(m). Factor p(a).
5*a*(a - 1)*(3*a + 2)
Let a(i) = -5*i**4 - 8*i**3 + 24*i**2 - 13*i + 5. Let x(p) = 2*p**4 - p**2 - 3*p + 1. Let y(d) = 2*a(d) + 6*x(d). Suppose y(o) = 0. What is o?
1, 2, 4
Let a(v) be the third derivative of v**6/30 - 8*v**5/15 + 7*v**4/2 - 12*v**3 - 33*v**2 - 3*v. Factor a(s).
4*(s - 3)**2*(s - 2)
Let l(o) be the first derivative of o**4/60 - o**3/3 + 5*o**2/2 - 32*o - 1. Let c(q) be the first derivative of l(q). Factor c(h).
(h - 5)**2/5
Suppose -39*g - 2*w = -35*g - 4, -g + w = 2. Factor 1/2*h**2 + g - 3/2*h.
h*(h - 3)/2
Let l(j) = -4*j**2 - 8*j + 8. Let k(v) = -3*v - 1. Let q(b) = 8*k(b) + l(b). Let q(d) = 0. What is d?
-8, 0
Let x(q) be the second derivative of -q**6/120 + q**5/40 + q**4/4 - q**3/6 - 15*q. Let j(s) be the second derivative of x(s). Let j(a) = 0. What is a?
-1, 2
Let t(n) = 86*n - 12038. Let p be t(140). Factor 24*h - 108 - 4/3*h**p.
-4*(h - 9)**2/3
Let v(x) be the third derivative of -x**7/210 + x**6/120 + x**5/10 - 4*x**2 + 35. Factor v(r).
-r**2*(r - 3)*(r + 2)
Let h be 6/8 + (-36915)/(-2300). Let -129/5*d - 6 - h*d**2 = 0. Calculate d.
-5/4, -2/7
Let j be ((-3)/(-2))/(((-15)/8)/(-5)). Let o be ((-8)/80)/((-1)/j). What is m in -2/5*m**3 - 4/5*m**2 - o*m + 0 = 0?
-1, 0
Let a(v) = v**4 - v**3 + v**2 + v + 1. Let h(g) = 346*g**4 - 2453*g**3 - 2265*g**2 - 661*g - 61. Let p(m) = 3*a(m) - h(m). Factor p(d).
-(d - 8)*(7*d + 2)**3
Let n(q) be the third derivative of -q**6/24 + q**5/12 + 5*q**4/24 - 5*q**3/6 - 106*q**2. Find v such that n(v) = 0.
-1, 1
Factor 89*r**4 - 50*r**4 - 8*r - 2*r**3 - 20*r**2 - 14*r**3 - 43*r**4.
-4*r*(r + 1)**2*(r + 2)
Factor 0*m**2 + 1/10*m**5 + 0*m + 0 + 3*m**4 + 45/2*m**3.
m**3*(m + 15)**2/10
Suppose 10*d + 7 = 27. Factor -1630 - 10*k**2 - 14*k + 1626 + 4*k**d.
-2*(k + 2)*(3*k + 1)
Let j(v) = 35*v**5 - 155*v**4 + 15*v**3 - 15. Let c(w) = w**5 - 2*w**4 - w**3 - 1. Let h(d) = -15*c(d) + j(d). Determine l so that h(l) = 0.
0, 1/4, 6
Suppose -5*c + 2*n = -3*n - 505, -2*c + 200 = -n. Suppose 105*h = c*h. Factor 0*s**2 - 8/7*s**4 + h*s + 0 - 2/7*s**5 - 8/7*s**3.
-2*s**3*(s + 2)**2/7
Let d(n) = -8*n**2 + 40*n + 8. Let o(s) = -23*s**2 + 121*s + 22. Let q(c) = -11*d(c) + 4*o(c). Find x such that q(x) = 0.
0, 11
Solve 4/5*y**3 - 96/5 - 48/5*y**2 + 28*y = 0 for y.
1, 3, 8
Let s(i) be the second derivative of i**8/23520 + i**7/8820 - 5*i**4/12 - 16*i. Let j(n) be the third derivative of s(n). Factor j(h).
2*h**2*(h + 1)/7
Let t(s) be the first derivative of -s**3/3 + 16*s**2 - 87*s + 343. Factor t(m).
-(m - 29)*(m - 3)
Let s be 8/5*(3/6)/((-14)/(-35)). Factor 0 + 4/11*d**3 - 2/11*d**4 + 0*d - 2/11*d**s.
-2*d**2*(d - 1)**2/11
Let x = -1683/20 - -422/5. Let q(i) be the second derivative of 1/2*i**3 + 0 - x*i**4 + 0*i**2 - i. Suppose q(f) = 0. Calculate f.
0, 1
Factor -4/3*m**3 + 20/3*m - 100 + 28/3*m**2.
-4*(m - 5)**2*(m + 3)/3
Suppose -3*l + 19 = 13. Factor 8*y**l + 8*y**3 - 9*y**2 - y**2.
2*y**2*(4*y - 1)
Let j be -18 + 31 + -24 + 11. Solve j - 2/7*c + 0*c**2 + 2/7*c**3 = 0.
-1, 0, 1
Let t(v) be the first derivative of v**3 - 5/4*v**4 + 2/3*v**6 + 14 - 3/5*v**5 + 0*v + 1/2*v**2. Let t(p) = 0. What is p?
-1, -1/4, 0, 1
Let t(g) be the first derivative of -g**6/2700 - g**5/900 + g**4/90 + 22*g**3/3 - 24. Let z(b) be the third derivative of t(b). Factor z(y).
-2*(y - 1)*(y + 2)/15
Let g = 2321/80 - 29. Let v(k) be the third derivative of -1/6*k**3 + g*k**6 + 1/420*k**7 + 0*k - 3*k**2 - 1/16*k**4 + 1/120*k**5 + 0. Factor v(n).
(n - 1)*(n + 1)**2*(n + 2)/2
Let q be ((-6)/16 + 4656/1152)*(-2)/(-11). Factor -1/3*c**2 + 0 + q*c.
-c*(c - 2)/3
Let f = -14670 + 73352/5. Solve 0*d + f*d**3 + 0 - 4/5*d**2 = 0 for d.
0, 2
Let x(j) = -j**3 + 79*j**2 + 91*j + 11. Let i(d) = -d**3 + 39*d**2 + 46*d + 6. Let o(l) = -13*i(l) + 6*x(l). Factor o(g).
(g - 6)*(g + 1)*(7*g + 2)
Let m(i) be the third derivative of -i**9/453600 + i**8/37800 - i**7/12600 + i**5/4 - 4*i**2. Let s(u) be the third derivative of m(u). Solve s(d) = 0.
0, 1, 3
Let g = 2482 + -2479. Factor 0 - 2/3*x**2 - 1/3*x**g + 0*x.
-x**2*(x + 2)/3
Let i = -1/86 + 107/1806. Let z(y) be the second derivative of 0*y**3 - 1/6*y**4 + 0 - 5*y - 1/5*y**6 + 0*y**2 - 3/10*y**5 - i*y**7. Factor z(f).
-2*f**2*(f + 1)**3
Let w = 5 - -4. Factor -9*m**4 + 3*m**2 + 12*m**4 + 9*m - 18 - w*m**3 + 12.
3*(m - 2)*(m - 1)**2*(m + 1)
Let p = 943 + -938. Find x such that 2*x - 12*x**p + 0*x**2 - 1/3 + 27*x**4 - 50/3*x**3 = 0.
-1/3, 1/4, 1/3, 1
Suppose 2*m - 3 = -1. Suppose -m = 2*l - 7. Suppose 2*f**5 - 7*f**3 - l*f**5 + 8*f**3 = 0. What is f?
-1, 0, 1
Let v(x) be the first derivative of -x**6/80 + 3*x**5/160 - 3*x - 5. Let r(w) be the first derivative of v(w). Factor r(d).
-3*d**3*(d - 1)/8
Let r = 57 + -53. Let x = 77 - 47. Suppose x*w + 7*w**r - 8*w**2 - 8*w**3 - 18*w + 5*w**4 - 4 - 4*w**5 = 0. What is w?
-1, 1
Suppose 2*q - 7*m - 4 = -5, 5*m + 4 = 3*q. Factor 0 + 2/3*o**q + 2/3*o**2 + 0*o - 2/3*o**4 - 2/3*o**5.
-2*o**2*(o - 1)*(o + 1)**2/3
Let i(t) be the third derivative of -t**9/181440 + t**8/10080 + 3*t**5/10 + 36*t**2. Let c(d) be the third derivative of i(d). Solve c(u) = 0 for u.
0, 6
Let x = 6439/26 + -495/2. Factor 2/13*l**4 - 2/13*l**2 + x*l - 2/13*l**3 + 0.
2*l*(l - 1)**2*(l + 1)/13
Let d = -606 - -611. Let n(l) be the first derivative of -3/10*l**d - 3/8*l**4 + 1/2*l**3 - 7 + 0*l + 0*l**2 + 1/4*l**6. Factor n(q).
3*q**2*(q - 1)**2*(q + 1)/2
Let m(l) be the first derivative of -l**4/2 + 10*l**3 - 1000*l + 379. Determine x, given that m(x) = 0.
-5, 10
Let c(x) be the third derivative of x**8/1680 - x**6/200 - x**5/150 + 27*x**2 + x. Factor c(u).
u**2*(u - 2)*(u + 1)**2/5
Let r = -48 - -44. Let o be 1/(-10) + (-2)/r. Factor -2/5*j**4 + 0 + 0*j**2 + 0*j**3 + o*j**5 + 0*j.
2*j**4*(j - 1)/5
Let v(l) be the second derivative of -5/6*l**3 - 5/2*l**2 + 1/4*l**5 + 0 + 10*l + 5/12*l**4. Factor v(o).
5*(o - 1)*(o + 1)**2
Let k(b) be the first derivative of -b**5/150 + b**4/20 - 2*b**3/15 + 11*b**2 - 12. Let a(s) be the second derivative of k(s). Factor a(d).
-2*(d - 2)*(d - 1)/5
Let a = -1/497 - -1493/994. Factor 0 - a*y - 3/4*y**2.
-3*y*(y + 2)/4
Suppose 2*z - 2 = -4*f, -5*f = -0*f - 2*z - 25. Let -58 - f*l**4 + 62 - 8*l**2 + 7*l**4 = 0. What is l?
-1, 1
Let g(f) be the second derivative of 3*f**5/4 - 47*f**4/12 + f**3 + 159*f. Find n such that g(n) = 0.
0, 2/15, 3
Suppose s = m + 4, s + 2*m - 4 = 6*m. Let i(a) be the second derivative of 0 + 1/12*a**3 - 1/24*a**s + 0*a**2 - 3*a. Factor i(j).
-j*(j - 1)/2
Let j(t) be the second derivative of -t**6/340 + t**5/102 - t**4/102 - 7*t**2/2 - 14*t. Let k(i) be the first derivative of j(i). Suppose k(l) = 0. What is l?
0, 2/3, 1
Suppose -302*c - 300*c = -894*c + 297*c. Let n = -364 + 1465/4. Factor -n*a**3 + c + 9/4*a**2 - 3/4*a + 3/4*a**4.
3*a*(a - 1)**3/4
Let m(f) be the third derivative of -f**8/30240 + f**7/3780 + f**6/360 - 11*f**5/60 - 9*f**2. Let a(c) be the third derivative of m(c). What is q in a(q) = 0?
-1, 3
Let y(r) be the second derivative of -r**4/60 + 4*r**3/3 + 2*r + 47. Determine v, given that y(v) = 0.
0, 40
Let n = -565/168 + 25/7. Let c(z) be the third derivative of 0 + 1/20*z**5 - n*z**4 + 1/3*z**3 - 1/210*z**7 - z**2 + 1/120*z**6 + 0*z. Let c(f) = 0. What is f?
-2, 1
Determine m, given that -9*m**3 - 3*m**2 + 15/2*m + 3/2*m**5 - 3/2*m**4 + 9/2 = 0.
-1, 1, 3
Let f(a) = -4*a**4 + 40*a**3 + 8*a**2 + 24*a - 8. Let i(j) = -3*j**4 + 27*j**3 + 5*j**2 + 15*j - 5. Let y(s) = -5*f(s) + 8*i(s). Solve y(n) = 0 for n.
0, 4
Suppose -55 = -5*r - 5*a, -2 = -2*r + a + 17. Let p(h) be the second derivative of 15/4*h**4 - 9*h - 50/3*h**3 + 0 + r*h**2. Determine k so that p(k) = 0.
2/9, 2
Suppose b = 14*b - 65. Let m(q) be the second derivative of -1/90*q**b + 2*q + 0*q**6 + 0 + 0*q**4 + 1/189*q**7 + 0*q**2 + 0*q**3. Suppose m(i) = 0. What is i?
-1, 0, 1
Let r(k) = 1664*k**4 - 1 - k + k**5 - 1664*k**4 + k**3. Let y(u) = 32*u**4 + 20*u**3 - 160*u**2 + 104*u + 4. Let h(z) = -4*r(z) - y(z). Factor h(g).
-4*g*(g - 1)**2*(g + 5)**2
Let p(x) be the third derivative of 19*x**2 + 1/105*x**7 - 4/3*x**3 - 1/3*x**4 + 1/15*x**6 + 0 + 1/10*x**5 + 0*x. What is n in p(n) = 0?
-2, -1, 1
Let i(s) be the first derivative of -s**3/3 + s**2 + 158. Factor i(l).
-l*(l - 2)
Let u be (0 - 31/(-3))/((-15 - -35) + -19). Let 22/3*a - 16/3*a**4 + 1 + u