0 - 2*y**2/5 + 110*y + 126. Let d(j) be the first derivative of u(j). Factor d(n).
(n - 4)*(n + 1)**2/5
Let f = 27 - 14. Let i be -3 + 0 - (-4 + 8) - (-23 - -4). Factor l**3 + i*l**2 - l**4 - 24*l**2 + l - 2*l**3 + f*l**2.
-l*(l - 1)*(l + 1)**2
Let t(u) = 23*u**4 + 9*u**3 - 15*u**2 + 19*u - 8. Let l(d) = 12*d**4 + d**3 + d**2 + d - 1. Let g(i) = 4*l(i) - 2*t(i). What is r in g(r) = 0?
1, 2, 3
Let p = -3881/4 + 971. Let u(l) be the first derivative of 0*l + 9 - p*l**2 - 9/4*l**3. Factor u(t).
-3*t*(9*t + 2)/4
Let x(i) = 4*i**3 + 23*i**2 + 10*i - 21. Let h be x(-5). Let r(j) be the second derivative of 0 + 1/70*j**5 + 6*j + 1/14*j**h + 0*j**2 + 2/21*j**3. Factor r(q).
2*q*(q + 1)*(q + 2)/7
Let j be (335/35 + -9)/((-2)/(-7)). What is a in 267*a**2 - 263*a**j + 8*a + 4*a = 0?
-3, 0
Let q(d) be the second derivative of 2*d**7/63 + 2*d**6/3 - 283*d**5/60 + 65*d**4/6 - 19*d**3/2 + 1042*d. Determine m so that q(m) = 0.
-19, 0, 1, 3/2
Factor -392*i**2 + 13694*i - 34*i**3 - 9*i**3 - 14510*i + i**4.
i*(i - 51)*(i + 4)**2
Suppose -2*r - t + 10 = 0, -8 - 12 = -4*r - 4*t. Suppose 6 = 7*w - r*w. Factor 1 + 4*b**2 + 192*b**3 - 1 - 194*b**w - 2*b.
-2*b*(b - 1)**2
What is x in -199/3*x**2 - 196/3*x**3 + 4/3*x**4 + 0 - 50/3*x = 0?
-1/2, 0, 50
Find h such that 0 + 11616/7*h + 176/7*h**2 + 2/21*h**3 = 0.
-132, 0
Let q = 21249/8 + -2656. Let n(p) be the first derivative of -q*p**4 - 19 + p + 2/3*p**3 - 5/4*p**2. Suppose n(a) = 0. What is a?
1, 2
Let m(f) = -2*f**3 + f**2 + f + 1. Let z be m(-1). Suppose -12 = z*w - 4*t, -3*w - 4*t + 10 = -2. Factor w*x + 2*x + 35*x**3 + x + x + 24*x**2.
x*(5*x + 2)*(7*x + 2)
Let i(a) be the third derivative of -a**5/390 - 171*a**4/52 + 1030*a**3/39 + 4*a**2 + 20*a - 3. Factor i(f).
-2*(f - 2)*(f + 515)/13
Let x be 113/((-399)/35 - 180/(-75)) - -15. Solve -2/9*q**2 + 2/9 + 22/9*q - x*q**3 = 0.
-1, -1/11, 1
Let j = 32196/7 - 32184/7. Let j*k + 3/7*k**2 - 36/7 = 0. What is k?
-6, 2
Let n(r) = 47*r**2 - 4*r - 12. Let i(x) = -142*x**2 + 12*x + 33. Let f(z) = 4*i(z) + 11*n(z). Find k, given that f(k) = 0.
0, 4/51
Let b(z) be the third derivative of z**8/420 + 26*z**7/525 + 32*z**6/75 + 148*z**5/75 + 16*z**4/3 + 128*z**3/15 - 380*z**2. What is d in b(d) = 0?
-4, -2, -1
Let l(t) be the first derivative of t**5/10 - 43*t**4/8 - t**3/2 + 127*t**2/4 + 43*t - 1441. Find s such that l(s) = 0.
-1, 2, 43
Let x(o) = 376*o - 62413. Let t be x(166). Factor 11 + 5/2*d**t - 35/2*d - 26*d**2.
(d - 11)*(d + 1)*(5*d - 2)/2
Let l(u) be the third derivative of -2*u**7/105 - 31*u**6/30 - 197*u**5/15 - 305*u**4/6 - 92*u**3 - 2167*u**2. Factor l(t).
-4*(t + 1)**2*(t + 6)*(t + 23)
Factor -12/7*t**3 - 6/7*t**2 + 32/7*t + 24/7 + 2/7*t**4.
2*(t - 6)*(t - 2)*(t + 1)**2/7
Let s(b) be the third derivative of b**7/1260 - 7*b**6/720 + 11*b**5/360 - 5*b**4/144 + b**2 + 45. Factor s(q).
q*(q - 5)*(q - 1)**2/6
Suppose 12*p + 467 - 479 = 0. Suppose 233*t - 231*t - y + p = 0, 4*t + 12 = 4*y. Factor -5/8*h**t - 7/2*h + 3/2.
-(h + 6)*(5*h - 2)/8
Suppose 809 = 2837*t - 4865. Let 400/9 + 244/9*m**t + 4/9*m**4 + 80*m - 8*m**3 = 0. What is m?
-1, 10
Let k be ((-1872)/(-780))/(31/(-20) - -2). Let o = 21 - 19. Factor -32/9 + 2/9*j**3 - o*j**2 + k*j.
2*(j - 4)**2*(j - 1)/9
Factor 147*h**2 + 464572 - 30797 + 234497 - 27132*h + 554763 + 28913.
3*(7*h - 646)**2
Let k(j) be the second derivative of -1/25*j**5 + 0*j**2 - 4/15*j**3 + 1/75*j**6 + j + 39 - 7/30*j**4. Factor k(f).
2*f*(f - 4)*(f + 1)**2/5
Solve 120*u**3 - 203 + 135*u**2 + 63 + 4 + 17*u**3 - 137*u + 22*u**4 - 21*u**4 = 0.
-136, -1, 1
Let a(q) be the first derivative of -3*q**5/5 - 183*q**4/2 - 3957*q**3 - 21594*q**2 - 41772*q + 1280. Suppose a(r) = 0. What is r?
-59, -2
Suppose -r + 5 = y + 8, 33 = 4*y - 5*r. Factor -1/2*l**y + 3/2*l - 1.
-(l - 2)*(l - 1)/2
Let n(a) = a**3 + 324*a**2 - 337*a - 6. Let h(b) = 4*b**3 + 976*b**2 - 1012*b - 16. Let l(m) = 3*h(m) - 8*n(m). Factor l(c).
4*c*(c - 1)*(c + 85)
Let g(r) be the third derivative of r**6/60 - 13*r**5/10 + 30*r**4 + 400*r**3/3 - 123*r**2 - 17. Factor g(f).
2*(f - 20)**2*(f + 1)
Let j(c) be the second derivative of c**5/5 + 95*c**4/3 + 11*c + 176. Find x, given that j(x) = 0.
-95, 0
Let i = -469/6 - -235/3. Let w(m) be the first derivative of -i*m**4 - 2/15*m**5 - 2/27*m**3 - 1/27*m**6 + 0*m**2 + 24 + 0*m. Factor w(u).
-2*u**2*(u + 1)**3/9
Suppose 536/11 - 1571/11*q**3 - 358/11*q**4 - 2014/11*q**2 - 260/11*q - 5/11*q**5 = 0. What is q?
-67, -2, -1, 2/5
Let -211*w**3 - 169*w**2 - 2*w**4 + 137*w**3 - 7*w**4 - 20 - 124*w = 0. Calculate w.
-5, -2, -1, -2/9
Let i(o) be the second derivative of -5*o**7/112 + 253*o**6/240 - 1271*o**5/160 + 397*o**4/32 + 1561*o**3/24 + 49*o**2/2 - o + 1478. What is r in i(r) = 0?
-1, -2/15, 4, 7
Let z be 1 - (30/3)/(-5). Factor 28*b - 52*b + 35*b**2 - 56*b - 5*b**z + 60.
-5*(b - 3)*(b - 2)**2
Let i be 14/(84/(-7533)) + (-9 - -5). Let x = i + 1260. What is z in -3*z + 0 + x*z**4 + 0*z**3 - 7/2*z**2 = 0?
-2, -1, 0, 3
Let j(m) = m**3 - 2*m**2 + 14*m - 5. Let w be j(4). Determine y so that 3*y**3 - 1029*y**2 - 20 + w*y + 1053*y**2 - 20*y + 74 = 0.
-3, -2
Let t(l) be the first derivative of -l**5/270 + 11*l**4/108 - 10*l**3/27 - 28*l**2 + 39. Let x(u) be the second derivative of t(u). Factor x(v).
-2*(v - 10)*(v - 1)/9
Let a(p) be the second derivative of p**8/6720 + p**7/224 - p**6/80 - p**5/15 - 65*p**3/2 - 23*p. Let m(r) be the second derivative of a(r). Solve m(o) = 0.
-16, -1, 0, 2
Suppose 8 + 66 - 9 = 13*x. Let w(g) be the third derivative of 1/60*g**6 + 0*g**3 + 0*g**4 + 0*g**x + 23*g**2 + 0*g + 0. Suppose w(s) = 0. Calculate s.
0
Let i(v) be the first derivative of -2*v**5/85 + 9*v**4/34 - 32*v**3/51 - 36*v**2/17 + 160*v/17 - 270. Suppose i(f) = 0. What is f?
-2, 2, 4, 5
Let f(i) be the third derivative of -1/30*i**5 - i**3 + 0 + 2*i + i**2 + 1/3*i**4. Factor f(z).
-2*(z - 3)*(z - 1)
Suppose -2*b = f, 5*b - 60*f + 71*f + 34 = 0. Solve -7/4*q + q**b + q**3 + 1/2 = 0 for q.
-2, 1/2
Let z(c) be the third derivative of 5*c**8/14 - 41*c**7/42 - 5*c**6/6 + c**5 - 2174*c**2. Determine u so that z(u) = 0.
-2/3, 0, 3/8, 2
Factor 49 - z**2 - 245 - 22*z - 13*z.
-(z + 7)*(z + 28)
Determine h so that -6055 - 3717*h**2 - 9889*h**2 + 30123*h - 10634*h**2 - 5898*h + 20*h**3 = 0.
1/2, 1211
Let -39754*o**2 + 340 - 372*o - o**3 + 73*o + 40096*o**2 - 382*o = 0. Calculate o.
1, 340
Let u(c) be the first derivative of 0*c**4 + 7/540*c**6 + 14 + 0*c**3 + 1/135*c**5 + 0*c + 5/2*c**2. Let b(w) be the second derivative of u(w). Factor b(h).
2*h**2*(7*h + 2)/9
Let p = 1012 - 904. Find i such that -177*i**2 + 0 - 305*i - 123*i**4 - 60 - 268*i**2 - 215*i**3 + p*i**4 = 0.
-12, -1, -1/3
Let 8/3*l - 14/9*l**2 - 11/9*l**3 + 0 + 1/9*l**4 = 0. Calculate l.
-2, 0, 1, 12
Let l(c) = -8*c**3 - 251*c**2 + 818*c - 547. Let g(r) = -15*r**3 - 505*r**2 + 1635*r - 1095. Let s(k) = -3*g(k) + 5*l(k). Determine a so that s(a) = 0.
-55, 1, 2
Suppose 3*k - 84 = -4*k. Suppose 0*g + k = 3*g. Factor -5*z**3 - 7*z**3 - 3*z**2 - 5*z**2 - g*z**4.
-4*z**2*(z + 1)*(z + 2)
Let n(o) be the second derivative of -o**6/6 + 10*o**5 - 865*o**4/4 + 5680*o**3/3 - 4480*o**2 + 32*o - 1. Factor n(r).
-5*(r - 16)**2*(r - 7)*(r - 1)
Find z such that 4*z**5 + 132*z**4 - 128*z**3 - 140*z**3 - 528*z**2 - 1440*z + 172*z**3 - 18*z**3 + 458*z**3 = 0.
-30, -3, -2, 0, 2
Let v(w) be the third derivative of 9*w**8/448 - 181*w**7/35 + 767*w**6/96 + 401*w**5/120 - 10*w**4/3 + w**2 + 7*w + 4. Solve v(q) = 0 for q.
-1/3, 0, 2/9, 1, 160
Determine a so that -3*a**4 + 1295*a**3 + 431/3*a - 2587/3*a**2 + 0 = 0.
0, 1/3, 431
Let b = -11 - -21. Suppose b*l = 3*l + 252. Find m, given that 3*m**4 + 9 + 8*m**3 + 5*m**3 + 30*m + 3*m**3 + l*m**2 + 2*m**3 = 0.
-3, -1
Let g(k) be the third derivative of 0*k**4 - 177*k + k**2 + 0 + 0*k**3 - 2/5*k**5 + 1/30*k**6. Factor g(z).
4*z**2*(z - 6)
Let g(w) be the first derivative of -w**3/6 - 2*w**2 + 33*w/2 + 33. Factor g(u).
-(u - 3)*(u + 11)/2
Factor -2*d**2 + 15/2*d + 0 - 1/6*d**3.
-d*(d - 3)*(d + 15)/6
Let x = 265776 - 265776. Determine q, given that x + 2/15*q**2 - 26/5*q = 0.
0, 39
Determine r so that 2391*r**2 + 1774*r**2 - 12*r + 30*r**4 - 28*r**3 - 4539*r**2 + 144 = 0.
-3, -2/3, 3/5, 4
Let k(o) be the first derivative of -o**6/6 + 76*o**5/5 + 79*o**4/4 - 154*o**3/3 - 359. Factor k(g).
-g