 40. Let y be 18/8 + (-30)/u. Factor 3/4*m**4 + 0 - 3/4*m**5 - 3/4*m**2 + y*m**3 + 0*m.
-3*m**2*(m - 1)**2*(m + 1)/4
Let x(a) be the second derivative of a**7/840 + a**6/360 - a**5/120 - a**4/24 - 23*a**3/6 - 16*a. Let t(k) be the second derivative of x(k). Factor t(s).
(s - 1)*(s + 1)**2
Let p(x) be the second derivative of x**7/189 - 2*x**6/135 - x**5/10 + x**4/27 + 8*x**3/27 - 3*x + 1. Let p(o) = 0. What is o?
-2, -1, 0, 1, 4
Let x = -13156/3 - -4080. Let j = x - -306. Factor -1/3*v**3 + 1/3*v**4 - j - v**2 + 5/3*v.
(v - 1)**3*(v + 2)/3
Let g be (-55)/(-275) + 108/60. Let 2/3*j**g + 0 + 0*j - 2/3*j**3 + 1/6*j**4 = 0. Calculate j.
0, 2
Let w(r) = -r**3 - r**2 - r. Let p(t) = 7*t**3 - 3*t**2 + 21*t - 26. Let u(y) = p(y) + 6*w(y). Let n(s) be the first derivative of u(s). What is g in n(g) = 0?
1, 5
Let v(g) be the second derivative of 3*g**6/20 - 33*g**5/20 + 97*g**4/24 + 22*g**3/3 + 4*g**2 - 762*g. Factor v(h).
(h - 4)**2*(3*h + 1)**2/2
Suppose -f - 209 = -c, -5*c + 5*f - 3*f = -1039. Let z be (86/(-8))/(3/(-12)). Suppose -c*j**2 - 75*j**4 + z*j + 41*j - 5 + 210*j**3 - 8 + 1 = 0. What is j?
2/5, 1
Factor -22/5 + 4*w + 2/5*w**2.
2*(w - 1)*(w + 11)/5
Suppose -7*z = -z + 84. Let i(a) = -26*a**2 - 76*a - 36. Let c(f) = -5*f**2 - 15*f - 7. Let k(j) = z*c(j) + 3*i(j). Let k(p) = 0. What is p?
-5/4, -1
Let b = 11 + -8. Determine n, given that 9*n**2 + b - 13*n**2 + 6*n + 7*n**2 = 0.
-1
Let h(k) = -1 + 10 - 1 - k + 2*k. Let n be h(-6). Factor n + 6 - 4 + 8*q + 4*q**2.
4*(q + 1)**2
Let k(c) = -4*c**2 + 207*c - 150. Let p be k(51). Let 0 - 2/5*a + 0*a**4 + 4/5*a**p + 0*a**2 - 2/5*a**5 = 0. What is a?
-1, 0, 1
Let g = -19126 + 19128. Let d be 9/2 - (-1)/(-2). Factor -1/4*i**5 + 3/4*i**d + 1/4*i**g - 3/4*i**3 + 0 + 0*i.
-i**2*(i - 1)**3/4
Let l = 1892524/315 - 6008. Let z(x) be the second derivative of -1/441*x**7 + 0*x**3 - 1/70*x**5 - l*x**6 + 0 + 0*x**2 + 0*x**4 + 12*x. Factor z(m).
-2*m**3*(m + 1)*(m + 3)/21
Let j be 8 - 8 - 7/12. Let x = -1/12 - j. Suppose 0 - x*t**4 + t + 2*t**3 - 5/2*t**2 = 0. Calculate t.
0, 1, 2
Let -5/3*g**2 - 1/3*g**3 + 0 - 4/3*g = 0. Calculate g.
-4, -1, 0
Let g be (-4)/((-4)/3) + (15 - 13). Let z(f) be the first derivative of 6 + 0*f**2 - 1/20*f**g + 0*f**4 + 0*f + 1/12*f**3. Let z(r) = 0. What is r?
-1, 0, 1
Let d(v) = -v**3 - 137*v**2 + 12*v + 1646. Let b be d(-137). Find q, given that -7/2*q**b + 17/6*q - 3/2*q**3 - 1/2 = 0.
-3, 1/3
Let u(f) be the second derivative of 3*f**5/20 - 7*f**4/4 - 17*f**3/2 - 27*f**2/2 - 3*f. Find b such that u(b) = 0.
-1, 9
Let i(r) be the first derivative of r**4/36 - 2*r**2/3 + 2*r - 11. Let u(z) be the first derivative of i(z). Solve u(m) = 0.
-2, 2
Let l = 4539 + -4537. Factor -8/3*o + 0 + 2/3*o**3 - 2*o**l.
2*o*(o - 4)*(o + 1)/3
Suppose -2*n = -4*k + 2, -k - n - 13 = -12. Let f be k*(4 + 45/(-10)). Factor -4/7*b**2 + f - 4/7*b.
-4*b*(b + 1)/7
Let q(f) be the second derivative of -7*f**5/26 + 17*f**4/78 - 2*f**3/39 + 24*f - 2. Factor q(g).
-2*g*(5*g - 1)*(7*g - 2)/13
Let z(m) be the first derivative of 1/10*m**5 + 0*m**3 + 4 + 0*m**2 + 6*m + 0*m**4. Let f(p) be the first derivative of z(p). Factor f(w).
2*w**3
Factor 6/11 - 5/11*w**3 + 2*w**2 - 23/11*w.
-(w - 3)*(w - 1)*(5*w - 2)/11
Suppose -5*p = -25, -2*l - 3*p + 29 = -0*p. Let i be ((-9)/42)/((-2)/l). Solve 0*f**3 + 0 - 1/4*f + i*f**2 - f**4 = 0.
-1, 0, 1/2
Let r be -6*6/12*(-4)/(-6). Let j be (r/12)/((-14)/(-8) - 2). Factor -2/3 + g + j*g**2.
(g + 2)*(2*g - 1)/3
Factor 23*x + 2*x**2 + 4*x**3 - 6211 + 0*x**2 - 6*x**2 - 87*x + 6131.
4*(x - 5)*(x + 2)**2
Determine u, given that 22/7*u + 4/7*u**4 + 24/7 + 2/7*u**5 - 24/7*u**3 - 4*u**2 = 0.
-4, -1, 1, 3
Let g = 540 - 538. Let k(r) be the second derivative of 0 - 1/120*r**6 + 2*r - 1/168*r**7 + 1/24*r**4 - 1/24*r**3 + 1/40*r**5 - 1/8*r**g. Factor k(z).
-(z - 1)**2*(z + 1)**3/4
Let y = -95 - -99. Suppose 3*f - y*n = 7 - 3, 2*n = f. Let 9/2*v**2 + 0 + 3*v + 21/2*v**f - 18*v**3 = 0. Calculate v.
-2/7, 0, 1
Let m(g) be the third derivative of -g**7/105 + g**6/60 + g**5/30 - g**4/12 + 101*g**2. Determine w, given that m(w) = 0.
-1, 0, 1
Let q(x) be the second derivative of -x**5/20 + x**3/6 - x**2/2 - 6*x. Let l(a) = -a**3 + 3*a**2 + 5*a - 1. Let h(c) = -l(c) + 2*q(c). Solve h(f) = 0.
-1
Let b(c) be the first derivative of -2/9*c**3 - 36 + 0*c + 4/3*c**2. Factor b(p).
-2*p*(p - 4)/3
Let v(k) = 4*k**4 - 64*k**3 + 60*k**2 + 72*k - 60. Let q(y) = 8*y**4 - 128*y**3 + 121*y**2 + 146*y - 120. Let b(d) = 4*q(d) - 9*v(d). Factor b(j).
-4*(j - 15)*(j - 1)**2*(j + 1)
Let s(f) be the third derivative of -f**7/1365 - 7*f**6/780 - f**5/26 - 3*f**4/52 - f**2 - 14. Factor s(n).
-2*n*(n + 1)*(n + 3)**2/13
Let w(b) = 3*b**4 - 18*b**3 + 27*b**2 + 4*b. Let l(a) = 28 - 27*a**2 + 3*a**4 + 18*a**3 - 28 - 6*a**4 - 3*a. Let f(t) = 4*l(t) + 3*w(t). Factor f(u).
-3*u**2*(u - 3)**2
Determine n so that 0 - 3/5*n**3 + 6/5*n**2 - 3/5*n = 0.
0, 1
Find w such that -33/5*w**2 + 4/5*w**3 + 8/5*w + 0 = 0.
0, 1/4, 8
Let y be (4/5)/(7/70). Let d = y + -5. Factor -s**2 + 0*s**2 - d + 0*s - 6*s + 10*s**2.
3*(s - 1)*(3*s + 1)
Let q(y) be the third derivative of -y**8/588 + 16*y**7/147 - 40*y**6/21 + 57*y**2 - 2*y. Suppose q(w) = 0. What is w?
0, 20
Let x(m) = m**2 - 2*m + 2. Suppose -4*h + 12 = 4. Let l(s) = -s**2 - 1. Let f(q) = h*l(q) + x(q). Determine a so that f(a) = 0.
-2, 0
Suppose 5*i - 39 = -9. Factor -8*x**2 - 1 - x**2 + i*x**2 + 13.
-3*(x - 2)*(x + 2)
Factor 0 - 3*d**2 - 18/7*d - 3/7*d**3.
-3*d*(d + 1)*(d + 6)/7
Let q = -1037 - -1038. Let s(h) be the first derivative of 1/6*h**3 + 0*h**2 - q + 1/4*h**4 + 0*h + 1/10*h**5. Factor s(d).
d**2*(d + 1)**2/2
Let t(z) be the first derivative of z**2/2 + 7*z + 2. Let b be t(-5). Factor 2 - 2*y**2 + 5*y**3 - 3*y**3 - b*y + 0*y.
2*(y - 1)**2*(y + 1)
Suppose -4*r - 3*g + 9 = 0, 5*r - 2*r = -3*g + 6. Factor -12*w**2 - 15*w**r - 193*w**4 + 5*w**5 + 91*w**2 + 173*w**4 + 11*w**2.
5*w**2*(w - 3)**2*(w + 2)
Let m = -196 - -199. Let i(q) be the second derivative of 0 + 1/3*q**4 + 0*q**2 - m*q + 0*q**3. Determine c, given that i(c) = 0.
0
Let u be (21/12*21)/66. Let p = -3/8 + u. Factor 2/11*l**5 + 0 + 0*l + 6/11*l**3 + 6/11*l**4 + p*l**2.
2*l**2*(l + 1)**3/11
Suppose 1120 - 1147 = -9*d. Solve 0 + 0*j - 2/5*j**d - 2/5*j**4 + 4/5*j**2 = 0.
-2, 0, 1
Let m(r) be the second derivative of 0*r**3 + 0 - 20*r + 1/42*r**7 + 1/12*r**4 + 0*r**2 + 3/20*r**5 + 1/10*r**6. Factor m(y).
y**2*(y + 1)**3
Let p(c) be the third derivative of 3*c**8/112 + c**7/280 - 3*c**6/80 + 33*c**2 + 2. Determine m so that p(m) = 0.
-3/4, 0, 2/3
Let r(j) = -3*j**2 - 72*j - 417. Let l be r(-10). Suppose 0*y + 0*y**l - 1/5*y**5 - 4/5*y**2 + 3/5*y**4 + 0 = 0. What is y?
-1, 0, 2
Let s(f) be the first derivative of f**8/560 + f**7/140 - f**5/20 - f**4/8 + 11*f**3/3 + 2. Let n(d) be the third derivative of s(d). Factor n(y).
3*(y - 1)*(y + 1)**3
Let q(f) be the first derivative of -2 - 7/10*f**4 - 4/15*f**3 - 8/25*f**5 + 0*f + 1/5*f**2. Factor q(v).
-2*v*(v + 1)**2*(4*v - 1)/5
Suppose -3*w = -33*j + 38*j, 4*j = 3*w. Let n(z) be the third derivative of -8*z**2 - 1/60*z**5 + 0*z**3 + 1/72*z**4 + j + 0*z. Factor n(d).
-d*(3*d - 1)/3
Find d, given that -1/3*d - 1/6*d**2 + 1/6*d**3 + 0 = 0.
-1, 0, 2
Let z(v) be the second derivative of v**4/4 - 32*v**3 + 1536*v**2 - 4*v + 4. Factor z(q).
3*(q - 32)**2
Let k be 7/4 - (1 + 0). Let p be (12/(-20))/(4 + 66/(-15)). Factor -3*r**2 + k*r**3 + 15/4*r - p.
3*(r - 2)*(r - 1)**2/4
Suppose 2 = 8*v - 7*v, 5*r + 2*v = 4. Let j(m) be the third derivative of 11*m**2 - 1/18*m**4 + 0 + r*m - 1/3*m**3 - 1/270*m**5. Factor j(s).
-2*(s + 3)**2/9
Let f(n) be the second derivative of -n**6/30 - 7*n**5/20 - n**4/2 - 3*n + 4. Determine h, given that f(h) = 0.
-6, -1, 0
Let s = 715 - 4289/6. Let i = 559/6 + -93. Find c such that -1/3*c**2 - 1/3*c**3 + s*c + i*c**5 + 1/6 + 1/6*c**4 = 0.
-1, 1
Let j(s) = s**3 - 7*s**2 + 6*s. Let u be j(6). Let m = 22628 + -22625. Factor 0 + u*o - 1/6*o**2 - 1/2*o**4 + 1/2*o**m + 1/6*o**5.
o**2*(o - 1)**3/6
Factor 8*u**2 + 4*u**4 + 2*u**5 + 12631 - 12631 - 14*u**3.
2*u**2*(u - 1)**2*(u + 4)
Suppose 5*q = -101 + 111. Solve 38*a - 6*a**5 + a**5 - 8*a - 15*a**4 + 75*a**3 - 85*a**q = 0 for a.
-6, 0, 1
Solve 246*b**3 + 3*b**4 - 288*b**3 - b**4 = 0 for b.
0, 21
Solve 4*x**2 + 91*x**2