- 1)
Factor -5192 - 12*a + 5192 + 2*a**4 - 16*a**3 + 26*a**2.
2*a*(a - 6)*(a - 1)**2
Let o be -25 - (3 - 3) - (0 - 2). Let c = o - -26. Let 52/7*d**c + 8/7 + 8/7*d - 54/7*d**2 - 2*d**4 = 0. What is d?
-2/7, 1, 2
Let c(m) be the third derivative of -m**7/735 + m**6/105 + 8*m**5/105 - 4*m**4/21 - 16*m**3/7 + 22*m**2. Find a such that c(a) = 0.
-2, 2, 6
Let d be 4/(-2 - (-108)/51). Factor 28*b**3 - 2*b**4 - d*b**3 + 0*b - b + 2*b**5 + 10*b**2 - 3*b.
2*b*(b - 1)**3*(b + 2)
Let d(x) = x**2 - x + 1. Let h(g) = 2*g**3 + 2 - 1 - 8*g + 20*g**2 + 15. Let m(n) = -28*d(n) + 2*h(n). Let m(b) = 0. Calculate b.
-1
Let c(q) be the first derivative of 0 - 16*q + 2 - 4*q**4 + 4*q**3 + 5*q**4 - 6. What is j in c(j) = 0?
-2, 1
Let v(r) be the first derivative of -r**8/84 + 2*r**7/35 - r**6/15 + 5*r**2/2 + 1. Let f(j) be the second derivative of v(j). Determine g, given that f(g) = 0.
0, 1, 2
Let x(y) be the third derivative of -y**6/360 - y**5/40 - y**4/12 - 7*y**3/3 - 21*y**2. Let l(t) be the first derivative of x(t). Factor l(s).
-(s + 1)*(s + 2)
Let o = -23763 + 166342/7. Factor -48/7*l - o*l**3 + 12/7*l**2 + 64/7.
-(l - 4)**3/7
Let v(c) = -3*c**4 - 53*c**3 + 197*c**2 - 208*c + 77. Let b(s) = -8*s**4 - 132*s**3 + 492*s**2 - 520*s + 192. Let l(r) = 5*b(r) - 12*v(r). Factor l(x).
-4*(x - 1)**3*(x + 9)
Let m = -210 - -178. Let r be ((-1)/(-3))/((-16)/m). Factor -r*y**3 + 0 + 0*y**2 + 0*y.
-2*y**3/3
Let w(o) = 5*o**4 - 167*o**3 + 640*o**2 - 778*o - 233. Let y(d) = -2*d**4 + 55*d**3 - 213*d**2 + 260*d + 78. Let c(m) = -2*w(m) - 7*y(m). Factor c(q).
(q - 5)*(q - 4)**2*(4*q + 1)
Let t(p) be the first derivative of -p**6/27 - 16*p**5/45 - 10*p**4/9 - 32*p**3/27 + 87. Factor t(m).
-2*m**2*(m + 2)**2*(m + 4)/9
Let w(m) = m. Suppose 0 = 4*i - 1 + 9. Let r(z) = 2*z**2 - 6*z. Let a be 5/(-5) - (-1 + 1). Let l(b) = a*r(b) + i*w(b). Factor l(h).
-2*h*(h - 2)
Let r(g) be the second derivative of g**6/6 + 9*g**5/2 - 5*g**4/4 - 140*g**3/3 - 90*g**2 + 2*g - 32. Suppose r(l) = 0. What is l?
-18, -1, 2
Suppose 5 = k + 4*k. Suppose 4*t + 8 = -2*d, -8*t = -3*d - 4*t + 18. Factor 3 - k + d*y**2 - y**2 - 3*y.
(y - 2)*(y - 1)
Let c(y) = -y**3 + y**2 + 1. Let d(b) = 8*b**3 - 118*b**2 + 310*b - 203. Let p(m) = 3*c(m) + d(m). Solve p(q) = 0 for q.
1, 2, 20
Suppose -3*p - 4*j + 56 = 0, 3*j = 5*p - 10*p + 75. Factor p*g**3 + 2*g**5 - 15*g**3 + 2*g**2 + g**3 - 2*g**4.
2*g**2*(g - 1)**2*(g + 1)
Let l(q) be the first derivative of -7*q**6/288 - 5*q**5/96 + 5*q**4/48 - 13*q**3 - 35. Let k(c) be the third derivative of l(c). Find i, given that k(i) = 0.
-1, 2/7
Suppose 3*z - 1 - 14 = -3*n, 16 = 5*z + 2*n. Let z*j - 6*j**5 - 6*j**5 + 14*j**5 - 4*j**3 - 3*j**4 - 3*j**4 - 6 + 12*j**2 = 0. Calculate j.
-1, 1, 3
Let u = -28547 - -199837/7. Factor -20/7*z**3 - u - 36/7*z - 48/7*z**2.
-4*(z + 1)**2*(5*z + 2)/7
Suppose 2*c = 5*p - 15, p - 30 = 10*c - 15*c. Factor 0*o + 2/11*o**p + 2/11*o**4 - 2/11*o**2 - 2/11*o**3 + 0.
2*o**2*(o - 1)*(o + 1)**2/11
Let h(b) = -11*b**2 + 45*b + 24. Let k(x) = -5*x**2 + 22*x + 11. Let j(t) = -2*h(t) + 5*k(t). Solve j(w) = 0 for w.
-1/3, 7
Let a(q) be the third derivative of -q**7/1890 + 67*q**6/1080 - 13*q**5/36 + 193*q**4/216 - 32*q**3/27 - 76*q**2. Solve a(f) = 0.
1, 64
Factor -15*x**3 - 12 + 7*x + 8*x + 276*x**4 - 273*x**4 + 9*x**2.
3*(x - 4)*(x - 1)**2*(x + 1)
Let b(u) be the third derivative of -9*u**7/70 + u**6/4 + 17*u**5/20 - u**4/4 + 57*u**2 + 1. Determine f, given that b(f) = 0.
-1, 0, 1/9, 2
Let o be (-22)/220 - 2/(-20). Let w(d) be the first derivative of o*d**2 - 1/3*d**3 + 0*d - 2 + 1/8*d**4. Solve w(c) = 0 for c.
0, 2
Let v(o) be the third derivative of -o**9/16632 - o**8/36960 - 5*o**4/4 - 18*o**2. Let u(g) be the second derivative of v(g). Find s such that u(s) = 0.
-1/5, 0
Let h(q) be the third derivative of -q**5/20 - q**4/2 + 21*q**3/2 - 22*q**2. Find g, given that h(g) = 0.
-7, 3
Let z(f) = -3*f**3 + 103*f**2 + 226*f + 153. Let s(x) = x**3 - 34*x**2 - 75*x - 52. Let b(i) = -11*s(i) - 4*z(i). Determine u so that b(u) = 0.
-1, 40
Factor 90/7 + 183/7*h + 6/7*h**2.
3*(h + 30)*(2*h + 1)/7
Factor -30*a**2 + 36*a + 2*a**3 + 80 - a**2 - 21*a**2 + 2*a**2 + 8*a**2.
2*(a - 20)*(a - 2)*(a + 1)
Let l(t) = -t**3. Let b(x) = -28*x**3 - 28*x**2 - 64*x - 48. Suppose -2*r - 52 = 4*i, 21 = -r - 0*r + 3*i. Let g(h) = r*l(h) + b(h). Factor g(f).
-4*(f + 2)**2*(f + 3)
Let i(q) be the first derivative of -11*q**4/12 + 2*q**3/9 + 33*q**2/2 - 6*q + 96. Solve i(s) = 0 for s.
-3, 2/11, 3
Let x(l) be the second derivative of l**7/84 - 3*l**6/20 + 27*l**5/40 - 9*l**4/8 + 3*l + 2. Factor x(z).
z**2*(z - 3)**3/2
Let m(k) be the third derivative of -2/15*k**3 - k**2 + 0*k + 0 + 1/150*k**5 + 1/60*k**4. Let m(z) = 0. What is z?
-2, 1
Suppose 5 - 2 = -3*g. Let l be 12/4 - (g - -2). Factor 13 - 6*a - 4 - a**l + 2*a**2.
(a - 3)**2
Find h such that -1086*h**4 + 108*h**5 - 5 + 611/4*h**2 + 179/4*h**3 - 2*h = 0.
-1/4, 2/9, 1/3, 10
Factor -66*s - 22*s - 68*s**2 - 73 + 41 - 12*s**3.
-4*(s + 1)*(s + 4)*(3*s + 2)
Let g(z) be the second derivative of z**6/165 + 3*z**5/11 - z**4/66 - 10*z**3/11 + 212*z. Solve g(c) = 0 for c.
-30, -1, 0, 1
Solve 1/2*t + 1/2*t**5 - t**3 + 0*t**2 + 0 + 0*t**4 = 0.
-1, 0, 1
Let n(p) be the second derivative of -p**4/78 + 10*p**3/39 - 9*p**2/13 + p + 31. Find b, given that n(b) = 0.
1, 9
Suppose -117 + 93 = -4*h. Let a(c) be the third derivative of 1/30*c**5 + 0*c + 0 - 5*c**2 + 4/15*c**3 - 1/300*c**h - 2/15*c**4. Suppose a(g) = 0. What is g?
1, 2
Let u(v) = -v**2 - v + 4. Let c be u(-2). Let 13 + 10*z**3 + 151*z - 49 - z**4 - 37*z**c - 91*z = 0. Calculate z.
2, 3
Let n be (-33)/2 + 60/(-8) + 7. Let c = -14 - n. Let -9/2 + c*g - 1/2*g**2 = 0. What is g?
3
Let z(m) = -3*m**5 + 27*m**4 - 27*m**3 + 9*m**2 - 6*m - 12. Let u(b) = b**4 - b**2 - 1. Suppose 0 = 6*a + 32 + 40. Let s(j) = a*u(j) + z(j). Factor s(h).
-3*h*(h - 2)*(h - 1)**3
Let d(l) be the third derivative of -l**6/600 + 17*l**5/150 - 8*l**4/3 + 256*l**3/15 - 234*l**2. Determine v, given that d(v) = 0.
2, 16
Factor 5*x**2 + 0*x - 13*x**2 + 4*x - 30 + 21 + 17 - 4*x**3.
-4*(x - 1)*(x + 1)*(x + 2)
Suppose -f = 4*u + 2*f - 28, 0 = -4*u + 2*f + 8. Let t be (-4 + (-4)/u)*-1. Factor 6*b**3 - 63*b**2 + 6*b**4 + 65*b**2 + 3*b**5 - 5*b**5 + 4*b**t.
2*b**2*(b + 1)**3
Determine n so that -80*n**2 + 15*n**5 + 560*n - 920*n**3 + 1368 - 82*n**5 - 1208 + 650*n**4 - 58*n**5 = 0.
-2/5, 2
Suppose -5 = -5*o + 5*q, -6*o = -5*o - 4*q + 2. Let x(n) be the first derivative of -16/9*n**3 - 5/6*n**o + 2/3*n - 3/4*n**4 + 7. Let x(w) = 0. What is w?
-1, 2/9
Factor -82/3*i + 20 + 14/3*i**2.
2*(i - 5)*(7*i - 6)/3
Suppose 13*g = -71 + 123. Factor 0*y**3 - 6/5*y**2 + 0 + 2/5*y**g + 4/5*y.
2*y*(y - 1)**2*(y + 2)/5
Let d(t) = t**2 - 119*t + 118. Let p be d(1). Factor 1/3*a**3 + 1/3*a - 2/3*a**2 + p.
a*(a - 1)**2/3
Let l be (14/6 - 1)/(36/54 - 0). Suppose 0*b**l - 2/7*b**3 + 0*b + 0 = 0. Calculate b.
0
Suppose -2*r = -3*r - 5*t - 21, -2*t - 2 = 2*r. Let j be r - 6 - 12*1/(-5). Find c such that -12/5*c - 18/5 - j*c**2 = 0.
-3
Suppose 199*l = 99*l + 96*l + 8. Let i = 7/20 - -29/20. Let 1/5*y**l - 6/5*y + i = 0. What is y?
3
Let z(h) be the first derivative of -7/12*h**3 + 0*h - 41 - 1/2*h**2. Let z(y) = 0. What is y?
-4/7, 0
Factor 2*u**5 + 164*u - 48*u**3 + 8*u**4 + 397*u - 145*u - 384 - 64*u**2.
2*(u - 2)**3*(u + 4)*(u + 6)
Let u = -129046/5 - -25810. What is b in -u*b + 4/5*b**3 - 8/5*b**2 + 8/5 = 0?
-1, 1, 2
Let b be 17/6 - (-114)/(-76). Solve 4/3 + 1/3*y**2 + b*y = 0 for y.
-2
Let u be 0 - (2 + (-2 - -1)). Let w(f) = 6*f - 5 - 6*f + f**2 + 4. Let d(p) = -2*p**2 + 6. Let z(j) = u*d(j) - 6*w(j). Factor z(s).
-4*s**2
Let a(g) be the first derivative of 3/25*g**5 - 1/10*g**6 + 3/10*g**4 - 2/5*g**3 + 3/5*g - 3/10*g**2 - 5. What is o in a(o) = 0?
-1, 1
Let g(t) be the second derivative of -3/100*t**5 - 12*t + 4/5*t**2 + 1/30*t**4 + 0 + 2/5*t**3 - 1/150*t**6. Factor g(w).
-(w - 2)*(w + 1)*(w + 2)**2/5
Let j(d) be the third derivative of 0 + 5/24*d**4 + 0*d**3 + 11*d**2 + 0*d - 1/12*d**5. Factor j(c).
-5*c*(c - 1)
Let r(s) = -s**3 - 5*s**2 - 2*s - 8. Let y be r(-5). Factor -8*a**4 - 4*a**y - 2*a**5 - 13*a**3 + 4*a**3 - a**3.
-2*a**2*(a + 1)**2*(a + 2)
Let d(n) be the first derivative of n**8/336 - n**7/56 + n**6/36 - 8*n**3/3 + 14. Let s(t) be the