t k(u) = -4*u**3 - 3*u**2 - 17*u + 9. Let f(l) = -l**3 - l**2 - 4*l + 2. Let d be 13/(-7) + (-6)/42. Let m(r) = d*k(r) + 9*f(r). Factor m(b).
-b*(b + 1)*(b + 2)
Let w(v) be the first derivative of -v**3 - 9*v**2/2 + 714*v + 2030. Let w(h) = 0. What is h?
-17, 14
Factor -24 + 2/5*t**2 - 56/5*t.
2*(t - 30)*(t + 2)/5
Determine u, given that -549*u**3 - 399*u + 741*u**2 + 113*u**4 - 2*u**4 + 24*u**5 + 2510 - 2438 = 0.
-8, 3/8, 1
Suppose -282*i + 8 = -280*i. Find w, given that 35*w**i - 11*w**4 + 16*w**3 - 18 - 16*w**4 - 44*w**2 + 48*w - 10*w**4 = 0.
1, 3
Let g be 4 + (50519/(-42))/((-6)/16). Let l = g + -3208. Find b, given that 4/9*b**2 - l*b - 4 = 0.
-1, 9
Suppose 12 + 12*a**4 + 6*a - 27*a**2 + 9/2*a**5 - 15/2*a**3 = 0. Calculate a.
-2, -2/3, 1
Factor 28*q**2 - 64*q + 100/3 + 8/3*q**3.
4*(q - 1)**2*(2*q + 25)/3
Let u = -183/7412 + 30563/37060. Factor 1/5*j**2 - u*j - 32/5.
(j - 8)*(j + 4)/5
Let g(o) be the third derivative of -o**6/420 - 87*o**5/70 - 65*o**4/21 + 4662*o**2. Factor g(a).
-2*a*(a + 1)*(a + 260)/7
Let v = -28106 + 28128. Let l(a) be the first derivative of a**3 + 0*a - 5/2*a**6 + 0*a**2 + v + 15/4*a**4 - 3/5*a**5. Suppose l(s) = 0. Calculate s.
-1, -1/5, 0, 1
Let y(n) be the third derivative of n**5/100 - 67*n**4/20 - 27*n**3/2 + 7*n**2 + 91*n. What is f in y(f) = 0?
-1, 135
Let x(s) be the third derivative of s**7/1470 + 19*s**6/280 - 22*s**5/21 + 22*s**4/7 + 512*s**3/21 + 11874*s**2. Determine w, given that x(w) = 0.
-64, -1, 4
Let v(r) be the third derivative of 0 + 242/27*r**3 - 1/270*r**6 + 23/135*r**5 - 143/54*r**4 + 0*r - r**2. Factor v(f).
-4*(f - 11)**2*(f - 1)/9
Let o(m) be the third derivative of -m**6/180 + 134*m**5/45 - 18221*m**4/36 + 35378*m**3/9 - 110*m**2 - m. Factor o(b).
-2*(b - 133)**2*(b - 2)/3
Factor 0 - 2532/5*s**2 - 96/5*s + 318/5*s**3.
6*s*(s - 8)*(53*s + 2)/5
Suppose -289 + 573 = 441*b + 284. Factor -6*d + b - 7/3*d**2.
-d*(7*d + 18)/3
Let k be (-291)/(-1649) + (-207)/(-2295). Find s, given that 0*s + 0 - 2/15*s**3 - k*s**2 = 0.
-2, 0
Factor -86811*s**2 - 76137*s**2 + 4*s**5 + 320132*s - 1316*s**4 - 159796*s**2 + 110200*s**3 - 106276.
4*(s - 163)**2*(s - 1)**3
Let j(a) be the third derivative of 0*a + 1/60*a**5 - 7/3*a**3 - 85*a**2 - 13/24*a**4 + 0. Suppose j(l) = 0. Calculate l.
-1, 14
Let u(v) be the first derivative of v**7/168 - 35*v**6/72 + 323*v**5/24 - 1445*v**4/24 - 56*v**3/3 - 65. Let l(j) be the third derivative of u(j). Factor l(m).
5*(m - 17)**2*(m - 1)
Suppose -t = 4*t - 80. Let z = -14 + t. Factor 7 - 39*n**z - 25*n**2 - 16*n - 9 + 1.
-(8*n + 1)**2
Let o be (-66)/(-360)*62/682. Let l(p) be the second derivative of p**3 - 17*p + 1/12*p**4 + 0 - 3/40*p**5 - o*p**6 + 2*p**2. Determine i so that l(i) = 0.
-2, -1, 2
Suppose 52*k = 43*k + 603. Solve 15*t**5 + 10*t**2 - 34*t**3 - 35*t**3 - 34*t**4 + 9*t**5 + 2*t + k*t**3 = 0.
-1/3, -1/4, 0, 1
Let w(a) be the second derivative of 1/22*a**4 - 7*a + 3 - 6/11*a**2 + 7/33*a**3. Determine k so that w(k) = 0.
-3, 2/3
Let t = -209 - -217. Find j, given that -9*j**2 - 1 + t*j + 2*j**3 + 1 + j**2 = 0.
0, 2
Let y be 26/(-30) + 1 - 1467/(-135). What is v in -7*v - 4*v**3 - 9*v**2 + 0*v - y*v**2 + 36 - 5*v = 0?
-3, 1
What is z in 635/3*z + 1/3*z**2 + 634/3 = 0?
-634, -1
Let p be 0*(21/14 - 1). Let q be (8*39/416)/(p + 1). Let -27/4*f**3 - 3/2*f + 15/4*f**4 - q*f**5 + 21/4*f**2 + 0 = 0. Calculate f.
0, 1, 2
Let o be 2/(-7) - (1148/(-1722))/((-7)/(-3)). What is p in -16/3*p**3 + 4*p**5 - 8/3*p**4 + 8/3*p**2 + 4/3*p + o = 0?
-1, -1/3, 0, 1
Let i = -5/17202 - -30583/5734. Factor 2/3*p**2 + 32/3 + i*p.
2*(p + 4)**2/3
Let v(b) be the third derivative of -7*b**6/600 + 43*b**5/300 - 23*b**4/40 + 3*b**3/10 + 24*b**2 + 80*b. Factor v(q).
-(q - 3)**2*(7*q - 1)/5
Let u(f) be the third derivative of -f**6/480 - 11*f**5/240 - 19*f**4/96 - 3*f**3/8 - 4*f**2 - 73. Factor u(g).
-(g + 1)**2*(g + 9)/4
Let k(c) be the first derivative of -c**4/6 + 122*c**3/9 - 369*c**2 + 3402*c - 159. Find h such that k(h) = 0.
7, 27
Let c(t) = -26*t**4 + 12*t**3 - 118*t**2 + 87*t + 234. Let x(h) = -3*h**4 - h**3 + h**2. Let j(v) = -c(v) + 9*x(v). What is o in j(o) = 0?
-26, -1, 3
Let b be 60/18*3 + -10. Let a be ((-112)/(-35) - -1) + b. Find s, given that 27/5*s**2 + 6/5 + 3/5*s**4 + 3*s**3 + a*s = 0.
-2, -1
Let b = 229 - 40. Factor 157*n + 256 - b*n + 6*n**2 - 5*n**2.
(n - 16)**2
Let r(k) = -21*k**4 - 19*k**3 + 428*k**2 - 1988*k + 4. Let a(d) = -5*d**4 - d**3 - d**2 - d + 1. Let v(q) = -4*a(q) + r(q). What is s in v(s) = 0?
-31, 0, 8
Factor 74 + 87*q + 86 - 100 + 4*q**3 - q**3 + 14*q**2 + 16*q**2.
3*(q + 1)*(q + 4)*(q + 5)
Let v(h) be the first derivative of 3/4*h**3 - 107 + 3/2*h**2 - h - 7/16*h**4. Factor v(t).
-(t - 2)*(t + 1)*(7*t - 2)/4
Let i(m) = 3*m**4 + 64*m**3 - 144*m**2 - 592*m + 1539. Let z(n) = -3*n**4 + n**3 - n. Let s(j) = -i(j) - 2*z(j). Determine d, given that s(d) = 0.
-3, 3, 19
Let m(z) be the third derivative of -1058/3*z**3 + 61*z**2 + 0 + 23/3*z**4 + 0*z - 1/15*z**5. Suppose m(f) = 0. Calculate f.
23
Let g(f) be the third derivative of f**6/156 - f**5/10 - 6*f**4/13 + 252*f**3/13 - 4511*f**2. Suppose g(j) = 0. What is j?
-21/5, 6
Suppose -449*b = 127*b - 2880. Factor b + 17/3*v + 1/3*v**2 - 1/3*v**3.
-(v - 5)*(v + 1)*(v + 3)/3
Let f(r) be the third derivative of -1/108*r**6 - r**2 + 1/30*r**5 + 1/945*r**7 + 2*r - 7/108*r**4 + 2/27*r**3 + 0. Determine w so that f(w) = 0.
1, 2
Suppose -52*r + 53*r + 19 = 0, -2*l - r - 13 = 0. Factor 5/2*s**l + 15/2*s**2 + 0*s + 0.
5*s**2*(s + 3)/2
Let c(l) be the first derivative of 2*l**6/3 - 1436*l**5/5 - 360*l**4 + 2954. What is z in c(z) = 0?
-1, 0, 360
Let n be 65/(-150) - (-16)/120. Let u = 1/2 - n. Factor 2/5*v**5 - 2/5*v + 0 + u*v**2 + 0*v**3 - 4/5*v**4.
2*v*(v - 1)**3*(v + 1)/5
Let f = 5/1801 - -435817/9005. Let n = f - 46. Factor 0*l**2 - 6/5*l**4 - 12/5*l**3 + n*l + 6/5.
-6*(l - 1)*(l + 1)**3/5
Let s(d) = d**2 + 56458*d + 508044. Let n be s(-9). Factor -2288/7*x - 200/7*x**2 - 4/7*x**n + 5408/7.
-4*(x - 2)*(x + 26)**2/7
Suppose 2*o - 16 = -3*s - 3, -5*o - s + 13 = 0. Let m be 5 - (-198)/(-51) - (o - 1). Factor -2/17*w**2 + 0 - m*w**3 + 0*w.
-2*w**2*(w + 1)/17
Let d(f) be the second derivative of f**5/480 - 25*f**4/192 - 16*f**2 - 5*f. Let b(z) be the first derivative of d(z). Factor b(a).
a*(a - 25)/8
Let i(t) = -7*t + 9. Let p be i(-3). Let y be 5/(-35)*(-105)/p. Factor -2*s + 2 + 1/2*s**3 - y*s**2.
(s - 2)*(s - 1)*(s + 2)/2
Let g(q) = 23*q**2 - 1470*q - 338. Let j(f) = 45*f**2 - 2942*f - 662. Let k(p) = 5*g(p) - 3*j(p). Find y, given that k(y) = 0.
-1/5, 74
Suppose 0 = 7*y - 67 - 108. Factor -y*c**3 - 20*c**4 - 5*c**5 - 3*c**2 - 3*c**2 - 4*c**2.
-5*c**2*(c + 1)**2*(c + 2)
Let s(f) be the first derivative of 22/7*f**3 + 40/7*f + 8*f**2 - 9/14*f**4 + 62. Factor s(x).
-2*(x - 5)*(3*x + 2)**2/7
Let c be ((-9)/(-28))/(((-2)/(-24))/(-28 + (-9144)/(-324))). Factor c*g**2 - 6/7 + 9/7*g.
3*(g + 2)*(2*g - 1)/7
Let s(v) = 3*v**5 - v**4 + v**3 + v**2 + v - 2. Let d(t) = 4*t**5 - t**4 - 2*t**3 + 3*t**2 + t - 2. Let b(a) = d(a) - s(a). Let b(y) = 0. Calculate y.
-2, 0, 1
Let h be 110/25 + ((-24)/10)/6. Factor -667*y**h + 657*y**4 + 11*y**2 + 2*y**5 - y**2 + 6*y**3 - 8*y.
2*y*(y - 4)*(y - 1)**2*(y + 1)
Let f = 20991 - 20987. Find n such that -2*n + 10/3*n**3 - f*n**2 + 8/3 = 0.
-4/5, 1
Let u(t) be the first derivative of t**6/6 + 4*t**5/5 - 21*t**4/4 - 2601. Let u(y) = 0. Calculate y.
-7, 0, 3
Suppose 21*d + 19*d - 57*d = -34. Let t(h) be the first derivative of -7/4*h**3 - 6 - 1/16*h**4 - 343/4*h - 147/8*h**d. Factor t(y).
-(y + 7)**3/4
Suppose -7*t - 1 = -36. Suppose 34*k = 39*k - t. Factor -3*w**2 - 38 - 35 - k - 30*w - 1.
-3*(w + 5)**2
Let x(h) be the third derivative of 0*h**4 - 6 + 4*h**2 + 0*h**3 + 2/3*h**6 - 3/14*h**7 + 1/3*h**5 + 0*h. Find t such that x(t) = 0.
-2/9, 0, 2
Let i(a) be the first derivative of a**4 + 680*a**3/3 + 14450*a**2 - 4593. Let i(m) = 0. Calculate m.
-85, 0
Let j be -4 + 3038/462 + 2/(198/9). Find g such that 0 - 7/3*g - 1/3*g**3 - j*g**2 = 0.
-7, -1, 0
Let c = -321861/7 - -45981. Factor -c - 3/7*v**2 + 9/7*v.
-3*(v - 2)*(v - 1)/7
Let f(l) be the third derivative of 19*l**2 - 1/40*l**5 - 1/4*l**3 + 0*l + 0 + 11/96*l**4 + 1/480*l**6. Find w, given that f(w) = 0.
1, 2, 3
Let i(p) be the third derivative of p**6/1