040 - x**7/8820 + x**6/5040 + x**5/420 + x**4/6 - x. Let f(p) be the third derivative of h(p). Solve f(w) = 0.
-2, -1, 1
Suppose 189/5*q + 3*q**2 - 78/5 = 0. Calculate q.
-13, 2/5
Let o = 3854 + -3854. Factor o - 3*f**2 - 3/2*f**3 + 0*f.
-3*f**2*(f + 2)/2
Let b(m) = m**2 - 3*m - 6. Let d be b(5). Suppose h + h = d. Factor 0*y**4 - h*y**4 - 4*y**2 + 5*y**3 + y**3.
-2*y**2*(y - 2)*(y - 1)
Suppose -24*t + 30 = -9*t. Let w(g) be the first derivative of -1/8*g**4 + 1/2*g**3 - 1/2*g**t + 3 + 0*g. Solve w(m) = 0.
0, 1, 2
Let s be (-18)/(-2 - -4) - 111/(-12). Factor -3/4 - s*v + 1/4*v**3 + 3/4*v**2.
(v - 1)*(v + 1)*(v + 3)/4
Let j(c) be the first derivative of 2 + 9/2*c**2 - 5*c + 3*c**3. Let u(n) = -28*n**2 - 26*n + 14. Let f(a) = 14*j(a) + 5*u(a). Solve f(r) = 0.
-2/7, 0
Factor -7*v - 48 + 163*v**2 - 162*v**2 + 40.
(v - 8)*(v + 1)
Let y be (-49)/(-104) - (-8)/52. Let p(c) be the second derivative of -7*c + 0 - y*c**4 + 0*c**2 + 3/10*c**5 + 1/4*c**3. Factor p(g).
3*g*(g - 1)*(4*g - 1)/2
Suppose -35*h - 25/2*h**2 + 0 = 0. Calculate h.
-14/5, 0
Let t be 99/60 + (-75)/60. Let -t*a**3 + 0 + 0*a + 6/5*a**2 = 0. What is a?
0, 3
Factor 147*y**2 - 316*y**2 + 174*y**2 - 1580*y + 124820.
5*(y - 158)**2
Let n(j) = -5*j - 1 + 3*j + j**2 + 4*j - j. Let u(p) = 2*p**2 - p + 2. Let s(a) = 12*n(a) - 4*u(a). What is r in s(r) = 0?
-5, 1
Let m(g) be the first derivative of 0*g**2 - 18 - 1/16*g**4 - 1/4*g**3 + g. Factor m(l).
-(l - 1)*(l + 2)**2/4
Let d be (4 - 90/21)*-7. Suppose -2*v = -3*v + d. Determine h, given that -4*h**3 + 16*h**4 - 12*h**4 - 4*h**v + 3*h**5 + h**5 = 0.
-1, 0, 1
Let a = -204 - -209. Let q(p) be the first derivative of 9/2*p**4 - 2*p**a + 0*p - 2*p**2 + 10/3*p**3 - 7/3*p**6 - 4. Determine c, given that q(c) = 0.
-1, 0, 2/7, 1
Let q be ((-88)/(-12) + -2)/(2/3). Let f be (-6)/16*q/(-2). What is v in -1/4*v**2 + f*v - 9/4 = 0?
3
Factor 3*t**2 + 3*t + 48*t - 31 - 2 - 21.
3*(t - 1)*(t + 18)
Let s = -28 + 32. Factor 2*o**3 - o - 13*o + 8 + s*o**2 + 0*o**2.
2*(o - 1)**2*(o + 4)
Suppose 2*n - 2*a = -0*a, -4*a + 20 = 0. Suppose v - n*v = -4*u - 8, 5*u + 2 = 3*v. Factor 1/4*h**v + 0 + 1/4*h**3 + 0*h**2 + 0*h.
h**3*(h + 1)/4
Let h(v) = -21*v**2 + 201*v - 255. Let k(i) = -11*i**2 + 100*i - 129. Let l(m) = -8*h(m) + 15*k(m). Factor l(y).
3*(y - 35)*(y - 1)
Let j(x) = 3*x**2 - 159*x + 158. Let r be j(52). Find s, given that -11/7*s - 2*s**4 - 24/7*s**r - 2/7 - 26/7*s**3 - 3/7*s**5 = 0.
-1, -2/3
Let k be (-49)/(-294) + 2777/(-6). Let y = k - -468. Solve -16/3*a + 4/3*a**5 + y*a**4 - 16/3*a**2 + 0 + 4*a**3 = 0.
-2, -1, 0, 1
Let f(y) = -7*y**4 - 37*y**3 - 128*y**2 + 5*y. Let x(b) = -3*b**4 - 18*b**3 - 64*b**2 + 2*b. Let h be (-5*1)/(4/(-4)). Let r(q) = h*x(q) - 2*f(q). Factor r(k).
-k**2*(k + 8)**2
Let g = -486 + 490. Factor 3/5*d**g + 2/5*d - 3/5*d**2 - 2/5*d**3 + 0.
d*(d - 1)*(d + 1)*(3*d - 2)/5
Let d(t) be the second derivative of -2/9*t**6 + 4*t - 7/15*t**5 + 0 + 0*t**2 - 1/3*t**4 - 2/63*t**7 + 0*t**3. Factor d(b).
-4*b**2*(b + 1)**2*(b + 3)/3
Let g(w) be the third derivative of w**5/5 - 11*w**4/6 + 4*w**3 + 55*w**2. Solve g(k) = 0 for k.
2/3, 3
Let a(p) be the first derivative of -2*p**7/63 - 4*p**6/45 + 2*p**4/9 + 2*p**3/9 + 2*p + 1. Let t(f) be the first derivative of a(f). Find m such that t(m) = 0.
-1, 0, 1
Suppose -z + 3 + 3 = 5*p, 2*p - 2*z - 12 = 0. Let t = -35373 + 247617/7. Determine m, given that 22/7*m - 22/7*m**3 + t - p*m**2 + 8/7*m**4 = 0.
-1, -1/4, 1, 3
Determine k, given that 20*k**2 + 0*k**2 - 4*k - 56 - 16*k**3 + 24*k**3 - 20*k**3 + 20*k**2 = 0.
-1, 2, 7/3
Let p(w) be the second derivative of w**7/630 - w**6/180 - w**5/15 + 7*w**4/12 + 6*w. Let o(i) be the third derivative of p(i). What is g in o(g) = 0?
-1, 2
Factor -31 + 236*l**2 - 440*l**2 - 17 + 9*l**3 + 36*l + 252*l**2.
3*(l + 2)*(l + 4)*(3*l - 2)
Suppose 2*s = 3*f, -5*s + 15 + 4 = 2*f. Let i(m) = -m + 10. Let y be i(8). Determine x so that -f*x + 6*x**2 + 8*x - 1 + x**y = 0.
-1, 1/7
Suppose 5*t = m - 62, 3*t + 0*m + 5*m + 26 = 0. Let k be (-28)/(-16) + (-3)/t. Factor g**2 + 6*g + 4*g**2 + 0*g**k - 2*g**2.
3*g*(g + 2)
Let v(k) be the second derivative of 0 + 16*k - 1/24*k**4 - 1/3*k**3 - 3/4*k**2. Factor v(d).
-(d + 1)*(d + 3)/2
Let u(c) be the first derivative of -c**6/24 - c**5/10 + c**4/8 + c**3/3 - c**2/8 - c/2 - 188. Suppose u(z) = 0. Calculate z.
-2, -1, 1
Let q(a) be the first derivative of a**7/2940 - 11*a**6/1260 + 40*a**3/3 - 28. Let k(y) be the third derivative of q(y). Factor k(p).
2*p**2*(p - 11)/7
Solve 0 + 0*r - 1/3*r**5 - 4*r**2 + 7/3*r**4 - 4/3*r**3 = 0.
-1, 0, 2, 6
Let l(v) be the second derivative of v**5/60 - v**4/4 + 3*v**3/2 - 5*v**2 + 15*v. Let x(f) be the first derivative of l(f). Determine b so that x(b) = 0.
3
Let j(m) be the third derivative of 1/180*m**6 + 29*m**2 + 0*m**3 + 0*m - 1/15*m**5 + 5/36*m**4 + 0. Determine t so that j(t) = 0.
0, 1, 5
Let y(w) be the third derivative of -w**6/240 - 13*w**5/24 - 341*w**4/16 + 363*w**3/4 + 46*w**2 + 2. Suppose y(n) = 0. Calculate n.
-33, 1
Let f(q) be the third derivative of 0*q**4 - 1/15*q**6 + 0 - 29*q**2 - 2/105*q**7 + 0*q - 1/15*q**5 + 0*q**3. Let f(y) = 0. What is y?
-1, 0
Let s(a) be the third derivative of a**5/150 - 13*a**4/6 + 845*a**3/3 + 9*a**2 + 6. Suppose s(n) = 0. What is n?
65
Find r, given that 36*r - 25 - 4*r**2 - 35*r + 73 - 16*r - 17*r + 4*r**3 = 0.
-3, 2
Let n(b) be the first derivative of 5/22*b**2 + 1/22*b**6 - 2/11*b**4 - 2 + 4/55*b**5 + 2/11*b - 2/11*b**3. Find c such that n(c) = 0.
-2, -1, -1/3, 1
Let p be 21/357 - (-11)/102. Find s such that 1/2 + p*s**2 - 2/3*s = 0.
1, 3
Let c be ((-16)/4)/(44/12 - 5). Factor -c*l - 1/2*l**2 - 4.
-(l + 2)*(l + 4)/2
Suppose -4*g + 102 = -g. Suppose 2*k - g = -2. Factor 19*s**2 + 1 + k*s + 13*s**2 + 1.
2*(4*s + 1)**2
Let q(p) be the second derivative of p**6/10 - 9*p**5/4 + 31*p**4/2 - 24*p**3 + 208*p + 1. Factor q(t).
3*t*(t - 8)*(t - 6)*(t - 1)
Let z(g) = 4*g**4 - 27*g**3 + 184*g**2 - 480*g + 403. Let b(i) = -i**4 + i**3 - 1. Let c(w) = -3*b(w) - z(w). Solve c(k) = 0 for k.
2, 10
Let m(z) be the second derivative of -2*z**7/21 - 22*z**6/15 - 36*z**5/5 - 12*z**4 - 325*z - 1. Solve m(q) = 0.
-6, -3, -2, 0
Let u = -5 + 12. Suppose -r - 2*q + 4 = 0, -3*r + 2*r - 5*q = -u. Factor 3*d**r + 2 - 2*d**2 - 2*d**2 + d + 0*d**2.
-(d - 2)*(d + 1)
Let v(l) be the second derivative of -1/210*l**5 + 0*l**3 - 37*l + 0*l**2 - 2/315*l**6 + 0 + 1/126*l**4. Solve v(w) = 0 for w.
-1, 0, 1/2
Let i(s) be the third derivative of -s**8/2352 + s**6/140 + 2*s**5/105 + s**4/56 - 19*s**2. Factor i(z).
-z*(z - 3)*(z + 1)**3/7
Let d be 2808/3460 + (8/2 - 5). Let a = 2/173 - d. Suppose a*b**2 + 3/5 - 1/5*b**3 + b = 0. What is b?
-1, 3
Let b(p) be the first derivative of 1/14*p**4 - 11 + 8/7*p**2 - 8/7*p - 10/21*p**3. What is o in b(o) = 0?
1, 2
Let s(u) = -u**2 + 8*u + 12. Let l(v) = -9*v**2 + 84*v + 120. Let j(o) = -2*l(o) + 21*s(o). Factor j(x).
-3*(x - 2)*(x + 2)
Solve 0 - 76/3*r + 224/3*r**2 + 4*r**3 = 0 for r.
-19, 0, 1/3
Let m(x) = 2*x**2 - 66*x + 70. Let h be m(32). Let w(u) be the second derivative of 0*u**2 + 1/18*u**4 - 2/9*u**3 + 0 + h*u. Factor w(q).
2*q*(q - 2)/3
Let h = 46 - 38. Factor -h*m - 4*m**4 - 40/3*m**3 - 4/3 - 16*m**2.
-4*(m + 1)**3*(3*m + 1)/3
Let p(n) be the first derivative of n**5/12 + 5*n**4/4 - 35*n**3/6 + 15*n**2/2 - 26. Let c(u) be the second derivative of p(u). Let c(t) = 0. Calculate t.
-7, 1
Let z(r) = 1. Let c(q) = 0*q**2 + 4*q - 9 + 7 - 2*q**2 + 4. Let k(t) = -c(t) - 4*z(t). Let k(p) = 0. What is p?
-1, 3
Factor 8 - 2*m**2 - 1945*m**3 + 1943*m**3 - m + 9*m.
-2*(m - 2)*(m + 1)*(m + 2)
Let -13/5*o**3 + 0*o + o**4 + 7/5*o**2 + 1/5*o**5 + 0 = 0. What is o?
-7, 0, 1
Let s(x) = x + 3. Let r be s(-3). Suppose 2*p - 3*y - 14 + 1 = r, p = 2*y + 8. What is l in 3*l + 11*l**p - 27*l**3 - 11*l**2 = 0?
-1/3, 0, 1/3
Let c be -1 + 1 + 1/(-3)*-9. Let k(g) be the first derivative of -2 - 4/3*g**2 - 8/9*g**c + 0*g - 1/6*g**4. Factor k(z).
-2*z*(z + 2)**2/3
Suppose -3*z + c = -234, -4*z + 224 = c - 88. Factor 6*g + 9*g**2 - z*g**3 - 4 + 4 + 81*g**3.
3*g*(g + 1)*(g + 2)
Let j = -170 - -210. Let u be (42 - j)/(0 + 1). Solve -2/7 - 6/7*p - 2/7*p**3 - 6/7*p**u = 0.
-1
Factor -45/2*t + 15/4*t**3 + 39/8*t**2 + 3/8*t**4 + 27/2.
3*(t - 1)**2*(t + 6)**2/8
Let s(h) be the second