(i) be the third derivative of -i**8/56 - 2*i**7/21 + i**6/30 + 8*i**5/15 + i**4/12 - 2*i**3 - 217*i**2 - i. Find g such that h(g) = 0.
-3, -1, 2/3, 1
Let v be (-6 + -5)*(0 - -2 - -11). Let q = -285/2 - v. Factor -1/4 - q*h - 1/4*h**2.
-(h + 1)**2/4
Factor -9 - 22*x**2 + 0*x**3 + 2*x**4 - 8*x**3 - 24*x + 0*x - 3*x**4.
-(x + 1)**2*(x + 3)**2
Let d(y) be the first derivative of -216*y**2 + 114*y**3 - 1/3*y**6 + 26/5*y**5 + 216*y - 9 - 67/2*y**4. Factor d(s).
-2*(s - 3)**3*(s - 2)**2
Solve -15*y**2 - 99*y**4 - 103*y**4 + 4*y**3 + 197*y**4 - 24*y**3 = 0.
-3, -1, 0
Let v(r) be the third derivative of r**5/12 - 115*r**4/24 - 103*r**2 + 1. Factor v(o).
5*o*(o - 23)
Let z(m) be the second derivative of 7*m**5/15 - 5*m**4/6 - 4*m**3/3 - 7*m**2 - 16*m. Let h(c) be the first derivative of z(c). Let h(t) = 0. Calculate t.
-2/7, 1
Let w(k) = -42*k**2 - 134*k - 124. Let x(j) = 8*j**2 + 27*j + 25. Let m(i) = -3*w(i) - 16*x(i). Solve m(f) = 0 for f.
-14, -1
Let d(g) be the second derivative of -3/2*g**2 + 0 + 1/2*g**3 - 4*g - 1/12*g**4 + 1/180*g**5. Let k(l) be the first derivative of d(l). Factor k(h).
(h - 3)**2/3
Let b be 4/6 + ((-6)/(-99))/(20/440). Factor -2/7*y**5 - 10/7*y**4 - 4/7*y - 18/7*y**3 + 0 - b*y**2.
-2*y*(y + 1)**3*(y + 2)/7
Let j(v) be the first derivative of -30*v**2 + 2 + 8*v - 68/3*v**3. Determine p so that j(p) = 0.
-1, 2/17
Let q(o) = -o**4 - o. Let l(j) = -9*j**4 + 2*j**3 - 26*j**2 - 61*j - 24. Let i(k) = 2*l(k) - 22*q(k). Factor i(d).
4*(d - 4)*(d + 1)**2*(d + 3)
Let x(k) be the first derivative of k**5/210 - k**4/42 + 4*k**2/21 + 20*k - 22. Let d(q) be the first derivative of x(q). Factor d(c).
2*(c - 2)**2*(c + 1)/21
Suppose x + 2*w = -4, -4*w - 50 = -5*x - 14. Suppose 0 = -7*z + x*z + 111. Factor 4*y + 37 - 4*y**3 + 4*y**2 - 4*y**4 - z.
-4*y*(y - 1)*(y + 1)**2
Let b(x) be the second derivative of 2*x**5/25 - x**3/5 + x**2/5 - 3*x - 14. Factor b(r).
2*(r + 1)*(2*r - 1)**2/5
Let z(u) = 2*u**3 + u**2 + 2*u + 2. Let l(d) = 20*d**3 + 122*d**2 + 229*d + 4. Let f(x) = -3*l(x) + 6*z(x). Determine y so that f(y) = 0.
-15/4, 0
Suppose 2*v = -g + 4*v - 8, -2*v - 16 = 5*g. Let i(a) = 3*a**3 + 6*a**2 - a. Let o(q) = -q**3 - q**2. Let h(d) = g*o(d) - i(d). Factor h(k).
k*(k - 1)**2
Let b be -4*(-2 + 9/12). Suppose -b*s - 3*d = 0, 2*s = d + d + 16. Factor -2*h**3 + 0*h**2 - 2*h**2 + 2*h**s - 2*h**3.
-2*h**2*(h + 1)
Let o = -4/475 - -1433/950. Determine h, given that -o*h**3 + 9/2 - 21/2*h + 15/2*h**2 = 0.
1, 3
Factor 4/3*u - 1/3*u**3 - 16/3 + 4/3*u**2.
-(u - 4)*(u - 2)*(u + 2)/3
Let z(s) be the second derivative of s**6/150 + 47*s**5/100 + 216*s. Solve z(k) = 0 for k.
-47, 0
Let p(h) be the second derivative of h**8/168 + 2*h**7/105 - h**5/15 - h**4/12 + h**2/2 + 17*h. Let r(j) be the first derivative of p(j). Factor r(c).
2*c*(c - 1)*(c + 1)**3
Let j(h) be the second derivative of h**4/54 - 2*h**3/9 + 8*h**2/9 - 9*h + 4. Solve j(i) = 0.
2, 4
Let q(n) be the third derivative of n**5/105 - 5*n**4/21 + 50*n**3/21 - 59*n**2. Factor q(b).
4*(b - 5)**2/7
Let m(a) be the second derivative of -a**5/170 - a**4/102 + a**3/3 - 15*a**2/17 + 138*a + 2. Factor m(y).
-2*(y - 3)*(y - 1)*(y + 5)/17
Let i(t) be the second derivative of t**5/120 - t**3/12 + t**2/2 + 5*t. Let u(q) be the first derivative of i(q). Solve u(g) = 0.
-1, 1
Suppose 87 = -3*l - 321. Let f = l + 410/3. Solve 4/3 - 2*u + f*u**2 = 0.
1, 2
Suppose 0 = s - 10 + 28. Let n be ((-2)/(-27))/((-6)/s). Factor -2/9*m**2 + 4/9*m - n.
-2*(m - 1)**2/9
Let u(k) be the third derivative of k**5/105 + k**4/42 - 20*k**3/7 - 278*k**2 - 1. Factor u(j).
4*(j - 5)*(j + 6)/7
Let q(k) be the second derivative of 9/2*k**3 - 33/80*k**5 + 0*k**2 + 1/40*k**6 + 0 + 3/2*k**4 + 38*k. Determine c so that q(c) = 0.
-1, 0, 6
Let t(g) be the third derivative of g**8/56 - g**7/10 + 7*g**6/40 - g**5/10 - 5*g**2 - 25*g. Let t(j) = 0. Calculate j.
0, 1/2, 1, 2
Let v(a) be the second derivative of 3*a**5/20 - a**4/2 - a**3/2 + 3*a**2 - 8*a - 12. Suppose v(f) = 0. What is f?
-1, 1, 2
Let c(n) be the second derivative of -n**5/150 - n**4/30 + n**3/5 - n**2/3 - 34*n + 1. Determine w so that c(w) = 0.
-5, 1
Let a = -51 + 65. Factor 3*u**2 - a + 2*u + 52*u + 257.
3*(u + 9)**2
Let b = -10 + 21. Let w be (((-1)/6)/(-1))/(b/33). Factor 0*o**2 + 0*o**3 - w*o**4 + 0 - 1/2*o**5 + 0*o.
-o**4*(o + 1)/2
Let s be 3 + 0 - (-2)/6*-3. Let j(y) be the second derivative of 1/12*y**3 - 1/2*y**s - 4*y + 0 - 1/40*y**5 + 1/12*y**4. Solve j(v) = 0.
-1, 1, 2
Let