6)
Let t(a) be the first derivative of 5/6*a**3 + 16 - 2*a + 2*a**2. Solve t(n) = 0 for n.
-2, 2/5
Let n = -492 + 498. Let m(w) be the first derivative of 1/24*w**n + 1/8*w**2 + 1/5*w**5 + 0*w + 3/8*w**4 + 6 + 1/3*w**3. Factor m(q).
q*(q + 1)**4/4
What is i in 0 + 32/3*i**2 - 4/3*i**5 + 28/3*i - 32/3*i**4 - 8*i**3 = 0?
-7, -1, 0, 1
Suppose 33*q - 50 = 8*q. Let s(x) be the third derivative of -1/12*x**3 + 1/32*x**4 + 0 - 1/240*x**5 + 3*x**q + 0*x. Find r such that s(r) = 0.
1, 2
What is q in -12/11 - 20/11*q - 9/11*q**2 - 1/11*q**3 = 0?
-6, -2, -1
Factor 13 + 3 + 98*s**3 - 12*s**2 - 45*s**3 - 49*s**3.
4*(s - 2)**2*(s + 1)
Let w(i) be the first derivative of -i**6/12 + i**5/5 + 3*i**4/4 - 2*i**3/3 - 13*i**2/4 - 3*i + 149. Determine r so that w(r) = 0.
-1, 2, 3
Let u be (-65)/(-140) + 28/98. Let 0*v + 9/8*v**3 + 3/8*v**4 + 0 + u*v**2 = 0. What is v?
-2, -1, 0
Suppose 8*o = 4*o + 12. Factor 30*a**3 + 26*a**3 - 53*a**o.
3*a**3
Let r(i) be the third derivative of -i**4/8 - i**3/6 + 10*i**2. Let f be r(-1). Factor -24*n**f + 8 - 20*n + 14*n**2 - 18*n**2.
-4*(n + 1)*(7*n - 2)
Factor 1/3*z**3 + 4/3*z**2 + 2 - 11/3*z.
(z - 1)**2*(z + 6)/3
Factor 100*t**3 - t**5 + t**4 - 4*t - 97*t**3 - t**4 + 4*t**2 - 2*t**4.
-t*(t - 1)**2*(t + 2)**2
Let f be (-6)/4 + (-4)/(-2). Let i(y) = 24*y - 118. Let d be i(5). Factor -1/4*x**d - f + 3/4*x.
-(x - 2)*(x - 1)/4
Let b(l) = 16*l**2 - 310*l + 4805. Let t(j) = 3*j**2 - 62*j + 961. Let m(w) = -2*b(w) + 11*t(w). Factor m(p).
(p - 31)**2
Let g(i) be the first derivative of 1/10*i**5 - 4 - 1/3*i**3 + 4*i + 0*i**2 + 0*i**4. Let c(w) be the first derivative of g(w). Let c(z) = 0. Calculate z.
-1, 0, 1
Let r be ((-2)/10)/(4/(-24)). Let p = -583/5 + 117. Suppose 0 - p*j - r*j**3 + 8/5*j**2 = 0. Calculate j.
0, 1/3, 1
Let i(f) be the first derivative of 2*f**3/3 + 4*f**2 - 24*f - 139. Factor i(s).
2*(s - 2)*(s + 6)
Let f(v) = -3*v - 36. Let g be f(-13). Determine q so that 0*q + 0 + 1/6*q**4 + 1/12*q**g + 0*q**2 = 0.
-1/2, 0
Let h(d) be the third derivative of 0*d + 0 - 3*d**2 - 5/8*d**4 - 1/12*d**5 + 0*d**3. Factor h(k).
-5*k*(k + 3)
Suppose 0 = -5*j + 2*s + 23, 3*s = -3*j + 2 - 5. Factor 37 + 38 - 45*i - 27*i**2 - 26*i**3 + 11*i**j + 12*i**3.
-3*(i - 1)*(i + 5)**2
Let v be ((-14)/6)/((-2)/30*5). Factor -12*u**3 + 7*u**5 - 2*u**5 + 10*u**4 - v*u**3 + 4*u**3.
5*u**3*(u - 1)*(u + 3)
Let d(j) be the third derivative of -j**6/1620 - j**5/540 + j**4/54 + j**3/6 - 16*j**2. Let g(n) be the first derivative of d(n). Let g(r) = 0. Calculate r.
-2, 1
Let m = 43 - 23. Suppose -8*w + m = -4*w. Suppose -w*x**2 + 0 - 3/4*x**3 + 49/4*x**5 + 35/2*x**4 + x = 0. What is x?
-1, 0, 2/7
Let a(i) = 5*i**3 - 10*i**2 - 41*i - 32. Let w(u) = -29*u**3 + 60*u**2 + 247*u + 192. Let v(n) = 34*a(n) + 6*w(n). Factor v(g).
-4*(g - 8)*(g + 1)*(g + 2)
Let r be -2 + 1 + 3 - 3. Let n(k) = 15*k**3 - 15*k**2 - 50*k - 10. Let u(t) = -t**2 - t + 1. Let o(l) = r*n(l) + 10*u(l). Factor o(a).
-5*(a - 2)*(a + 1)*(3*a + 2)
Let b(n) be the first derivative of -n**6/2 + 3*n**5 - 9*n**4/4 - 13*n**3 + 12*n**2 + 36*n + 55. Find x such that b(x) = 0.
-1, 2, 3
Let d(q) = -2*q**3 + 429*q**2 + 25*q - 5. Let k(w) = -3*w**3 + 429*w**2 + 30*w - 6. Let b(p) = -6*d(p) + 5*k(p). Factor b(n).
-3*n**2*(n + 143)
Suppose 57 = 43*r - 29. Factor -r*w**3 + 0 - 4/9*w - 22/9*w**2.
-2*w*(w + 1)*(9*w + 2)/9
Let s(a) = -33*a**2 - 33*a + 88. Let y(u) = -28*u**2 - 32*u + 88. Let t(f) = 4*s(f) - 5*y(f). Find w such that t(w) = 0.
-11/2, 2
Suppose -i = 3 - 5. Factor 5*n + 2*n - 3*n**3 + 3*n**i - 3*n + 2*n**3.
-n*(n - 4)*(n + 1)
Let x(w) be the first derivative of 1/12*w**3 + w + 1/2*w**2 - 9. Factor x(h).
(h + 2)**2/4
Solve -14435*h**3 + 14435*h**3 - 27*h**2 + 3*h**4 = 0.
-3, 0, 3
Let b be (-42)/48 + (1 - (5 + -5)). Suppose -1/8*p + 0 + 0*p**2 + b*p**3 = 0. Calculate p.
-1, 0, 1
Let j(k) be the first derivative of 27/2*k**2 - 3/2*k**3 + 3 + 1/16*k**4 - 54*k. Factor j(c).
(c - 6)**3/4
Let k = 21 + 5. Suppose -5*c - l + 4 = -2, 5*l + k = 3*c. Factor -6/5*q + 0 + 3/5*q**c.
3*q*(q - 2)/5
Let r be (21/147)/(61/(-21) + 3). Let c(q) be the first derivative of 2*q**3 + 6 + 3*q + r*q**4 + 1/2*q**6 - 9/2*q**2 - 9/5*q**5. Determine z so that c(z) = 0.
-1, 1
Let n(t) = -7*t**2 - 50*t. Let j(g) = 4*g**2 + 24*g. Let k(w) = 5*j(w) + 3*n(w). Factor k(u).
-u*(u + 30)
Suppose -8 = -2*m - 2. Factor -6*v**2 - 9*v**m + 7*v - v + 3*v**2.
-3*v*(v + 1)*(3*v - 2)
Factor 195/4*n + 169/4 + 1/4*n**3 + 27/4*n**2.
(n + 1)*(n + 13)**2/4
Let h(z) be the second derivative of z**6/6 - 5*z**5/4 - 5*z**4/3 + 50*z**3/3 - 675*z. Factor h(c).
5*c*(c - 5)*(c - 2)*(c + 2)
Let l(s) be the second derivative of s**4/27 - 8*s**3/27 - 4*s. Factor l(b).
4*b*(b - 4)/9
Suppose -12*n + 67 = 7, -5*n = -q - 23. What is o in -15/2*o**q - 5/2*o**3 + 0 - 5*o = 0?
-2, -1, 0
Let s(n) = -n**2 + 12*n + 16. Let q be s(13). Suppose -b = q*b - 12. Suppose f**4 + 0*f + b - f**3 + 3*f**3 - 2*f - 4*f**2 + 0 = 0. What is f?
-3, -1, 1
Let d(j) be the first derivative of 3*j**4/16 + j**3/4 - 15*j**2/2 + 13. Factor d(b).
3*b*(b - 4)*(b + 5)/4
Suppose 4/5*b**3 - 2*b**2 + 2/5*b**4 + 0 - 12/5*b = 0. Calculate b.
-3, -1, 0, 2
Let i(w) = -w**2 + 6*w. Let v be i(6). Suppose m + 2*c + 2 = -v, 5*m + 2*c - 14 = 0. Factor 2*u**5 + u**4 + 0*u**m - 2*u**5 - u**5.
-u**4*(u - 1)
Let z(l) be the first derivative of -l**3/36 + l**2/4 - 3*l/4 + 13. Find q such that z(q) = 0.
3
Let f be (-4)/(-14) - (-4)/(-14). Suppose f = 4*w - 25 - 11. Let 3*n**4 + w*n**4 - n - 7*n**2 + 7*n**3 - n = 0. Calculate n.
-1, -1/4, 0, 2/3
Let g(h) = 2*h - 17. Let y(w) = w - 9. Let m(u) = -4*g(u) + 7*y(u). Let q be m(2). Suppose -4*t**4 - q*t**2 + 2*t**4 - t**2 + 6*t**2 = 0. What is t?
-1, 0, 1
Determine s, given that 27/2 + 39*s - 3/2*s**4 + 9*s**3 + 36*s**2 = 0.
-1, 9
Factor -16*o**2 - 2*o**3 - 12 - o**3 + o**2 + 24*o + 6*o**3.
3*(o - 2)**2*(o - 1)
Let d be 15/(900/8) - (-16)/30. Let m(z) be the second derivative of 0 - 3*z + 1/63*z**7 + 4/9*z**3 + 0*z**2 + d*z**4 + 13/30*z**5 + 2/15*z**6. Factor m(k).
2*k*(k + 1)**2*(k + 2)**2/3
Let d(x) = 14*x**2 + 6 - 17*x - 3 + x**2 - 1. Let m(k) = 5*k**2 - 6*k + 1. Let c(b) = -6*d(b) + 17*m(b). Factor c(u).
-5*(u - 1)*(u + 1)
Let l(b) be the third derivative of -b**7/840 + b**5/120 - 13*b**3/6 - 13*b**2. Let z(f) be the first derivative of l(f). Factor z(g).
-g*(g - 1)*(g + 1)
Suppose -6*d = -2*d - 12. Let s(v) = -v**2 + 4*v + 3. Let t be s(d). Determine i, given that -14*i**4 + 2 + 10*i**3 - t*i**3 - 2 = 0.
0, 2/7
Suppose 0 = 2*w - 5*z - 13, z = 5*w - 0*z - 21. Let 16/9*y**3 - 8/9*y**2 + 2/9*y**5 + 0*y - 10/9*y**w + 0 = 0. What is y?
0, 1, 2
Suppose 3*k - 5*f = 17, 0 = -3*k - f - 0 + 11. Determine c so that -7*c**2 + 8*c**3 + 2 - 5*c**3 + 6*c**2 - 3*c - c**k = 0.
-1, 1, 2
Let c(m) = -8*m**2 + 56*m. Let k(j) = -7*j**2 + 58*j. Let i(w) = -4*c(w) + 5*k(w). Determine g, given that i(g) = 0.
0, 22
Factor -66/5*r + 92/5*r**2 - 2/5*r**5 - 12*r**3 + 18/5 + 18/5*r**4.
-2*(r - 3)**2*(r - 1)**3/5
Let r(y) be the first derivative of y**6/3 - 14*y**5 + 64*y**4 - 248*y**3/3 + 289. Factor r(k).
2*k**2*(k - 31)*(k - 2)**2
Let g(m) be the third derivative of -16*m**2 + 1/30*m**6 - 1/30*m**5 + 0*m**4 + 0*m**3 + 0*m - 1/105*m**7 + 0. Factor g(k).
-2*k**2*(k - 1)**2
Let o(n) be the second derivative of n**4/12 + 11*n**3/6 + 11*n**2 + 5*n. Let q be o(-9). Suppose -4*g**q + 4*g**5 + 396*g - 396*g = 0. What is g?
0, 1
Suppose 0 = r + 4*r - 210. Let j = r + -39. Factor 93*o**j + 51/2*o - 57*o**4 + 27/2*o**5 - 72*o**2 - 3.
3*(o - 1)**4*(9*o - 2)/2
Let y be -6 + (30/(-5))/(-3). Let w be 4*(-3)/(y - 2). Suppose -3*l**2 + l**2 + 2*l**2 + 4*l**w - 2*l = 0. Calculate l.
0, 1/2
Let u(w) be the third derivative of w**7/280 + 53*w**6/160 + 135*w**5/16 - 729*w**4/32 - 1078*w**2. Factor u(x).
3*x*(x - 1)*(x + 27)**2/4
Let r be 0/(-1) + 12/6. Factor -r*y**2 + 11*y - 22*y + 3*y - 6.
-2*(y + 1)*(y + 3)
Suppose r = 3*n + 15, 3 = r - 0*n + 3*n. Let m be r*(-4 + 3 - -2). Solve 6*y**3 - 2*y**4 + m*y**2 - y**4 + y**2 - y**2 = 0.
-1, 0, 3
Let t(m) be the third derivative of 0*m - 1/72*m**4 + 0*m**3 + 0 - 1/36*m**5 - 1/90*m**6 + 2*m**2. Let t(d) = 0. What is d?
-1, -1/4, 0
Solve -30/7 - 32/7*a**2 + 61/7*a + 1/7*a**3 = 0.
1, 30
Let v(s) = -7*s**4 - 103*s**3 - 1567*s**2 - 2813*s - 1357. Let o(t) = 10*t**4 + 155