). Find t such that 1/4 + 3/4*t + s*t**3 + 3/4*t**2 = 0.
-1
Suppose -3*y + 936 = -3*k, -k = -y - 4*k + 320. Let o = y - 5336/17. Factor 4/17*l - 6/17*l**2 + o.
-2*(l - 1)*(3*l + 1)/17
Let r(b) be the first derivative of -4*b**5/5 - 4*b**4 + 20*b**3/3 - 291. Factor r(v).
-4*v**2*(v - 1)*(v + 5)
Let l(a) be the second derivative of 19 + a + 1/10*a**6 - 7/12*a**4 - 1/42*a**7 + 0*a**3 + 2*a**2 + 1/20*a**5. Factor l(k).
-(k - 2)**2*(k - 1)*(k + 1)**2
Factor -5*w**5 + 7*w**5 + 39*w**4 + 39*w**4 + 92*w**3 + 16*w**4.
2*w**3*(w + 1)*(w + 46)
Factor -160/7 - 4/7*q + 2/7*q**2.
2*(q - 10)*(q + 8)/7
Let 0 + 123/4*k**2 - 15/4*k**4 - 45/2*k - 21/4*k**3 + 3/4*k**5 = 0. What is k?
-3, 0, 1, 2, 5
Let z be 5 - (6 - (2 + 42)). Factor -6 - z*o**2 - 3*o**3 + 8*o**2 + 9*o + 35*o**2.
-3*(o - 1)**2*(o + 2)
Suppose -11*f - 749 = -892. Suppose 3*s - f + 4 = 0. Factor -44/3*g**2 + 20/3 - 10/3*g**s + 34/3*g.
-2*(g - 1)*(g + 5)*(5*g + 2)/3
Let m(s) be the second derivative of 47/24*s**4 - 41/40*s**5 - 1/84*s**7 - 3/2*s**3 + 0 + 0*s**2 + 13/60*s**6 + 7*s. Suppose m(k) = 0. Calculate k.
0, 1, 2, 9
Let a(f) = -2*f**2 + 9*f + 1. Let x(d) = -23*d**2 + 1011*d - 892. Let b(l) = 12*a(l) - x(l). Determine c so that b(c) = 0.
-904, 1
Let g(k) = 95*k**3 + 1725*k**2 - 216025*k + 8639975. Let j(i) = -4*i**3 + 3*i**2 + i + 1. Let c(n) = -g(n) - 25*j(n). Find o such that c(o) = 0.
120
Let g(l) be the first derivative of -1/24*l**4 + 0*l + 0*l**2 + 0*l**3 + 128. Determine c, given that g(c) = 0.
0
Let x(i) = i**3 + 8*i**2 + 11*i - 3. Suppose 5*d + 162 = 132. Let r be x(d). Find s such that 0 + 0*s - 3/5*s**2 - 3/5*s**4 - 6/5*s**r = 0.
-1, 0
Let h = -1791/11 - -656. Let d = h - 493. Factor 14/11*g - d*g**2 + 0.
-2*g*(g - 7)/11
Let i = 77581/30 - 2586. Let a(l) be the second derivative of 0*l**2 - 1/8*l**5 + 0*l**3 + 1/12*l**4 + i*l**6 + 0 - 12*l. Factor a(n).
n**2*(n - 2)*(2*n - 1)/2
Let p(y) be the third derivative of 0*y + 1/120*y**4 - 9 - 4/15*y**3 + 3*y**2 - 1/600*y**6 + 2/75*y**5. Solve p(u) = 0 for u.
-1, 1, 8
Suppose 0 = 9*g + 205 + 92. Let f be 7 - (-253)/g - 14/(-3). Factor f*a + 10*a**2 + 2/5.
2*(5*a + 1)**2/5
Let v be (-1)/10*(-260 + 270)*-4. Factor -4/21 - 6/7*m**2 - 2/3*m - 2/21*m**v - 10/21*m**3.
-2*(m + 1)**3*(m + 2)/21
Let m(v) be the first derivative of 3*v**5/140 + 3*v**4/28 + v**3/7 - 147*v - 101. Let b(q) be the first derivative of m(q). Suppose b(l) = 0. What is l?
-2, -1, 0
Let u(b) be the third derivative of 2*b**6/15 - 11*b**5/5 + 28*b**4/3 - 8*b**3 - 55*b**2 - 11. Factor u(f).
4*(f - 6)*(f - 2)*(4*f - 1)
Let w(j) be the third derivative of -13*j**8/1680 + 2*j**7/45 - j**6/45 - 157*j**4/24 - 83*j**2 - 2. Let l(x) be the second derivative of w(x). Factor l(b).
-4*b*(b - 2)*(13*b - 2)
Let p be 2/30 - (126/(-6) + 62450/3000). Find h, given that -p*h**2 - 5/2 + 7/4*h = 0.
2, 5
Suppose -5*b + 30 + 48 = u, -b + 2*u + 20 = 0. Solve -3*x - 40*x**3 - 3 + 38*x**2 - b + 42*x**3 + x - 19 = 0 for x.
-19, -1, 1
Let l(d) be the first derivative of d**5/60 + 2*d**4/9 + 13*d**3/18 + d**2 + 144*d - 303. Let b(a) be the first derivative of l(a). Let b(z) = 0. What is z?
-6, -1
Let l be (23 + (-3441)/155)*5*2. Let k(z) be the first derivative of l*z + 1 - 2*z**2 - 4/3*z**3. Factor k(f).
-4*(f - 1)*(f + 2)
Let r(l) be the third derivative of l**8/560 + 2*l**7/63 + l**6/15 + 5*l**4/8 + 2*l**3/3 + 48*l**2. Let y(m) be the second derivative of r(m). Factor y(k).
4*k*(k + 6)*(3*k + 2)
Let z be (-4)/(-39) - (-38674)/9516. Let 10/3*k**2 - z*k - 5/6*k**3 + 5/3 = 0. Calculate k.
1, 2
Let n(y) be the third derivative of y**6/480 - y**5/15 - 31*y**4/24 - 22*y**3/3 - 5*y**2 + 35*y. Factor n(i).
(i - 22)*(i + 2)*(i + 4)/4
Let y(s) = -s**3 + 4*s**2 + 77*s. Suppose -708 + 543 = -15*b. Let r be y(b). Factor r*k - 2/7*k**2 + 1/7*k**3 + 0.
k**2*(k - 2)/7
Let w be (4*1 + ((-24080)/(-176))/(-35))/((-2)/(-11)). Let 0 - 1/2*b + w*b**2 = 0. What is b?
0, 1
Let c be 5*1/(40/(-96)). Let a be c/(-28) + (96/(-42))/(-8). What is g in 5/7*g**3 + 4/7 - 3/7*g**2 - 1/7*g**4 - a*g = 0?
-1, 1, 4
Factor -2/3*u**2 + 98/3*u - 172.
-2*(u - 43)*(u - 6)/3
Let y(x) be the second derivative of -x**4/18 + 80*x**3/9 + 27*x**2 + 429*x. Suppose y(r) = 0. Calculate r.
-1, 81
Let d be -3 + 9*-5 + -3. Let k = d + 144. What is z in z**3 + k - 93 = 0?
0
Suppose 120 = 8*g - 216. Suppose 9*y = -24 + g. Factor -3/4 + 5/4*r - 1/4*r**y - 1/4*r**3.
-(r - 1)**2*(r + 3)/4
Let h(t) be the third derivative of 0*t + 3/10*t**5 + 5/8*t**4 + 0 + 135*t**2 + 1/140*t**7 + 3/40*t**6 + 3/4*t**3. Let h(v) = 0. Calculate v.
-3, -1
Factor -720/13 - 2/13*i**2 - 6*i.
-2*(i + 15)*(i + 24)/13
Let x(l) be the second derivative of 5*l**7/42 - 37*l**6/6 - 81*l**5/2 - 215*l**4/6 + 805*l**3/6 + 615*l**2/2 - 552*l. Find m such that x(m) = 0.
-3, -1, 1, 41
Let d be -30*4/20*5/(-26). Let z = d + -77/78. Let 2/3*x**2 - 2/3 + 1/6*x**3 - z*x = 0. Calculate x.
-4, -1, 1
Let f be (378/105)/((-3)/(-2))*5. Let c be ((-33)/(-6) + -3)/(2/f). What is x in 46*x + x**3 - 22*x - c*x + 6*x**2 = 0?
-3, 0
Let v = -9/394 - -2575/121352. Let j = 2459/3080 - v. Find a such that -2/5*a**2 + j - 2/5*a = 0.
-2, 1
Let k(r) be the first derivative of 55/3*r**3 + 107/12*r**4 + 1/9*r**6 + 8*r + 107/6*r**2 + 9/5*r**5 + 157. Let k(t) = 0. What is t?
-8, -3, -1, -1/2
Let b = 128433/5714 - -66/2857. Solve -10 - b*o**2 - 5/4*o**4 - 25*o - 35/4*o**3 = 0.
-2, -1
Let c = 1/129 + 341/387. Suppose 3*h = d - 6, -h = 3*d - 5230 + 5192. Factor -c*f**h + 0 - 16/9*f + 4/9*f**3 + 2/9*f**4.
2*f*(f - 2)*(f + 2)**2/9
Suppose 105*n - 163 = 152. Let d(p) be the second derivative of 0*p**4 + 0*p**2 + 16*p - 2/3*p**n + 1/20*p**5 + 0. Solve d(m) = 0.
-2, 0, 2
Let d(x) be the second derivative of 1/84*x**7 - 1/4*x**3 + 9*x + 0*x**6 + 0*x**2 - 1/3*x**4 + 0 - 3/20*x**5. Factor d(w).
w*(w - 3)*(w + 1)**3/2
Suppose 0 = -5*d + 10. Let h = 4 - d. Factor -l**2 + 6*l - l - h*l**2 - 2*l.
-3*l*(l - 1)
What is l in 16360*l + 261*l**4 + 4453 + 1007 + 4119*l**2 - 271*l**4 + 2685*l**3 + 8106*l**2 = 0?
-2, -1/2, 273
Let t(r) be the third derivative of r**5/140 - 79*r**4/28 + 157*r**3/14 - 4424*r**2. Factor t(l).
3*(l - 157)*(l - 1)/7
Let d be 3/14 - (-12)/(-56). Let o(y) be the first derivative of d*y**2 - 3/4*y**4 - 3*y**3 + 12*y - 10. Find z, given that o(z) = 0.
-2, 1
Suppose -3*d + j - 32 = 0, 3*d - 5*j - 40 = 8*d. Let g be (d/6)/5 - (0 + -1). Factor g + 1/6*z**2 - 2/3*z.
(z - 2)**2/6
Factor 54*q**4 - 84*q**3 + 60*q**4 + 155*q**4 - 34*q**3 + 28*q**4 - 5*q**5.
-q**3*(q - 59)*(5*q - 2)
Let b(i) be the third derivative of 5*i**8/336 + 11*i**7/42 + 7*i**6/4 + 16*i**5/3 + 20*i**4/3 - 10*i**2 - 38. Determine z so that b(z) = 0.
-4, -2, -1, 0
Suppose -108 = -4*z - 58*z + 78. Let k(n) be the second derivative of 0*n**2 - 1/18*n**4 + 0 + 20*n - 1/135*n**6 + 1/30*n**5 + 1/27*n**z. Factor k(d).
-2*d*(d - 1)**3/9
Let q(x) be the third derivative of -x**8/1008 - 11*x**7/180 - 62*x**6/45 - 4757*x**5/360 - 1385*x**4/36 - 425*x**3/9 + 12931*x**2. Find f, given that q(f) = 0.
-17, -10, -1, -1/2
Let p be 7/5 + 2/2. Suppose 1747*m + 61 + 17 = 1786*m. Factor -3/5*a**m - p + 3*a.
-3*(a - 4)*(a - 1)/5
Determine z so that -5*z**2 + 75*z**3 + 79289*z**5 + 5*z**2 - 80*z**4 - 79284*z**5 = 0.
0, 1, 15
Let s = 12/23 - -284/161. Suppose 0 = -109*x + 78*x + 313*x. Find f, given that -s*f**3 - 2/7*f**5 + 8/7*f**2 + 10/7*f**4 + x*f + 0 = 0.
0, 1, 2
Let z be (-4)/((-282)/225 + (-56)/700). Solve -145/3*u**2 - 125/6 + 1/6*u**5 - 17/6*u**4 + 325/6*u + 53/3*u**z = 0.
1, 5
Let r = -719 - -729. Suppose -2 = -x + 63*s - 59*s, 0 = 5*x - s - r. Factor 2/7*h - 2/7*h**3 - 2/7*h**x + 0 + 2/7*h**4.
2*h*(h - 1)**2*(h + 1)/7
Let v(r) = -9*r**2 + 546*r - 495. Let j(i) = -8*i**2 + 537*i - 494. Let w(l) = -6*j(l) + 5*v(l). Find a such that w(a) = 0.
1, 163
Let g be ((-15)/(-10))/(1/4). Suppose -16860 = 90*f - 100*f. Suppose 2*t**5 + g*t**2 + 6*t - 8*t**3 + 1682*t**4 - f*t**4 - 2*t**2 = 0. What is t?
-1, 0, 1, 3
Let t be 4/(-3) - -1 - (-9712)/48. Factor t*a**4 + 33*a**2 - 142 + 36*a - 5*a**3 - a**3 - 205*a**4 + 34.
-3*(a - 2)**2*(a + 3)**2
Let t = 1419095/2005031 + -92/24157. Let o = t + -11/83. Factor -4/7*l**3 + 2/7*l**4 + o*l - 2/7*l**2 + 0.
2*l*(l - 2)*(l - 1)*(l + 1)/7
Let i(c) = -6*c**3 - 6*c**2 - 2*c. Let d(n) = -15*n**3 - 447*n**2 + 1322*n - 888. Let p(g) = d(g) - 2*i