derivative of 0 + 20*f**2 + 5/12*f**4 + 15*f + 5*f**3. Factor m(h).
5*(h + 2)*(h + 4)
Let g(f) be the first derivative of -4*f**5/15 - 32*f**4/3 + 512*f**3/9 + 4096*f**2 - 49152*f - 5527. Factor g(v).
-4*(v - 8)**2*(v + 24)**2/3
Suppose -42*n - 27593 - 20539 = 0. Let c = -10310/9 - n. Determine o, given that 1/3 + 1/9*o**2 + c*o = 0.
-3, -1
Let g = -4/1249037 - -14988512/21233629. Solve -16/17 + g*j - 6/17*j**3 + 22/17*j**2 = 0.
-1, 2/3, 4
Let n(b) = 59*b**3 - 310*b**2 - 24637*b - 93638. Let i(q) = -266*q**3 + 1240*q**2 + 98550*q + 374553. Let g(f) = 2*i(f) + 9*n(f). Factor g(k).
-(k + 4)*(k + 153)**2
Suppose -5*o - 17 = 5*k - 52, -o + 27 = 5*k. Solve 48*m**2 + 12*m + 28 - 46*m**o - 30*m = 0 for m.
2, 7
Let c(a) be the third derivative of 0*a - 1/450*a**6 + 0*a**4 - 26 + 0*a**3 - a**2 + 0*a**5 - 1/1575*a**7. Solve c(j) = 0.
-2, 0
Suppose -2*m - m - 2*f = -438, 0 = 2*m - 4*f - 276. Factor -4*o**3 + 14*o + 28*o - m + 8*o**2 + 13*o + 5*o.
-4*(o - 3)**2*(o + 4)
Let o be ((-207)/15 - 0) + 4/5. Let c = o + 17. What is m in m**5 - 146*m**c - 7*m**5 - 30*m**3 + 119*m**4 - 9*m**2 = 0?
-3, -1, -1/2, 0
Determine i, given that 315*i + 5338*i**2 + 5334*i**2 + 1782 + i**3 - 10668*i**2 - 2*i**3 = 0.
-9, 22
Let u(h) = -h**2 + 3*h - 1. Let r(g) = -26 + 40*g + 6 - 17 + 4*g**2 - 10*g**2 + 7. Let o(t) = -r(t) + 4*u(t). Factor o(v).
2*(v - 13)*(v - 1)
Let a(f) = 24*f - 10. Let x be a(-1). Let u be -2 - (25/70)/5*x. Suppose 9/7*m - u*m**2 + 3/7 - 9/7*m**3 = 0. What is m?
-1, -1/3, 1
Let y(z) be the third derivative of z**7/42 + z**6/6 - 39*z**5/4 - 2926*z**2. Determine q so that y(q) = 0.
-13, 0, 9
Let a = 104841 + -1362925/13. Let 4/13*r**2 + 8/13*r**3 - 10/13*r + 4/13 - a*r**4 + 2/13*r**5 = 0. What is r?
-1, 1, 2
Let q be -55*(-44)/1331 - 6/(-33). Factor 56/5*j**q + 32/5 + 2/5*j**4 + 72/5*j + 18/5*j**3.
2*(j + 1)*(j + 2)**2*(j + 4)/5
Suppose 0 = -238*x + 617*x. Let t(w) be the third derivative of 26*w**2 + 7/3*w**3 - 2/3*w**4 + 1/30*w**5 + 0 + x*w. Let t(d) = 0. What is d?
1, 7
Factor 272*y + 90830*y**2 + 1494 - 5*y - 3*y**3 - 91076*y**2.
-3*(y - 3)*(y + 2)*(y + 83)
Let m(o) be the second derivative of -1/4*o**4 - 14*o - 5 - 3*o**2 - 3/2*o**3. Factor m(d).
-3*(d + 1)*(d + 2)
Determine l, given that 1350*l**5 + 174*l**2 - 226*l**3 + 1356*l**5 + 50*l**4 - 2704*l**5 = 0.
-29, 0, 1, 3
Suppose -6/5*c**4 + 16/5*c + 0 + 4/5*c**3 - 2/5*c**5 + 24/5*c**2 = 0. What is c?
-2, -1, 0, 2
Determine p so that -57116*p + 47524/5 - 194026/5*p**3 + 1753/5*p**4 + 430333/5*p**2 - 4/5*p**5 = 0.
1/4, 1, 218
Let o(i) = 119*i**4 - 216*i**3 + 87*i**2 - 18 + 16*i**3 + 22 - 19*i. Let j(s) = 2*s**4 + s**2 + s - 1. Let y(r) = 6*j(r) + 2*o(r). Let y(a) = 0. What is a?
1/5, 1
Let a(r) = 47*r**3 - 17093*r**2 - 141211*r - 283211. Let u(i) = 150*i**3 - 54705*i**2 - 451875*i - 906275. Let y(g) = -35*a(g) + 11*u(g). Factor y(k).
5*(k - 708)*(k + 4)**2
Let j(p) = -33*p**4 + 48*p**3 + 4554*p**2 + 50529*p + 15. Let b(o) = -2*o**4 - 6*o**2 - o + 1. Let q(n) = -15*b(n) + j(n). Factor q(m).
-3*m*(m - 52)*(m + 18)**2
Factor -82*g - 16*g - 140*g + 47*g - 202 - 9*g + 2*g**2.
2*(g - 101)*(g + 1)
Let v(a) = -7*a**2 - 134*a - 591. Let n be v(-7). Find f, given that 5/3*f**3 + 4/3*f**4 - n - 31/3*f**2 - 56/3*f = 0.
-2, -1/4, 3
Let g be 28/(-378) + 110/27. Factor 15*s**3 - 3*s**4 + s**2 - 10*s**2 + 0*s + 12 - 15*s + 4*s**2 - g*s**2.
-3*(s - 4)*(s - 1)**2*(s + 1)
Let z = -184195 + 184200. Let -2/5*i**z + 0*i**3 + 0*i + 0*i**2 + 0 + 2/5*i**4 = 0. What is i?
0, 1
Let b(v) = -6*v**2 + 636*v - 899. Let s(p) = 2*p - 15. Let o(g) = b(g) - 5*s(g). Factor o(n).
-2*(n - 103)*(3*n - 4)
Suppose -5*i + 366 = 351. Let m(n) be the third derivative of 1/10*n**6 - 4*n**2 + 0 - 1/2*n**i + 0*n**5 + 0*n - 3/8*n**4. Determine d, given that m(d) = 0.
-1/2, 1
Let i be 330/(-15) - (-2 - (-2 - -6)). Let q(k) = -k**3 - 15*k**2 + 21*k + 83. Let l be q(i). Factor -3/2*c**2 + 9/8*c**l + 0 + 7/8*c**4 - 1/2*c.
c*(c - 1)*(c + 2)*(7*c + 2)/8
Let k(u) be the second derivative of -u**4/16 + 69*u**3/8 - 120*u**2 + u + 19. Factor k(x).
-3*(x - 64)*(x - 5)/4
Find x, given that 5*x**2 - 12*x + 93*x**4 - 290*x**4 + 98*x**4 + 94*x**4 + 15*x**3 - 3*x = 0.
-1, 0, 1, 3
Factor -52*t**2 + t**3 + 83 + 100*t - 26 - 30 - 27.
t*(t - 50)*(t - 2)
Let q(n) be the first derivative of -2187*n**6 + 324*n**5/5 + 26243*n**4/2 - 432*n**3 + 4*n**2 - 2420. Find i, given that q(i) = 0.
-2, 0, 1/81, 2
Let m = 70 - 70. Suppose m = u - 2*u, u + 620 = 4*f. Find d such that 114*d + 262*d**2 + 24 + 18*d**5 + 254*d**3 + f*d**4 - 41*d**4 + 14*d = 0.
-3, -1, -2/3
Let s(w) = 13*w**2 + 35*w - 35. Let p(o) = -6*o**2 - 17*o + 17. Let b(g) = -9*p(g) - 4*s(g). Let d be b(1). Factor 4/7*u - 10/7*u**d + 0.
-2*u*(5*u - 2)/7
Let f = 445 + -425. Suppose 3*h = 3*q + 4*h - 13, 5*q - 5*h - 15 = 0. Factor 16*d**2 - q*d - 16*d**3 - 65*d**3 + f*d**2.
-d*(9*d - 2)**2
Let y(m) be the second derivative of m**9/68040 - m**8/7560 + m**7/2835 - m**4/4 + m**3/6 + 33*m + 1. Let d(p) be the third derivative of y(p). Factor d(c).
2*c**2*(c - 2)**2/9
Let k(w) be the third derivative of 0*w - 40/3*w**3 - 1/15*w**5 + 9 + 1/30*w**6 + 8*w**2 - 8/3*w**4. Find u, given that k(u) = 0.
-2, 5
Let l(b) be the second derivative of -5*b**7/28 + 157*b**6/20 - 327*b**5/5 + 233*b**4 - 404*b**3 + 300*b**2 - 5452*b. Determine j so that l(j) = 0.
2/5, 2, 25
Let o(s) be the first derivative of s**3/18 - s**2/4 - 35*s/3 - 2454. Determine b, given that o(b) = 0.
-7, 10
Let f = -396030 - -3960301/10. Let j be 3 + -2 - (-1)/1. Suppose -f*s**j - 3/10 - 2/5*s = 0. What is s?
-3, -1
Solve 1/2*j**2 + 59/2 + 30*j = 0 for j.
-59, -1
Let v(w) = -11*w**2 + 31*w - 28. Suppose -2*c = p + 14, -5*p + 2*c = 4 + 6. Let z(b) = 13*b**2 - 32*b + 29. Let a(y) = p*z(y) - 5*v(y). Factor a(g).
3*(g - 8)*(g - 1)
Suppose 0 = -6*t - 101 + 110 + 183. Let d(x) be the first derivative of 0*x - t - 1/16*x**4 - 3/8*x**2 + 1/3*x**3. Let d(o) = 0. Calculate o.
0, 1, 3
Let z(s) be the second derivative of s**5/4 + 55*s**4/6 - 5*s**3/6 - 55*s**2 - 2375*s. Factor z(i).
5*(i - 1)*(i + 1)*(i + 22)
Factor -62/3 - 2/3*y**2 - 64/3*y.
-2*(y + 1)*(y + 31)/3
Let d be (-4)/14 + 4/14. Suppose 0 = x + 2*n - 465 + 437, x = 9*n - 126. Factor x*j + d - 2/13*j**2 + 2/13*j**3.
2*j**2*(j - 1)/13
Let n be 9/21 + (-72)/21 - -10. Factor -6 - n + 5 + t**2 - 9 + 1 + 15*t.
(t - 1)*(t + 16)
Let s(u) = 5*u**2 - 44*u - 7. Let f be (1440/384)/(10/24). Let q be s(f). Factor 10/9*y + 2/9*y**q + 0.
2*y*(y + 5)/9
Factor -45 + 13/2*c + 1/2*c**2.
(c - 5)*(c + 18)/2
Determine v so that 2/19*v**3 - 34/19 - 2*v**2 + 70/19*v = 0.
1, 17
Let o(w) be the first derivative of -w**4/4 - 30*w**3 - 1350*w**2 + 44*w - 16. Let n(m) be the first derivative of o(m). Let n(g) = 0. Calculate g.
-30
Let x(a) be the second derivative of a**4/4 + 149*a**3/14 + 9*a**2 - 1229*a. Solve x(d) = 0 for d.
-21, -2/7
Let z(o) = 4*o + 6*o - 4*o - 21 - o. Let m be z(5). Let -a + 21*a**3 + 4*a**5 - 16*a**2 - 15*a + 16*a**m - 9*a**3 = 0. What is a?
-2, -1, 0, 1
Factor 2/7*t**4 + 0*t + 0*t**2 - 556/7*t**3 + 0.
2*t**3*(t - 278)/7
Let o(g) be the third derivative of 0*g**6 + 1/30*g**5 - 1/735*g**7 + 13 + 0*g**3 + 6*g**2 + 0*g + 1/14*g**4. Find m such that o(m) = 0.
-2, -1, 0, 3
Suppose 5*f - 9*m + 7*m - 201 = 0, -154 = -4*f + 5*m. Factor 19*r**3 + 7*r**4 + 108*r**2 + r**4 + 52*r - 4*r**4 + f*r**3.
4*r*(r + 1)**2*(r + 13)
Let c(w) = -w**3 + 2*w**2 - 2*w - 3. Let b be c(-2). Suppose -2*r = 11 - b. Factor 19*u + 4*u**4 + 20*u**3 - 8*u**2 + 40*u**2 - r*u.
4*u*(u + 1)*(u + 2)**2
Factor 31*x - 1470 - 5*x**2 + 123*x - 329*x.
-5*(x + 14)*(x + 21)
Let z = 1641060 - 8205268/5. Solve 0 - 24/5*i**2 + 0*i - 14/5*i**4 - z*i**3 - 2/5*i**5 = 0 for i.
-3, -2, 0
Suppose d - 3*x = -14, -10*d - x = -7*d + 22. Let r be 3*(1 + d/9). Factor -w + 6 - r*w**4 + 7/3*w**3 - 13/3*w**2.
-(w - 3)**2*(w - 2)*(w + 1)/3
Let s be 0/((-91)/((-3367)/222)). Factor 0 + s*w - 8/7*w**2 - 15/7*w**3 - 6/7*w**4 + 1/7*w**5.
w**2*(w - 8)*(w + 1)**2/7
Let j(i) be the first derivative of 29*i**3/12 - 11*i**2/4 - 3299. Factor j(q).
q*(29*q - 22)/4
Let s(p) be the second derivative of p**6/15 - p**5/2 - 11*p**4/3 - 16*p**3/3 + 269*p - 2. Factor s(g).
2*g*(g - 8)*(g + 1)*(g + 2)
Suppose -41*y = -46*y - 160. Let m be ((-30)/y)/((-18)/(-24)). Suppose 0*r**2 + 15/2 - 35/4*r + m*r**3 