 Factor q(c).
2*c**2*(c - 1)*(c + 1)/19
Let b(x) be the first derivative of 218*x**3/3 - 537*x**2 - 80*x + 7538. Factor b(t).
2*(t - 5)*(109*t + 8)
Let o(u) = -7*u**2 - 2495*u - 1064. Let c be o(-356). Factor -2/7*y**2 - 18/7*y - c.
-2*(y + 2)*(y + 7)/7
Let h(t) be the second derivative of 1/24*t**6 + 0*t**2 - 1/168*t**7 - 124*t + 0 + 0*t**4 + 0*t**5 + 0*t**3. Factor h(c).
-c**4*(c - 5)/4
Let i be (4*5/30)/((-1)/15). Let d be ((-50)/10)/(i/4). Find h such that -22 + 8 + d*h + h**2 + 5*h**2 + 6 = 0.
-4/3, 1
Let u be ((-1182)/21 - -52) + 6. Factor u*a + 2 - 2/7*a**2.
-2*(a - 7)*(a + 1)/7
Let a(s) be the second derivative of -s**6/1080 + 2*s**5/15 - 8*s**4 + s**3/2 - 12*s**2 + 22*s. Let i(p) be the second derivative of a(p). Factor i(x).
-(x - 24)**2/3
Let c = -6/7 - -134/91. Suppose 867 - 239 = 157*q. Find p, given that -8/13*p + 6/13*p**3 + 0 - c*p**2 + 4/13*p**q - 2/13*p**5 = 0.
-1, 0, 2
Let w be 19/((-323)/(-221)) + 18/(-2). Let n(t) be the second derivative of 3/4*t**2 + 1/32*t**w + 0 + 1/4*t**3 - 19*t. Factor n(o).
3*(o + 2)**2/8
Let l(r) = r**3 - 19*r**2 + 9*r - 3. Let z(v) = -4*v**3 + 96*v**2 - 44*v + 16. Let u be ((-24)/(-3))/(5/(-10)). Let j(p) = u*l(p) - 3*z(p). Factor j(y).
-4*y*(y - 3)*(y - 1)
Let g(s) be the third derivative of -s**7/25 - s**6/200 + 2377*s**2. Let g(r) = 0. Calculate r.
-1/14, 0
Let t = -10 - 998. Let i = -5037/5 - t. Factor -1/5 + z - i*z**2 - 9/5*z**3.
-(z + 1)*(3*z - 1)**2/5
Find w, given that -50*w**2 - 5*w**3 - 2 + 22*w + 10*w - 27*w + 2*w**4 + 50*w**2 = 0.
-1, 1/2, 1, 2
Let h(c) be the first derivative of -c**4/32 + 13*c**3/6 - 40*c**2 + 288*c + 2492. Factor h(w).
-(w - 36)*(w - 8)**2/8
Factor 0 - 2/19*k**2 + 386/19*k.
-2*k*(k - 193)/19
Let k be (0 - 72/16)*(-4)/6. Let v be (-204)/(-54) + 2*k/27. Factor v*d - 8*d + 2*d**2 - 4*d**2.
-2*d*(d + 2)
Let j be ((-1080)/(-70) + -15)/((-69)/(-46)). Find a, given that 0 + 4/7*a + 6/7*a**2 - j*a**4 + 0*a**3 = 0.
-1, 0, 2
Let m = 682 + -677. Suppose -2 = -m*s + 18. Factor -4/3*p**3 + 0*p + 2/3*p**s + 2/3*p**2 + 0.
2*p**2*(p - 1)**2/3
Suppose 2*v - 11 + 7 = 2*x, -5*x - 5*v + 30 = 0. Factor 8*m - 12*m + 20*m - 4*m**x.
-4*m*(m - 4)
Let u = 166 + -161. Factor 22*t**4 + 18*t**u - 6*t**3 + t**3 + 4*t**3 + 5*t**3.
2*t**3*(t + 1)*(9*t + 2)
Let u be ((-8)/3)/((-12)/18). Let g be (-2)/(((-4)/(-1432))/((-2)/u)). Factor -346*m + 3*m**2 - m**2 + 16 + g*m.
2*(m + 2)*(m + 4)
Suppose -5*p = -11*y + 9*y - 58, 5*p + 3*y - 63 = 0. What is x in 92*x - p*x + 5*x**2 - x**2 + 26 + 80*x**2 + 2*x**4 + 32*x**3 = 0?
-13, -1
Let l(m) be the first derivative of -2*m**5/65 - 27*m**4/26 + 56*m**3/39 + 26. Factor l(z).
-2*z**2*(z - 1)*(z + 28)/13
Determine q, given that -378075*q**3 + 3/4 - 4263/4*q + 379140*q**2 = 0.
1/710, 1
Let l(o) be the first derivative of -o**7/210 - o**6/25 + 124*o + 23. Let t(j) be the first derivative of l(j). Find u such that t(u) = 0.
-6, 0
Let v(k) be the first derivative of 24 - 1/90*k**5 + 5/54*k**4 - k**2 - 26*k - 1/9*k**3. Let x(g) be the first derivative of v(g). Solve x(i) = 0 for i.
-1, 3
Suppose 2*v = -v + l + 7, 0 = -v + 5*l - 21. Suppose v = 15*d - 13*d. Factor 75*y**5 - 42*y**5 - 37*y**5 + 4*y**d - 12*y**3 + 12*y**4.
-4*y**2*(y - 1)**3
Suppose -53*b - 250 = -58*b. Let a be 3*(4/18 - b/(-18)). Let -22*u + 9*u**3 - 26*u + 39*u**3 + 57*u**2 + a + 9*u**4 - 11*u**2 = 0. What is u?
-3, 1/3
Suppose -82*d**2 + 5*d**3 - 2*d**3 + 6*d**2 + d**3 = 0. What is d?
0, 19
Suppose 120*f - 116*f = -324. Let t be (-7)/(-14) + f/(-6). Suppose 1 + t*h + 6*h**2 + 2*h**3 + 3 - 32*h + 6 = 0. Calculate h.
-5, 1
Let l = 39174 + -195852/5. Determine b so that -l*b - 4/5 + 4/5*b**5 + 6/5*b**4 - 26/5*b**2 - 2*b**3 = 0.
-1, -1/2, 2
Find z, given that 35*z**2 + 67*z**2 - 178*z**2 + 72*z**2 - 2840*z = 0.
-710, 0
Let d be (-3 + 7 + -10)*(-7)/3. Factor 2 + d*t + 6 + 9 - 17 - 2*t**2.
-2*t*(t - 7)
Let n = 8564 - 77074/9. Let o(x) be the second derivative of n*x**2 + 1/27*x**3 + 0 - 1/54*x**4 + 8*x. Determine j so that o(j) = 0.
-1, 2
Let a = -11833233/7 - -1690469. Suppose -a*u - 2/7*u**2 + 52/7 = 0. Calculate u.
-26, 1
Let u(z) be the second derivative of -z**5/40 - 43*z**4/24 - 97*z**3/6 - 38*z**2 + 1074*z. Factor u(m).
-(m + 1)*(m + 4)*(m + 38)/2
Suppose 2 = -506*s + 8 - 6. Determine f so that 0 + s*f + 2/7*f**3 - 4/7*f**2 = 0.
0, 2
Let b(m) be the third derivative of 1/15*m**5 + 84*m + 0 + 19/96*m**4 - 2*m**2 + 1/8*m**3. Factor b(p).
(p + 1)*(16*p + 3)/4
Suppose -5*v - 138 = s - 30, 0 = 5*v - 4*s + 93. Let l be v*(8/(-3))/4. Factor -25*k**3 + 15*k**3 + l*k**3 + 3*k**2 + 4*k + 5*k**2.
4*k*(k + 1)**2
Let -24/5 + 108/5*k + 9/5*k**3 + 54/5*k**4 - 138/5*k**2 = 0. Calculate k.
-2, 1/2, 2/3
Let m(w) = -w**2 + 220*w + 5324. Let q be m(-22). Find z such that -12/5*z**2 - 4*z**3 + 4/5*z**5 + 0 + q*z - 4/5*z**4 = 0.
-1, 0, 3
Let s be -3*(50/60)/((-5)/70). Let j be s*((-22)/45)/(-11). Factor -j*a + 10/9*a**2 - 2/9*a**3 + 2/3.
-2*(a - 3)*(a - 1)**2/9
Let g be (6 - 0) + 4 - 90/12. Let j(k) be the second derivative of 1/4*k**4 + 9*k**2 - 28*k + g*k**3 + 0. Factor j(q).
3*(q + 2)*(q + 3)
Let h be -1*226/(-8) + (-206)/3090 + 714/(-90). Determine q so that -27/2*q**3 + 48*q**2 + h*q**5 + 3 - 81*q**4 + 93/4*q = 0.
-1/3, 1, 4
Let h = 355 - 349. Let d be 2/h - (-90)/378. Factor -1/7*s + 0 - d*s**2.
-s*(4*s + 1)/7
Find z, given that 39*z**3 - 47 - 34 - 89 + 1671*z + 540*z**2 - 98 - 2 = 0.
-9, -5, 2/13
Let a(v) be the second derivative of v**6/75 + 41*v**5/2 + 1023*v**4/10 + 3067*v**3/15 + 1022*v**2/5 + 3408*v. Let a(g) = 0. What is g?
-1022, -1
Let q(n) = -4*n - 9. Let v be q(-6). Let j(z) = -6*z**2 - 21*z - 9. Let d be j(-3). Factor -v*b + 268*b**2 + 0 + 20 - 273*b**2 + d.
-5*(b - 1)*(b + 4)
Let x(o) = -31*o**2 - 91*o + 26. Let s(l) = 2. Let h(r) = 6*r**2 + 18*r - 9. Let n(j) = 5*h(j) + 10*s(j). Let c(w) = 4*n(w) + 5*x(w). What is i in c(i) = 0?
-3, 2/7
Let l(r) be the second derivative of -32*r**6/105 - 66*r**5/35 - 39*r**4/14 - 9*r**3/7 - 1013*r. Solve l(f) = 0 for f.
-3, -3/4, -3/8, 0
Let k(d) be the second derivative of d**7/147 - 3*d**5/70 + d**4/21 + 782*d. Factor k(c).
2*c**2*(c - 1)**2*(c + 2)/7
Let q(w) = -w**3 + 3*w**2 - 2*w + 6. Let m(r) = -2*r**3 - 363*r**2 - 337*r + 2136. Let o(b) = m(b) + q(b). Factor o(f).
-3*(f - 2)*(f + 3)*(f + 119)
Let i(u) = -u**3 + 14*u**2 + 800*u - 288. Let h be i(36). Factor 4/3*v**5 + 4/3*v**4 - 4*v**3 - 20/3*v**2 - 8/3*v + h.
4*v*(v - 2)*(v + 1)**3/3
Let x(l) = 6*l**2 + 538*l + 1720. Let s(a) = 2*a**2 + 183*a + 574. Let c(k) = 8*s(k) - 3*x(k). Factor c(o).
-2*(o + 4)*(o + 71)
Determine y so that -13/6*y**4 + 0*y**2 + 0*y - 1/3*y**3 + 0 = 0.
-2/13, 0
Suppose 0 = -3*v - 3*n, 9*v - 14*v - 2*n + 9 = 0. Factor 16*m**2 + v*m**2 + 7*m + 3*m + 15*m**3 - 3*m**2 - 13*m**3 - 28.
2*(m - 1)*(m + 2)*(m + 7)
Let m be 14/(-40) - -12*(-22)/(-352). Find o, given that -4/5*o**3 + 0 + m*o**2 + 0*o = 0.
0, 1/2
Suppose 137*y = 52*y + 35*y. What is n in 3/2*n**4 + y - n**3 - n - 7/2*n**2 = 0?
-1, -1/3, 0, 2
Let y be 340/(-204) + (-88)/(-24). Factor -89/6*c**y + 29/3*c + 4 + 7/6*c**3.
(c - 12)*(c - 1)*(7*c + 2)/6
Let 3*x**2 - 27*x - 18*x + 3364 - 71*x + 6*x**2 - 8*x**2 = 0. What is x?
58
Suppose 0 - 13/4*n**2 + 9*n + 1/4*n**3 = 0. What is n?
0, 4, 9
Let p(h) be the first derivative of -29/4*h**4 + 1/5*h**5 - 17 - 28*h + 29/2*h**2 + 9*h**3. Let p(b) = 0. Calculate b.
-1, 1, 28
Let z(v) be the second derivative of -3*v**5/20 + 143*v**4/4 - 280*v**3 + 834*v**2 - 7546*v. Factor z(h).
-3*(h - 139)*(h - 2)**2
Let 5*q**3 - 29*q + 1/2*q**4 + 6*q**2 + 35/2 = 0. What is q?
-7, -5, 1
Determine f so that 43*f**3 + 20*f**3 + 18 - 139*f**2 + 29*f**3 + 45*f**4 - 41*f**3 - 80*f**2 + 105*f = 0.
-3, -2/15, 1
Let r(l) be the third derivative of l**7/1260 - l**6/72 - 119*l**5/360 + 3091*l**2 - 2*l. Factor r(t).
t**2*(t - 17)*(t + 7)/6
Let i = 71611/60 + -5963/5. Let n(h) be the second derivative of -5/3*h**3 - 1/5*h**5 + i*h**4 - h + 3/2*h**2 + 0. Let n(t) = 0. Calculate t.
3/4, 1
Let f be (-40)/(-30) + ((-3)/(-6))/(3/(-6)). Factor 0 - f*y - 1/6*y**2.
-y*(y + 2)/6
Let g(o) be the first derivative of 5*o**3/3 - 315*o**2 - 5183. Factor g(i).
5*i*(i - 126)
Let s = -8/227 - -8455/1589. Let u be 6/49*630/135. Let 3*f**3 + u + s*f**2 + 4/7*f**4 + 24/7*f = 0. What is f?
-2, -1, -1/4
Let u(z) be the third derivative of -z