) = 0. Calculate c.
1/2, 2, 10
Let y be (-2)/8*(37/9 - 5) + 0. Factor -2/9*u**2 + 4/9 + y*u.
-2*(u - 2)*(u + 1)/9
Suppose -14*o**2 + 9*o**2 - 84 + 5*o**2 + 4*o**2 + 16*o = 0. Calculate o.
-7, 3
Factor -1/5*b**3 + 0*b - 22/5*b**2 + 0.
-b**2*(b + 22)/5
Let 22*y**2 + 190*y - 2*y**3 - 16 - 6 - 188*y = 0. What is y?
-1, 1, 11
Let x(d) be the third derivative of 0*d + 16*d**2 + 5/2*d**3 + 0 + 1/12*d**5 - 5/6*d**4. Solve x(w) = 0 for w.
1, 3
Let r(f) = -f + 24. Let o be r(22). Suppose -p - 10*p = o*p. Factor 2/5 + p*q - 2/5*q**2.
-2*(q - 1)*(q + 1)/5
Find y, given that -2 + 4*y**3 + 5 + 1 - 12*y + 4 + 0 = 0.
-2, 1
Let a be 52/286 + ((-96)/108)/(11/(-6)). Find j, given that 2*j**2 + a*j**3 + 4/3*j + 0 = 0.
-2, -1, 0
Factor 0*i + 6/23*i**4 + 20/23*i**3 + 6/23*i**2 + 0.
2*i**2*(i + 3)*(3*i + 1)/23
Factor 3*a**4 - 6*a**3 + 12*a + 4*a**2 - 12*a**2 - a**2 + 7 + 5.
3*(a - 2)**2*(a + 1)**2
Let b(w) be the third derivative of w**5/60 + 5*w**4/8 + 9*w**3 - 7*w**2 - 7*w. Suppose b(l) = 0. Calculate l.
-9, -6
Factor 100*y**2 + 4*y**3 + 193*y + 0*y**2 - 676 + 379*y.
4*(y - 1)*(y + 13)**2
Suppose 664 = -313*t + 1573 + 1595. Let 8/7 + 20/7*w - t*w**3 - 44/7*w**2 = 0. Calculate w.
-1, -2/7, 1/2
Let z be (-5)/(-2)*(-4 + 20). Determine o so that 6*o**3 + 5*o**2 + 49*o**3 + 30*o**4 + 5*o**5 - z - 60*o + 5*o**2 = 0.
-2, -1, 1
Let v = 40 + 0. Suppose 0*b + v = 5*b. Solve -b - 2*x - x + 2*x + 6 + x**2 = 0.
-1, 2
Let r(s) be the first derivative of s**5/35 + s**4/7 - 18*s - 36. Let z(w) be the first derivative of r(w). Factor z(x).
4*x**2*(x + 3)/7
Let r(i) be the second derivative of -1/24*i**3 + 0 + 1/48*i**4 - 9*i + 0*i**2. Solve r(z) = 0 for z.
0, 1
Let d be (-8)/(-660)*9/36. Let b(l) be the third derivative of 4*l**2 + 1/132*l**4 - d*l**5 + 0 + 0*l + 0*l**3. Find k, given that b(k) = 0.
0, 1
Let d(n) = 5*n**2 - 16*n - 21. Let h(t) = -4*t**2 + 16*t + 20. Let g(w) = 6*d(w) + 7*h(w). Factor g(j).
2*(j + 1)*(j + 7)
Determine c so that -3*c**2 + 2469 + 109*c + 227*c - 2808 + 6*c**2 = 0.
-113, 1
Factor -23*f + 3*f**3 - 10*f + 25*f - f**3.
2*f*(f - 2)*(f + 2)
Let t(r) = -r**3 + 8*r**2 + 9*r + 2. Let z be t(9). Suppose -z*i = 3*i - 80. Solve -5*b**3 - 1 - i*b + 1 + b**3 + 16*b**2 = 0 for b.
0, 2
Let b = 86 - 86. Let p be (-8)/(-14) + (b - 0). Determine i so that 8/7*i + p*i**3 - 8/7 + 2*i**2 = 0.
-2, 1/2
Let t(l) be the second derivative of -2*l**6/15 + 8*l**5/5 - 22*l**4/3 + 16*l**3 - 18*l**2 - 101*l. Factor t(k).
-4*(k - 3)**2*(k - 1)**2
Let n(u) be the first derivative of 2*u**3/3 + u**2 - 13*u - 12. Let z(o) = -3*o**2 - 3*o + 12. Let f(a) = -2*n(a) - 3*z(a). Suppose f(l) = 0. What is l?
-2, 1
Let t(w) be the third derivative of w**8/112 - 4*w**7/35 + 19*w**6/40 - 2*w**5/5 - 5*w**4/2 + 8*w**3 - 299*w**2. Let t(l) = 0. Calculate l.
-1, 1, 2, 4
Let h = 1 - -6. Suppose -4*b - 3*f = -25, 3*f + 0*f = 4*b - h. What is q in -2*q + 4*q - b*q**3 + q**2 - 2 + q**2 + 2*q**3 = 0?
-1, 1
Let t = 4943/4 - 1235. Factor 0*u**2 + 0*u + t*u**4 + 0 - 3/4*u**3.
3*u**3*(u - 1)/4
Suppose 0 - 16*b - 9/2*b**4 - 36*b**2 - 1/4*b**5 - 97/4*b**3 = 0. Calculate b.
-8, -1, 0
Let x(s) = -s**4 - 2*s**3 - s**2 + s - 1. Let p(a) = 10*a**4 - 56*a**3 - 70*a**2 + 62*a + 78. Let r(b) = -p(b) - 6*x(b). Find f, given that r(f) = 0.
-1, 1, 18
Determine a, given that -15*a**3 + 0*a**5 - 5*a**5 + 20*a - 3800*a**4 + 3775*a**4 + 25*a**2 = 0.
-4, -1, 0, 1
Factor -1588*j**3 - 72*j**4 - 2736*j**2 + 475*j - 4*j**5 - 27*j**4 - 1771*j - 53*j**4.
-4*j*(j + 1)**2*(j + 18)**2
Let d(n) = -n**2 + 5*n - 26. Let s be d(6). Let v be ((-152)/s + -5)/(1/(-3)). Factor -v + 3/4*i**2 + 2*i.
(i + 3)*(3*i - 1)/4
Let a(m) = m**4 + 4*m**3 + 2*m**2 - 8*m. Suppose 0 = -2*q - 2*l - 4, -q - 10 = 4*q - 2*l. Let x(z) = z**3 + z**2 - z. Let r(v) = q*a(v) - 2*x(v). Factor r(w).
-2*w*(w - 1)*(w + 3)**2
Let g = -88 + 82. Let t(p) = 9*p**4 + 25*p**2 - 21*p. Let m(f) = 2*f**4 + 6*f**2 - 5*f. Let x(n) = g*t(n) + 26*m(n). Solve x(o) = 0 for o.
-2, 0, 1
Let g(u) = -u**2 - 5*u + 8. Let t be g(-6). Suppose 4*d = 10 + t. Factor -5*x + 10*x + d*x**2 + 1 - 2*x + x**3.
(x + 1)**3
Factor 128*l**3 - 275*l**2 + 3 + 434*l**2 - 267*l**2 - 23*l.
(l - 1)*(4*l + 1)*(32*l - 3)
Let u(k) be the first derivative of -3*k**5/20 - 3*k**4/8 + k**3/4 + 3*k**2/4 + 95. Let u(h) = 0. Calculate h.
-2, -1, 0, 1
Let m be 0*((18/12 - -1) + -3). Factor m + 2/3*k**2 + 2/9*k**3 + 4/9*k.
2*k*(k + 1)*(k + 2)/9
Suppose 0 = 38*r - 43 - 109. Factor 4/5*t**r + 0*t**3 + 2/5*t - 4/5*t**2 - 2/5*t**5 + 0.
-2*t*(t - 1)**3*(t + 1)/5
Let r = 49 + -55. Let p be (3/9)/((-4)/r). Solve -2*t**4 - 7/2*t**3 - t**2 + p*t + 0 = 0 for t.
-1, 0, 1/4
Let t(n) = -n**3 - n**2 - n + 1. Let h(s) = -15*s**3 - 20*s**2 - 5. Suppose -4*u = 16 - 12. Let y(d) = u*h(d) - 5*t(d). Factor y(w).
5*w*(w + 1)*(4*w + 1)
Let o = 1/6 + 157/6. Let x = o - 25. Determine n, given that x*n + 1/3*n**2 + 4/3 = 0.
-2
Solve -4*x - 8/3*x**2 + 8/3*x**4 - 4/3*x**5 + 16/3*x**3 + 0 = 0.
-1, 0, 1, 3
Suppose -4*i - 92 = -27*i. Let k(v) be the second derivative of 0*v**3 + 1/5*v**5 + 0 - 1/4*v**2 + v + 1/20*v**6 + 1/4*v**i. Suppose k(n) = 0. What is n?
-1, 1/3
Let v(j) be the first derivative of 2*j**5/85 + 38*j**4/17 + 2888*j**3/51 + 801. Factor v(d).
2*d**2*(d + 38)**2/17
Let y(a) = 4*a - 10. Let b be y(3). Let g be b*(-57)/(-90) + 4/(-6). Solve 1/5*q + 0 + 3/5*q**3 - g*q**2 - 1/5*q**4 = 0.
0, 1
Let d(m) be the second derivative of 4*m**7/63 - 4*m**6/9 + 11*m**5/10 - m**4 + 2*m + 2. Factor d(q).
2*q**2*(q - 2)*(2*q - 3)**2/3
Let p(c) = 2*c**2 - 49*c - 57. Let h be p(26). Let t be 6/h*(-4)/(-4). Determine v so that t + 3/7*v**2 - v = 0.
1/3, 2
Let u(z) be the second derivative of 1/6*z**6 - 5/14*z**7 + 1/2*z**5 + 0*z**3 + 0*z**4 + 0*z**2 + 0 - 2*z. Factor u(j).
-5*j**3*(j - 1)*(3*j + 2)
Suppose 4*o - 5 = 15. Let t(d) = -2*d + 12. Let n be t(o). Factor -c**2 - 3*c**n - 1 + 7 - 2.
-4*(c - 1)*(c + 1)
Solve -113*n**2 - 162*n - n**4 - 256 + 20*n**3 + 482*n - 19*n**2 = 0 for n.
2, 8
What is k in 340/3*k - 2/3*k**2 - 14450/3 = 0?
85
Let a(w) = 3*w**3 + 56*w**2 + 2*w - 51. Let i(b) = -2*b**3 - 28*b**2 + 26. Let n(l) = -2*a(l) - 5*i(l). Factor n(t).
4*(t - 1)*(t + 1)*(t + 7)
Let k be ((-8)/5)/(-1 + (-276)/(-280)). Determine c, given that -36*c**4 - 71*c**4 + 332*c**3 + k*c - 73*c**4 - 16 - 284*c**2 + 36*c**5 = 0.
1/3, 2/3, 1, 2
Factor 0 - 4/3*s + 1/3*s**2.
s*(s - 4)/3
Factor 2/3*u**4 + 0 - 26/3*u**2 - 2*u**3 + 10*u.
2*u*(u - 5)*(u - 1)*(u + 3)/3
Let d(s) be the third derivative of -9*s**2 + 0 - 1/105*s**5 + 0*s + 1/21*s**4 - 2/21*s**3. Find i, given that d(i) = 0.
1
Suppose 0 = -3*u + 6, w + w = -4*u + 234. Let o = w - 111. Factor 3/2*h**o - 3/2*h**4 + 3/2*h**5 + 0*h - 3/2*h**3 + 0.
3*h**2*(h - 1)**2*(h + 1)/2
Solve 10/3*a**3 - 8/3*a + 0*a**4 + 0*a**2 + 0 - 2/3*a**5 = 0.
-2, -1, 0, 1, 2
Let s(d) be the second derivative of d**6/24 + 3*d**5/20 - d**4/48 - d**3/2 - d**2/2 - 292*d. Solve s(f) = 0.
-2, -1, -2/5, 1
Let x(h) be the third derivative of 14*h**2 - 1/96*h**4 + 0*h**3 + 1/48*h**5 - 7/480*h**6 + 0*h + 0 + 1/280*h**7. What is u in x(u) = 0?
0, 1/3, 1
Let z(s) = -605*s - 18610. Let b(k) = -k**2 + 604*k + 18611. Let h(v) = 5*b(v) + 6*z(v). Factor h(q).
-5*(q + 61)**2
Let m(u) = -u**2 + 4*u + 14. Let o be m(6). Factor 11*c**o - 16*c**2 + 3 - 3 + 15*c.
-5*c*(c - 3)
What is f in -2/3*f**2 + 50/3*f - 44 = 0?
3, 22
Suppose -36/7*p**2 - 39/7*p + 6*p**3 - 3/7*p**5 + 0 + 36/7*p**4 = 0. What is p?
-1, 0, 1, 13
Let m(a) be the first derivative of -a**9/15120 + a**8/4200 - a**6/900 + a**5/600 + a**3/3 + 2. Let k(q) be the third derivative of m(q). Factor k(w).
-w*(w - 1)**3*(w + 1)/5
Let u(t) = t**2 - 10*t - 2. Let y be u(-3). Let k = 37 - y. Solve 1/5*q**5 + 2/5*q**4 + k - 1/5*q + 0*q**3 - 2/5*q**2 = 0.
-1, 0, 1
Let a(z) = -31*z**4 + 48*z**3 - 120*z**2 + 103*z - 45. Let n(w) = 7*w**4 - 12*w**3 + 30*w**2 - 26*w + 11. Let x(b) = -2*a(b) - 9*n(b). What is o in x(o) = 0?
1, 9
Suppose 2/7*p**2 - 2/7*p**3 + 6/7 + 10/7*p = 0. What is p?
-1, 3
Let u(m) be the third derivative of -6*m**2 - 1/3*m**4 - 1/30*m**6 + 0*m + 0*m**3 - 1/5*m**5 + 0. What is i in u(i) = 0?
-2, -1, 0
Let b(r) = 13*r**3 + 3311*r**2 - 181500*r + 3327500. Let m(a) = -2*a**3 - 662*a**2 + 36300*a - 665500. Let l(z) = 2*b(z) + 11*m(z). Factor l(q).
4*(q - 55)**3
Suppose -8*j + 18 = -14. Factor 4*k - 