45. Let d(x) = -3*c(x) + 10*g(x). Factor d(m).
-(m - 31)*(m - 5)**2
Let t(w) be the third derivative of -w**5/150 - 19*w**4/30 + 368*w**3/15 - 6165*w**2. Factor t(g).
-2*(g - 8)*(g + 46)/5
What is r in -313/2*r**3 - 41/2 - 623/2*r**2 - 8*r**5 + 329/2*r + 332*r**4 = 0?
-1, 1/4, 1, 41
Let m(g) be the first derivative of -g**4/6 + 598*g**3/9 + 1208*g**2/3 + 808*g + 942. Factor m(a).
-2*(a - 303)*(a + 2)**2/3
Let f(p) be the first derivative of 4*p**3/3 + 570*p**2 + 5600*p + 4874. Determine d so that f(d) = 0.
-280, -5
Suppose 67*i - 168*r + 170*r = 63*i + 12, -10 = -5*r. Factor 0*u**i + 2/5*u**3 - 4/5 - 6/5*u.
2*(u - 2)*(u + 1)**2/5
Let l(m) = 3*m**3 + 24*m**2 + 19*m - 4. Let g(z) = 7*z**3 + 51*z**2 + 39*z - 10. Let u(v) = 6*g(v) - 15*l(v). What is q in u(q) = 0?
-17, -1, 0
Factor -414/7*n + 208/7 + 204/7*n**2 + 2/7*n**3.
2*(n - 1)**2*(n + 104)/7
Let s(l) be the third derivative of 4/9*l**3 + 0*l**5 + 0*l - 1/6*l**4 + 1/90*l**6 + 4 + l**2. Factor s(d).
4*(d - 1)**2*(d + 2)/3
Let v(b) = 5*b**4 - 5*b**3 - 9*b**2 - b + 4. Suppose 7*t - 59 = -24. Let i(o) = 9*o**4 - 9*o**3 - 17*o**2 - o + 8. Let s(y) = t*v(y) - 3*i(y). Factor s(l).
-2*(l - 2)*(l - 1)*(l + 1)**2
Suppose -90*z**4 + 4509/7*z + 3198/7*z**3 - 5784/7*z**2 - 1290/7 - 3/7*z**5 = 0. Calculate z.
-215, 1, 2
Suppose 43*z = 12*z - 31. Let q be ((z + -1)*3 + 6)/1. Suppose -12/5*m**2 + 0 + q*m + 2*m**3 - 2/5*m**4 = 0. What is m?
0, 2, 3
Suppose 65*v = 28*v + 74. Factor -180*n**v + 18*n**4 - 811 + 811 - 3*n**5 + 33*n**3 - 300*n.
-3*n*(n - 5)**2*(n + 2)**2
Let c(p) be the second derivative of -9*p**6/5 + 21*p**5/4 + 53*p**4/12 - 14*p**3 - 10*p**2 - 5484*p. Suppose c(h) = 0. What is h?
-5/6, -2/9, 1, 2
Let l = 782749 + -782747. Factor 2 + 1/4*s**3 - 5/4*s**l + 1/2*s.
(s - 4)*(s - 2)*(s + 1)/4
Factor -85*s + s**3 - 2164*s**2 + 2159*s**2 + 89*s.
s*(s - 4)*(s - 1)
Suppose 0 = -224*i + 216*i + 40. Suppose w - 28 = 5*o, -5*w - i = 6*o - 2*o. Factor -9/4*p**2 + 0 - 3/4*p**w - 3/2*p.
-3*p*(p + 1)*(p + 2)/4
Let c be 1/(1/(-4)*-2). Suppose 3*y = 4*k - 2*y - 66, y - 26 = -2*k. What is o in -10*o**2 + k*o**c - 9*o**2 + 30*o = 0?
0, 6
Suppose 3*a = 3, 9*a = v + 10*a - 5. Determine k so that 15*k**3 + 120*k**2 + 238*k - 6*k**v + k**4 - 334*k - 304*k = 0.
-5, 0, 4
Let n(a) = 11*a**3 - 112*a**2 - 15*a + 116. Let r(x) = 90*x**3 - 894*x**2 - 123*x + 927. Let f(j) = 33*n(j) - 4*r(j). Factor f(w).
3*(w - 40)*(w - 1)*(w + 1)
Find c such that -1490 - 174*c**3 - 3193*c - 82*c - 1181*c**2 + 293*c + 172*c**3 - 313*c**2 = 0.
-745, -1
Factor -5*s**4 + 288*s**3 + 5 + 2*s**4 - 576*s - 5 - 369*s**3 + 462*s**2.
-3*s*(s - 3)*(s - 2)*(s + 32)
Suppose 28 - 36 = -4*i. Factor -22*y**3 + 19*y**3 + 12 - y**2 - 8*y**i.
-3*(y - 1)*(y + 2)**2
Let r be ((-78)/27 - -3)*(-60 + 62). Find q such that -r*q**2 + 16/9 + 4/9*q = 0.
-2, 4
Let r(x) = -x**3 - 2*x**2 + 3. Let o(v) = 4*v**3 + 24*v**2 - 86*v - 110. Let b(p) = -2*o(p) - 4*r(p). Factor b(w).
-4*(w - 4)*(w + 1)*(w + 13)
Let d = -605 + 607. Let c be 4 - 6*(-24)/(-63). Determine j, given that -c*j + 0 - 3/7*j**3 + 15/7*j**d = 0.
0, 1, 4
Let y = 98705 + -98702. Factor -9/7*n**2 - 1/7*n**y + 10/7*n + 0.
-n*(n - 1)*(n + 10)/7
Let a = 355967/2 + -177983. Let 0*t**2 + a*t**5 + 0 + 0*t + 2*t**4 + 2*t**3 = 0. Calculate t.
-2, 0
Let h(l) be the third derivative of -7*l**6/24 - 43*l**5/12 + 265*l**4/12 + 40*l**3/3 - 293*l**2 - 2. Factor h(r).
-5*(r - 2)*(r + 8)*(7*r + 1)
Let m = -9136039/10 - -913604. Factor 0 - 2/5*h**3 - 1/10*h**2 + 3/5*h - m*h**4.
-h*(h - 1)*(h + 2)*(h + 3)/10
Let q(c) = 63*c**2 + 363*c + 594. Let j(w) = -4*w**2 - 4*w. Let a(v) = 15*j(v) + q(v). Factor a(s).
3*(s + 2)*(s + 99)
Let x(b) be the first derivative of 4*b**3/3 + 488*b**2 + 1936*b + 6047. Find u, given that x(u) = 0.
-242, -2
Let l(f) be the first derivative of 14/9*f**2 + 231 - 2/27*f**3 + 0*f. Factor l(n).
-2*n*(n - 14)/9
Let q = 72 + -74. Let c be 2*q/(-4) + (-13 - -54). Factor 2*k**3 + 4*k**4 + c*k**2 - 27*k**4 - 36*k + 13*k**4 + 2*k**5.
2*k*(k - 3)**2*(k - 1)*(k + 2)
Let j(y) = -2467*y**2 - 4959*y + 76. Let o(x) = 1233*x**2 + 2480*x - 44. Let w(l) = 4*j(l) + 7*o(l). Let w(n) = 0. Calculate n.
-2, -2/1237
Let f(a) be the third derivative of a**6/90 - 4*a**5/15 + 8*a**4/3 - 12*a**3 - a**2 - 13. Let x(j) be the first derivative of f(j). Suppose x(c) = 0. What is c?
4
Let v = -306 + 313. Suppose v*l = 9*l - 4. Find w such that -w + 1/3 + w**3 - 1/3*w**l = 0.
-1, 1/3, 1
Let l(h) be the first derivative of -595*h**4 - 2*h**3/3 + 192. Factor l(w).
-2*w**2*(1190*w + 1)
Let i(x) be the first derivative of -1/6*x**6 - 4/3*x**3 + 4/5*x**5 + 2*x**2 - 3/4*x**4 - 157 + 0*x. Find n, given that i(n) = 0.
-1, 0, 1, 2
Let j(v) = 15*v**2 - 40*v + 36. Let m(d) = -d**2 + d - 4. Let h(f) = -2*j(f) - 18*m(f). Factor h(x).
-2*x*(6*x - 31)
Let s = -713 - -811. Let j be 56/s*(-6)/(36/(-21)). Solve 16/19*c - 8/19 - 6/19*c**j = 0 for c.
2/3, 2
Suppose -3*d - 1823 = m, -3*d + 24*m - 1811 = 28*m. Let a = d + 4873/8. Factor -1/8*z**3 - a*z**4 + 1/8*z + 0 + 1/8*z**2.
-z*(z - 1)*(z + 1)**2/8
Suppose 0 = -7*c + 6*c + 5. Suppose -c*u = 4*g - 319, 2*u + 2*u = 2*g + 250. Factor -3*m**2 + 28*m - u + 67 + 27*m**2.
4*(m + 1)*(6*m + 1)
Suppose 1/5*a**4 - 67/5*a - 43/5*a**2 - 6 - a**3 = 0. Calculate a.
-3, -1, 10
Let a = 395 - 399. Let z be 96/144 - a/(-6). Factor z*o**2 - 2/9*o**5 + 0*o**3 + 0 - 2/9*o**4 + 0*o.
-2*o**4*(o + 1)/9
Let q(a) be the second derivative of a**6/120 + a**5/10 - 43*a**4/48 + 29*a**3/12 - 3*a**2 + 148*a. Let q(z) = 0. Calculate z.
-12, 1, 2
Let t(u) be the first derivative of 3/2*u**2 - 11/12*u**3 + 3/16*u**4 - u - 90. What is i in t(i) = 0?
2/3, 1, 2
Let v(w) be the third derivative of w**5/270 + 113*w**4/54 - 920*w**3/27 - 17*w**2 - 23*w + 1. Find c such that v(c) = 0.
-230, 4
Let i be ((-26)/546)/(7/(-84))*(-81)/(-12). Let -i - 30/7*j - 3/7*j**2 = 0. Calculate j.
-9, -1
Let s(k) be the second derivative of -k**5/80 - 25*k**4/4 - 912*k**3 + 11552*k**2 + 11*k - 207. Solve s(d) = 0 for d.
-152, 4
Let h be 1 + (-6)/(-4)*2. Let g be 7 - ((3 + 2 - -5) + -7). Factor -n + n - 19*n**h + 16*n**g + 3*n**2.
-3*n**2*(n - 1)*(n + 1)
Let r(i) be the third derivative of 5*i**8/336 - 32*i**7/21 - 11*i**6/2 + i**2 + 2*i + 668. Factor r(h).
5*h**3*(h - 66)*(h + 2)
Let l = 42 + -39. Let w(t) be the third derivative of -1/600*t**6 + 0 + 4*t**2 - 1/100*t**5 + 1/15*t**l + 1/1050*t**7 + 1/120*t**4 + 0*t. Factor w(b).
(b - 2)*(b - 1)*(b + 1)**2/5
Let n(p) be the third derivative of -p**7/350 + 3*p**6/40 - 61*p**5/100 + 21*p**4/40 + 49*p**3/5 + 2752*p**2. Let n(r) = 0. Calculate r.
-1, 2, 7
Let n(r) be the second derivative of r**6/30 + r**5/20 - 7*r**4/3 - 38*r**3/3 - 24*r**2 - 127*r + 4. Let n(a) = 0. What is a?
-4, -2, -1, 6
Let u = 505 - -17. Let s = 524 - u. Factor 0*q + 1/8*q**s - 1/8*q**5 + 1/8*q**3 + 0 - 1/8*q**4.
-q**2*(q - 1)*(q + 1)**2/8
Let j = 9829 + -9817. Let a(d) be the first derivative of -3/5*d**5 - j*d**2 + 9*d + 6*d**3 + 0*d**4 - 4. Let a(y) = 0. Calculate y.
-3, 1
Let z(u) = -u**3 - 8*u**2 - 10*u - 14. Let v be z(-8). Let l = v - 63. Factor 80*a**3 - 32 + 13*a + 40*a**2 - 68*a**3 + l*a.
4*(a + 2)**2*(3*a - 2)
Solve 10/3*y**4 + 0 + 25/3*y**3 - 8*y - 10/3*y**2 - 1/3*y**5 = 0.
-2, -1, 0, 1, 12
Let d(x) be the third derivative of 2*x**5/15 - 7*x**4/6 + 12*x**3 - 7*x**2 - 4. Let q(f) = 7*f**2 - 30*f + 72. Let n(a) = 3*d(a) - 4*q(a). Factor n(i).
-4*(i - 6)*(i - 3)
Determine b, given that 2/11*b**3 + 480/11 + 62/11*b**2 + 356/11*b = 0.
-24, -5, -2
Let u = -86718 - -86718. Solve 0 + u*g + 6/7*g**2 - 6/7*g**3 = 0.
0, 1
Determine y, given that -269/3*y - 139/3*y**2 - 19/3*y**3 + 1/3*y**4 - 50 = 0.
-3, -2, -1, 25
Suppose 315*q**5 + 23*q**2 - 23*q**4 - 8*q**3 + 7*q**3 - 314*q**5 = 0. Calculate q.
-1, 0, 1, 23
Let f = -294 - -297. Determine x, given that 41*x**2 - 80*x**3 - 16 + 51*x**2 - 24*x + 14*x**4 + 14*x**f = 0.
-2/7, 1, 2
Let z(r) = -4*r. Let c = 15 - 51. Let y(f) = f**2 + 38*f + 1. Suppose -4*x = j + 12, -2*x - 5 + 1 = 0. Let a(b) = c*z(b) + j*y(b). Suppose a(o) = 0. What is o?
-1
Let a = -458 - -462. Suppose -u - 4*s = 3*u - 12, u + a*s - 6 = 0. Suppose 1/7*l - 1/7*l**u + 2/7 = 0. Calculate l.
-1, 2
Find j such that 17*j**5 + 46*j**3 - 6*j**4 + 28*j + 62*j**2 - 128*j**2 - 19*j**5 = 0.
-7, 0, 1, 2
Let t = 1445570 - 1445567. Factor 18*z