d j, given that -106*j + 56*j**2 + 304 - 13*j - 156*j + 4*j**3 - 89*j = 0.
-19, 1, 4
Let j(d) be the first derivative of 46 + 31/4*d**2 + 0*d + 1/10*d**5 - 1/6*d**3 - 31/8*d**4. Factor j(o).
o*(o - 31)*(o - 1)*(o + 1)/2
Let l(s) = s**2 - 13*s + 19. Let z be l(10). Let n(v) = 5*v**2 + 35*v - 11. Let b(d) = 12*d - 42 + 71 - 33 + 2*d**2. Let a(h) = z*b(h) + 4*n(h). Solve a(q) = 0.
0, 4
Let a = 11581 - 11576. Let f(l) be the first derivative of 5/8*l**4 - 19 - a*l**3 + 25/4*l**2 + 0*l. Factor f(y).
5*y*(y - 5)*(y - 1)/2
Let c(q) be the first derivative of -7*q**6/450 - 8*q**5/75 - 2*q**4/15 - 2*q**3/3 - 6*q - 79. Let h(i) be the third derivative of c(i). Factor h(k).
-4*(k + 2)*(7*k + 2)/5
Factor 5/2*n**3 + 0 + 42250*n + 650*n**2.
5*n*(n + 130)**2/2
What is y in -141 + 69*y + 3/4*y**2 = 0?
-94, 2
Let f be ((-9)/(-6))/(((-84)/40)/(-7)). Factor 46*l**f + l - 20*l**5 - 25*l**5 - 2*l**3.
l*(l - 1)**2*(l + 1)**2
Let n(d) be the second derivative of -2*d**6/15 - 4*d**5/5 + 11*d**4/3 + 20*d**3 - 2725*d. Solve n(g) = 0 for g.
-5, -2, 0, 3
Let v(d) be the first derivative of 10*d**2 - 5/4*d**4 - 152 + 0*d**3 + 0*d. Factor v(a).
-5*a*(a - 2)*(a + 2)
Let s = 775 - 771. Let k be (5 - (-801)/(-162))*s. Factor -2/9*g**2 + 2/9 - 2/9*g + k*g**3.
2*(g - 1)**2*(g + 1)/9
Let j(a) be the first derivative of 1/60*a**6 + 4*a**2 + 21*a + 35 - 8/3*a**3 - 1/5*a**5 + a**4. Let m(b) be the first derivative of j(b). Factor m(f).
(f - 2)**4/2
Suppose -8*d + 5 = -2*q - 9*d, -q - 5*d = 25. Let y(p) be the second derivative of -36/11*p**2 - 1/66*p**4 + 4/11*p**3 - p + q. Factor y(s).
-2*(s - 6)**2/11
Let o(q) be the second derivative of q**6/60 + 39*q**5/80 - 19*q**4/8 - 85*q**3/24 + 33*q**2/4 + 51*q - 19. Suppose o(u) = 0. What is u?
-22, -1, 1/2, 3
Let t be (-2)/(-6)*(-165)/(-110). Let v(g) be the first derivative of 9 + 1/9*g**3 + t*g**2 - 2/3*g - 1/4*g**4 + 1/15*g**5. Suppose v(f) = 0. Calculate f.
-1, 1, 2
Let z = 392219 - 392215. Factor 4/5*s**z + 0 + 0*s - 8/5*s**3 + 0*s**2.
4*s**3*(s - 2)/5
Let n = -13539 + 13539. Let f(p) be the second derivative of 0*p**2 + 0*p**4 - 19*p - 3/5*p**5 + 0*p**3 + n + 8/15*p**6 - 2/21*p**7. Find r such that f(r) = 0.
0, 1, 3
Suppose 0 = -4*u - 0*u - 3*h + 254, 5*h = u - 75. Let k = 68 - u. Factor -4*o**4 - 12 + 8*o - o**2 + 17*o**2 + 0*o**4 - 8*o**k.
-4*(o - 1)**2*(o + 1)*(o + 3)
Let m(x) be the first derivative of 2*x**5/85 - 30*x**4/17 + 900*x**3/17 - 13500*x**2/17 + 101250*x/17 + 2648. Determine k so that m(k) = 0.
15
Factor -380/11 + 2/11*x**2 - 378/11*x.
2*(x - 190)*(x + 1)/11
Let w = 4171792/18513 + -25280/121. Let a = 152/9 - w. Factor -2/17*l + a*l**2 - 6/17*l**3 + 0.
-2*l*(l - 1)*(3*l - 1)/17
Let o(l) = -3*l**2 - 45*l - 150. Let k(r) = -3*r**2 - 46*r - 151. Let n = 339 + -343. Let c(h) = n*o(h) + 3*k(h). Find a such that c(a) = 0.
-7
Let j(n) be the third derivative of n**6/600 - 16*n**5/75 + 221*n**4/30 + 2312*n**3/15 - 2*n**2 + 91. Factor j(c).
(c - 34)**2*(c + 4)/5
Factor -98*d**4 - 81*d**2 + 97*d**3 + 10*d**4 - 11*d**2 - 2*d**5 + 85*d**3.
-2*d**2*(d - 1)**2*(d + 46)
Let m(r) be the second derivative of 1/150*r**5 + 28*r + 1/30*r**4 + 0*r**3 + 0 - 9/2*r**2. Let b(h) be the first derivative of m(h). Factor b(j).
2*j*(j + 2)/5
Let h(z) be the third derivative of -z**6/480 - z**5/20 + 3*z**4/8 + 14*z**3/3 - 88*z**2 + 3*z. Solve h(k) = 0.
-14, -2, 4
Let o(v) be the third derivative of -7*v**6/660 - 19*v**5/55 - 8*v**4/33 + 889*v**2. Factor o(s).
-2*s*(s + 16)*(7*s + 2)/11
Let g = 18431/4 + -4607. Let n(t) be the first derivative of 4*t**3 + 0*t - 9 - g*t**4 - 6*t**2. Factor n(o).
-3*o*(o - 2)**2
Suppose 0 = -23*b + 21*b + 5*s - 5, 0 = -6*b - 3*s + 39. Let o(i) be the first derivative of -4/9*i**3 + b + 16/3*i + 0*i**2. Factor o(d).
-4*(d - 2)*(d + 2)/3
Suppose 0*v - 4*v + 5 = -u, 2*v = 4. Suppose u*c + 3 = 9. Factor 2*b**2 - b**4 - 3*b**4 + b**4 + b**c.
-3*b**2*(b - 1)*(b + 1)
Let a(s) be the first derivative of -s**4 + 32/3*s**3 + 0*s - 32*s**2 - 44. Factor a(v).
-4*v*(v - 4)**2
Let t(y) = -47*y**2 + 386*y + 11. Let k(i) = -81*i + 9 - 11 + 9*i**2 + 4*i. Let h(z) = -11*k(z) - 2*t(z). Factor h(r).
-5*r*(r - 15)
Let o(l) be the third derivative of -l**5/60 - 9*l**4/4 + 55*l**3/6 + 8*l**2 - 36*l. Factor o(a).
-(a - 1)*(a + 55)
Suppose -5*s = 4*s - 45. Factor -4*r + 4*r**2 + r - s*r**2 - 3*r.
-r*(r + 6)
Factor -1/8*k**4 + 0*k - 15/8*k**3 + 0 - 13/4*k**2.
-k**2*(k + 2)*(k + 13)/8
Suppose -1158 = -5*c + 2*c. Suppose -11*i + 14*i - 3*u = 21, 3*i = -u + 5. Solve -15*o**2 + 386*o - o**i - 2*o**3 - c*o = 0.
-5, 0
Let k(m) = 5*m**2 + 39*m + 34. Let q(j) be the second derivative of -j**4/2 - 19*j**3/3 - 16*j**2 - 289*j. Let d(z) = -6*k(z) - 7*q(z). Factor d(t).
4*(t + 1)*(3*t + 5)
Let g be (1/(-10)*4)/((-1)/(-25)). Let z be 1/(-2) - 5/g. Solve 7*p**3 - p**2 - 4 + 0*p**3 + 5*p**4 + z*p**5 + 0 - 8*p + p**5 = 0 for p.
-2, -1, 1
Let g(t) be the second derivative of 2*t**5/45 - 7*t**4/6 - 19*t**3/27 + 16*t**2/3 - 2038*t. Suppose g(v) = 0. What is v?
-1, 3/4, 16
Let s(j) be the second derivative of j**5/4 + 10915*j**4/12 + 5962315*j**3/6 + 5951405*j**2/2 + 997*j. Factor s(m).
5*(m + 1)*(m + 1091)**2
Suppose 4*g - 161 = 107. Let 42*r - 22 - g + 3*r**2 + 128 = 0. What is r?
-13, -1
Let f = 36908 + -848876/23. Factor -2/23*t**2 + 0 - f*t.
-2*t*(t + 4)/23
Let n(k) = 5*k**4 - 280*k**3 + 489*k**2 + 798*k - 24. Let t(m) = 2*m**4 - 112*m**3 + 195*m**2 + 319*m - 10. Let h(p) = -5*n(p) + 12*t(p). Factor h(y).
-y*(y - 54)*(y - 3)*(y + 1)
Let w = 838 - 836. Suppose q - 3*d - 3 = -4*d, -q + w*d = 0. Factor -4/7*y**q - 88/7*y - 484/7.
-4*(y + 11)**2/7
Let y be (-13)/((-104)/64) + (-6 - -2). Determine l so that 248*l - 256*l**3 - y*l**5 - 248*l + 64*l**4 = 0.
0, 8
Let d = 395563 + -70014443/177. Let x = -30/59 + d. Find w, given that -x*w**2 - 4/3 - 2*w = 0.
-2, -1
Let x(q) = -2*q + 3*q - 2*q**2 + 9 + 0*q - q**3 - 10 + 0*q. Let g(a) = 5*a**4 + 16*a**3 + 12*a**2 - 4*a + 4. Let j(z) = -g(z) - 4*x(z). Factor j(b).
-b**2*(b + 2)*(5*b + 2)
Let c be (366/48)/(5 + 11598/(-2316)). Let w = -981 - c. Factor 4/3*y**2 + w*y**4 + 0 + 0*y + 2/3*y**3.
y**2*(y + 4)**2/12
Factor 77618/7 + 788/7*v + 2/7*v**2.
2*(v + 197)**2/7
Solve -464/5*m - 44/5*m**3 + 304/5 + 48*m**2 + 1/5*m**4 = 0 for m.
2, 38
Let m(f) be the second derivative of f**5/25 + 77*f**4/15 + 278*f**3/3 + 670*f**2 - 257*f + 1. Let m(t) = 0. Calculate t.
-67, -5
Factor 78/5 - 1/5*s**3 + 39/10*s**2 + 166/5*s.
-(s - 26)*(s + 6)*(2*s + 1)/10
Factor -2/19*u**2 + 154/19 - 8*u.
-2*(u - 1)*(u + 77)/19
Let s = -385 - -519. Suppose -4*j**2 + 6 - 14*j + s*j - 146 - 11*j**2 - 5*j**3 = 0. Calculate j.
-7, 2
Determine f so that -249*f**2 - 273*f - 157*f + 430*f**3 + 276 + 122 - 5*f**4 - 171*f**2 + 27 = 0.
-1, 1, 85
Let m(l) be the third derivative of 1/70*l**7 + 1/20*l**5 + 0*l**4 + 0*l + 1/20*l**6 + 44 + 0*l**3 + 3*l**2. Factor m(j).
3*j**2*(j + 1)**2
Suppose 2*k + 2 = -9*s + 10*s, 2*k = 4*s + 22. Let v(h) = -9*h**2 - 9*h - 3. Let t(o) = -23*o**2 - 28*o - 8. Let a(d) = s*v(d) + 3*t(d). Solve a(c) = 0 for c.
0, 4
Let l(s) be the first derivative of s**3/3 + 4*s**2 + 19. Determine t, given that l(t) = 0.
-8, 0
Let x = -359 - -356. Let o(q) = q**4 - q + 2. Let z(s) = 8*s**4 + 8*s**3 + 18*s**2 + 9*s + 19. Let b(i) = x*z(i) + 21*o(i). Factor b(w).
-3*(w + 1)**3*(w + 5)
Let m(p) be the first derivative of -5*p**3/3 - 765*p**2/2 - 760*p - 1453. Factor m(u).
-5*(u + 1)*(u + 152)
Let t(u) be the third derivative of -u**7/6300 + u**6/1350 - u**5/900 + 25*u**3/2 + 12*u**2. Let v(j) be the first derivative of t(j). Factor v(a).
-2*a*(a - 1)**2/15
Factor 148*x + 410*x**2 - 5*x**4 + 1190*x**3 - 1065*x**3 + 9*x + 123*x.
-5*x*(x - 28)*(x + 1)*(x + 2)
Let x = 100166 - 100166. Factor 8*r + x - 2/3*r**2.
-2*r*(r - 12)/3
Let x(m) be the third derivative of -3 + 3/40*m**6 - 1/112*m**8 - 1/20*m**5 + 0*m**3 + 1/70*m**7 - m**2 + 0*m - 1/4*m**4. Solve x(g) = 0.
-1, 0, 1, 2
Let o(j) = -6*j**3 - j**2 - j + 1. Let f(h) = 5*h**3 + 185*h**2 + 390*h + 175. Let a(x) = -f(x) - 5*o(x). Let a(b) = 0. What is b?
-1, -4/5, 9
Let w(a) = -a**2 - 17*a + 114. Let q(d) = d - 8. Let p be q(13). Let b be w(p). Factor 1/9*i**5 + 0*i**2 + 0*i - 2/3*i**3 - 5/9*i**b + 0.
i**3*(i - 6)*(i + 1)/9
Factor -3/7*s + 3/7*s**2 - 36/7.
3*(s - 4)*(s + 3)/7
Let n(u) be the second deriv