y**2 - t*y**2 - y**2 + 4 + 2*y**2 - 4*y = 0.
2
Factor 198/7 + 2/7*k**2 - 72/7*k.
2*(k - 33)*(k - 3)/7
Let y(d) be the second derivative of -d**5/4 - 85*d**4/12 + 5*d**3/6 + 85*d**2/2 + 299*d. Suppose y(z) = 0. What is z?
-17, -1, 1
Let b = -549/16192 - -1749991/12095424. Let q = b + 1/2988. Factor 13/9*k + 7/9*k**2 - 1/9*k**3 + 2/3 - q*k**4.
-(k - 3)*(k + 1)**2*(k + 2)/9
Let m(k) be the third derivative of 97*k**2 - 1/30*k**5 - 1/24*k**4 + 0 + 1/120*k**6 + 1/3*k**3 + 0*k. Let m(p) = 0. What is p?
-1, 1, 2
Find m such that -86/3 + 10/3*m**2 + 428/3*m = 0.
-43, 1/5
Let j = -1368 + 2737/2. Let i(m) be the first derivative of -5 + 1/9*m**3 - j*m**2 + 2/3*m. Solve i(p) = 0 for p.
1, 2
Let x(w) be the third derivative of -w**6/30 + 1178*w**5/15 - 2353*w**4/6 + 784*w**3 + 353*w**2 - 2*w + 5. Factor x(f).
-4*(f - 1176)*(f - 1)**2
Let w(x) = 46*x**2 + 2774*x + 2728. Let z(o) = -9*o**2 - 555*o - 546. Let u(i) = -5*w(i) - 26*z(i). Let u(k) = 0. Calculate k.
-139, -1
Let n = -57354 - -172066/3. Determine i, given that 2*i**3 + 0 + 1/3*i**4 + 3*i**2 + n*i = 0.
-4, -1, 0
Factor 3/5*o**2 - 249/5 - 246/5*o.
3*(o - 83)*(o + 1)/5
Let l be (-420)/(-441)*4*36/96. Solve 0 - l*h**2 + 1/7*h**3 + 25/7*h = 0.
0, 5
Let q be 3 + 27*(-74)/(-3). Factor 192 + q*z**2 - 336*z**2 - 48*z - 330*z**2.
3*(z - 8)**2
Let f(w) = 1494*w**3 + 1638*w**2 + 104*w - 80. Let l(j) = 499*j**3 + 546*j**2 + 35*j - 27. Let d(g) = 3*f(g) - 8*l(g). Factor d(c).
2*(c + 1)*(7*c + 2)*(35*c - 6)
Let n(y) be the third derivative of 0*y + 7/144*y**4 - 1/720*y**6 - 49*y**2 + 0*y**3 + 0 + 1/60*y**5. Suppose n(j) = 0. Calculate j.
-1, 0, 7
Suppose 0 = 3*z - 0 - 24. Let h(b) = 110*b - 218. Let m be h(2). Factor -12*d + 4 - z*d**2 + 2*d**2 + m*d.
-2*(d + 2)*(3*d - 1)
Suppose 4*r + 2*m = m + 7, -5*m - 28 = -r. Factor -2 - 4*n**4 + n**2 + 2*n**4 + 7*n**2 + n**5 - 7*n + 4 - 2*n**r.
(n - 1)**4*(n + 2)
Factor 10*z + 43 - 96 - 41*z**2 + 22*z + 45*z**2 - 79.
4*(z - 3)*(z + 11)
Let q(l) be the third derivative of -l**7/1890 + 119*l**6/1080 + l**5/180 - 359*l**4/216 + 119*l**3/27 + 229*l**2. Determine y, given that q(y) = 0.
-2, 1, 119
Let n(i) = 45*i**3 - 2765*i**2 + 16400*i - 24570. Let z(x) = 8*x**3 - x**2 - 5*x. Let f(h) = -n(h) + 5*z(h). Let f(d) = 0. What is d?
3, 546
Let s(u) = -u**4 + 728*u**3 + 2193*u**2 + 2189*u + 728. Let l(a) = -a**3 - 2*a**2 - 4*a - 2. Let h(o) = -3*l(o) + s(o). Factor h(i).
-(i - 734)*(i + 1)**3
Let g(q) be the second derivative of q**4/78 - 527*q**3/39 + 1050*q**2/13 - 290*q + 2. Let g(b) = 0. Calculate b.
2, 525
Suppose a = -5*i + 137, 0 = -3*i - 3*a + a + 78. Suppose i*m = 27*m + 252. What is h in 6*h**4 - 4*h**5 + 16*h**2 - 24*h**3 + 10*h**4 + 248*h - m*h = 0?
0, 1
Find v, given that -32/17*v**4 + 352/17*v**3 + 386/17*v**2 - 22/17*v - 24/17 = 0.
-1, -1/4, 1/4, 12
Let w(b) be the third derivative of -b**7/105 - 19*b**6/20 - 73*b**5/6 - 253*b**4/4 - 150*b**3 + 2*b**2 + 15. What is h in w(h) = 0?
-50, -3, -1
Let x(i) be the second derivative of i**8/3360 - 5*i**7/168 + 125*i**6/144 + 43*i**3/3 + 2*i + 7. Let r(m) be the second derivative of x(m). Factor r(t).
t**2*(t - 25)**2/2
Let r(k) = -k**3 - 43*k**2 - 296*k - 305. Let d be r(-7). Factor 0*z + 0 + 5/4*z**4 - 7/4*z**d + 3/4*z**2 - 1/4*z**5.
-z**2*(z - 3)*(z - 1)**2/4
Let x(m) be the first derivative of -m**6/2 + 39*m**5/5 + 195*m**4/4 + 51*m**3 + 9548. Let x(j) = 0. Calculate j.
-3, -1, 0, 17
Suppose 0 = -5*j + 10*j + 45. Let r(v) = v**3 + 11*v**2 + 18*v + 8. Let y be r(j). Solve -4*h**3 + y - 3*h**2 + 4*h - h**2 + 2 - 6 = 0 for h.
-1, 1
Let o(l) be the first derivative of -l**4/28 - 2*l**3/7 + l**2/2 - 12336. Factor o(g).
-g*(g - 1)*(g + 7)/7
Suppose 72*v = 71*v + 4. Factor -89*a**3 - 2*a**v - 13*a + 20*a**2 - 3*a + 87*a**3.
-2*a*(a - 2)*(a - 1)*(a + 4)
Let n(j) be the second derivative of -j**4/60 - 191*j**3/30 + 98*j**2 - 13825*j. Let n(h) = 0. What is h?
-196, 5
Let o(a) be the third derivative of a**5/20 + 47*a**4/8 + 273*a**3 - 8310*a**2. Let o(j) = 0. What is j?
-26, -21
Determine j so that 715*j**3 + 44*j**4 - 143*j - 747*j**3 + 3*j**5 + 17*j - 5*j**5 - 204*j**2 = 0.
-1, 0, 3, 21
Let i(l) be the first derivative of 3*l**4/4 + 828*l**3 + 257094*l**2 - 413. Factor i(t).
3*t*(t + 414)**2
Let r(w) = -2*w**2 - 45*w - 9. Let q be r(-22). Let a = 54 - q. Suppose -115*b**2 + 16*b + 44*b**3 - 22*b**2 + a*b**2 = 0. Calculate b.
0, 2/11, 2
Let n(p) be the first derivative of p**5/40 - 9*p**4/16 + 65*p**2/2 - 71. Let o(m) be the second derivative of n(m). What is g in o(g) = 0?
0, 9
Let w(l) be the first derivative of l**3/9 + 66*l**2 - 397*l/3 - 4295. Factor w(j).
(j - 1)*(j + 397)/3
Let k(r) be the first derivative of 7 - 16/7*r**4 + 32/7*r - 48/7*r**2 - 1/21*r**6 + 16/3*r**3 + 18/35*r**5. Factor k(d).
-2*(d - 2)**4*(d - 1)/7
Let j(p) be the second derivative of 0 + 1/3*p**4 + 4/3*p**2 - p**3 - 1/30*p**5 + 224*p. Find k, given that j(k) = 0.
1, 4
Let h = -18 + 21. Suppose h*n + q = -2*n + 14, 8 = 2*q. Factor -x**3 + 3*x**n - 39*x + x**2 + 43*x - x**4.
-x*(x - 2)*(x + 1)*(x + 2)
Suppose m - 5*i - 49 + 22 = 0, -3*i = -m + 17. Find z such that -6/5*z**3 - 8/5*z**m + 0 + 8/15*z + 14/15*z**4 = 0.
-1, 0, 2/7, 2
Let p be (3302/455 - 7)*21/18. Let a(w) be the second derivative of -1/105*w**7 + 0*w**2 - p*w**5 + 20*w - 3/25*w**6 + 0 + 0*w**3 + 5/6*w**4. Solve a(t) = 0.
-5, 0, 1
Let j be 8/(-24) - 48631/(-26598). Let i = j - -2/403. Solve 0 + i*l - 3/4*l**3 + 9/4*l**4 - 9/4*l**2 - 3/4*l**5 = 0.
-1, 0, 1, 2
Suppose 2/11*h**5 + 12/11 - 12/11*h**3 - 4/11*h**4 - 38/11*h + 40/11*h**2 = 0. Calculate h.
-3, 1, 2
Determine t, given that 45*t + 91/2 - 1/2*t**2 = 0.
-1, 91
Let 210/17*n**3 + 2/17*n**5 + 0 + 0*n - 216/17*n**4 + 428/17*n**2 = 0. What is n?
-1, 0, 2, 107
Let i be (-3 - (-4)/1 - 3)/(264/(-11)). Let g(q) be the third derivative of -30*q**2 + 0*q + 1/24*q**4 - 1/120*q**5 - i*q**3 + 0. What is m in g(m) = 0?
1
Let t(a) be the third derivative of -a**6/60 + 103*a**5/210 + 67*a**4/21 + 68*a**3/21 + 416*a**2. Find w such that t(w) = 0.
-2, -2/7, 17
Let v(s) be the third derivative of -32/9*s**3 + 0*s**4 + 0*s + 1/45*s**5 - 294*s**2 + 0. Suppose v(r) = 0. What is r?
-4, 4
Let h(u) be the third derivative of u**7/70 + 3*u**6/5 + 21*u**5/20 - 23*u**4/4 - 803*u**2 - 1. Suppose h(b) = 0. Calculate b.
-23, -2, 0, 1
Let t(q) be the third derivative of -q**5/330 - 7*q**4/11 + 85*q**3/33 - 82*q**2. Factor t(d).
-2*(d - 1)*(d + 85)/11
Let v(r) = 28*r**5 + 8*r**4 + 320*r**3 + 292*r**2 - 24*r. Let z(d) = 2*d**5 - 5*d**4 + 3*d**2 - 2*d. Let q(i) = -v(i) + 12*z(i). Factor q(w).
-4*w**2*(w + 1)*(w + 8)**2
Let c be (-12)/(-54)*126/(-70) + 1066/1040. Find h such that -21/8*h**2 - 1/2 - 7/8*h**3 + c*h**4 + 3/8*h**5 - 2*h = 0.
-1, -2/3, 2
What is u in 69*u**2 - 123*u**2 + 64*u**2 - 35*u**3 - 250*u**4 - 40*u**3 = 0?
-2/5, 0, 1/10
Suppose -2*g = 4*d - 34, 20 = 5*d - 4*g - 29. Solve -52 + 282*m - 13*m**2 - d*m**2 + 44*m**2 = 0 for m.
-13, 2/11
Let y(k) be the first derivative of 361*k**4/32 + 95*k**3 + 693*k**2/16 + 27*k/4 + 1789. What is s in y(s) = 0?
-6, -3/19
Let h be (4/(-6))/(4/(-138)). Suppose 25*a - h*a - 8 = 0. Factor 3*c**3 + 0*c**2 - 8*c**a + 2*c**3 - 8*c + 8*c**2 + 2*c**5 + c**3.
2*c*(c - 2)**2*(c - 1)*(c + 1)
Let d(q) be the third derivative of -5/3*q**4 + 0*q**3 + 0*q - 1/300*q**6 + 0 - 101*q**2 - 2/15*q**5. Determine u so that d(u) = 0.
-10, 0
Let o(t) be the third derivative of -t**6/32 - 39*t**5/80 + 53*t**4/32 - 9*t**3/8 - t**2 - 1828. Solve o(x) = 0.
-9, 1/5, 1
Suppose 3890 = -5*l + 5*p, -58*l + 57*l = -5*p + 762. Let r = l - -802. Suppose -56/5*t**2 - 22*t - 6/5*t**3 + r = 0. Calculate t.
-5, 2/3
Suppose 0*t - 4/9*t**3 + 0 - 2/9*t**4 - 2/9*t**2 = 0. Calculate t.
-1, 0
Let x be 2 + (1465/335 - 7). Let z = x - -285/134. Let 3/2*c**2 - 1/2*c - z + 1/2*c**3 = 0. Calculate c.
-3, -1, 1
Let s be 195/(-20) + 75 + -67 + 15/4. Solve 0*h**s - 2*h + 1/6*h**3 - 8/3 = 0 for h.
-2, 4
Let j(q) be the first derivative of 4/3*q + 1/12*q**4 - 4/9*q**3 - 1/6*q**2 + 89. Factor j(r).
(r - 4)*(r - 1)*(r + 1)/3
Let g = 59 + 1. Suppose -5*i - 45 + g = 0. Solve -c**4 - c + c**2 + 3*c + c**5 + 0*c - 3*c**i = 0 for c.
-1, 0, 1, 2
Let l be ((-238)/1071)/(8/(-144)). Factor -7/2*r**3 + l + 9*r**2 - 10*r + 1/2*r**4.
(r - 2)**3*(r - 1)/2
Let k(n) be the first derivative of -2