 + 33)
Solve 473 - 542*x + 1802*x + 415*x**3 - 416*x**3 + 312*x**2 + 791 = 0 for x.
-2, 316
Let g(b) = 2*b**2 + 39*b + 394. Let j(t) = t**2 + 40*t + 396. Let k(f) = -2*g(f) + 3*j(f). Factor k(l).
-(l - 50)*(l + 8)
Let y(z) be the second derivative of 1/18*z**4 + 10/9*z**3 + 0*z**2 + 63*z + 1. Factor y(h).
2*h*(h + 10)/3
Let x = 3 - -4. Let m(y) = y**3 - 7*y**2 + 3*y - 14. Let d be m(x). Factor -5 - 4 + 3*p**3 - 2*p**2 + 7 - d*p.
(p - 2)*(p + 1)*(3*p + 1)
Let v(f) be the third derivative of 0*f + 1/90*f**6 + 1/5*f**5 - 7/6*f**4 - 37/6*f**3 + 0 + 34*f**2. Let x(j) be the first derivative of v(j). Factor x(w).
4*(w - 1)*(w + 7)
Let 1/2*h**2 + 16*h - 450 = 0. What is h?
-50, 18
Suppose 0 = 184*c - 264*c + 240. Let w(l) be the first derivative of 27 - 2*l - 3*l**c + 11/2*l**2. Factor w(f).
-(f - 1)*(9*f - 2)
Let a(g) be the second derivative of 0*g**2 + 3/80*g**5 + 0*g**3 - 5/16*g**4 + 1 + 27*g. Factor a(r).
3*r**2*(r - 5)/4
Let a(g) be the second derivative of g**5/60 - g**4/4 + 4*g**3/3 - 40*g**2 + 69*g. Let z(v) be the first derivative of a(v). Let z(s) = 0. Calculate s.
2, 4
Let d(x) be the first derivative of -x**4/12 + x**3/3 + 60*x**2 + 2300*x/3 - 3601. Solve d(p) = 0.
-10, 23
Suppose 0 = -104*f + 100*f + 4*z, -5*z = 5*f - 20. Suppose -2 = 22*x - f. Factor -1/8*a + 1/8*a**3 + x*a**2 + 0.
a*(a - 1)*(a + 1)/8
Let m(t) be the third derivative of 9*t**3 + 0 - t**2 - 1/2*t**4 + 1/90*t**5 - 15*t. Factor m(w).
2*(w - 9)**2/3
Let m(g) be the second derivative of -2*g**7/105 - 8*g**6/25 - 6*g**5/5 - 28*g**4/15 - 6*g**3/5 + 10761*g. Determine u so that m(u) = 0.
-9, -1, 0
Let o(p) be the third derivative of -51*p**2 + 0*p - 2*p**3 - 1/120*p**6 + 1/12*p**5 + 1/3*p**4 + 0. Find g, given that o(g) = 0.
-2, 1, 6
Suppose -27907 = 11*n - 27940. Suppose -1/8*z**n + 0 + 0*z + 0*z**2 - 1/8*z**4 = 0. What is z?
-1, 0
Suppose -q - 8 = -5*q. Solve 87*r**5 + 36*r**3 - 29*r**5 - 100*r + 6*r**5 + 212*r**q - 224*r**4 + 12 = 0.
-1, 1/4, 1, 3
Suppose -2*w = 5*n - 5, -6*n + 4*n - 12 = -2*w. Suppose 35*f**4 - 63*f**4 + w*f**2 - 45*f**3 - 22*f**4 = 0. What is f?
-1, 0, 1/10
Let j(t) = -2*t - 16. Let h be j(-8). Suppose -4*d - 4273 + 4289 = h. Factor -3/2 - 1/2*m**d - 6*m**2 + 5*m + 3*m**3.
-(m - 3)*(m - 1)**3/2
Let y(m) be the first derivative of 1/3*m + 49 - 1/12*m**2 - 1/18*m**3. Factor y(f).
-(f - 1)*(f + 2)/6
Let t be (1 + 20/7)*(22 + (-5500)/264). Factor -t*c**2 + 0*c + 6*c**3 + 0 - 3/2*c**4.
-3*c**2*(c - 3)*(c - 1)/2
Suppose 8*z - 7*z - 691 = 4*h, -8*z - 3*h + 5388 = 0. Let i(s) be the first derivative of 19 - z*s - 3*s**3 + 135/2*s**2 + 1/20*s**4. Factor i(r).
(r - 15)**3/5
Let k(m) be the second derivative of -m**8/504 + m**7/63 - 2*m**6/45 + 2*m**5/45 + 161*m**2/2 + 2*m - 7. Let s(h) be the first derivative of k(h). Factor s(f).
-2*f**2*(f - 2)**2*(f - 1)/3
Let v = 98 - 12. Let h = 96 - v. Factor -l - 12*l**3 - 9*l**4 + 3*l**4 - 14*l**5 + 13*l**5 - 2*l - h*l**2.
-l*(l + 1)**3*(l + 3)
Suppose 2*w = 8 + 2. Let g be (w + -1)/4 + 1. Factor 15*y - 4*y**3 - g*y**3 + 3*y**3 - 2*y**3 + 10*y**2.
-5*y*(y - 3)*(y + 1)
Determine u so that -32 + 920/3*u + 402*u**3 - 2456/3*u**2 - 54*u**4 = 0.
2/9, 3, 4
Let h = -971 + 815. Let x = h + 627/4. Suppose x*p + 0 - 3/2*p**2 + 3/4*p**3 = 0. What is p?
0, 1
Suppose 0 = -5*m + l + 53, -6 = -m + 3*l + 13. Suppose b = 2*t - 5 + 11, -4 = -5*b - 3*t. Suppose 11*i**b + i**2 - m*i**2 = 0. Calculate i.
0
Let b be 12/8 + ((-135)/2 - 0). Let x be (-12)/b - 1215/(-33). Factor x*z + 320 - 39*z + 5*z**2 + 82*z.
5*(z + 8)**2
Suppose 2*l + 0*l + 14 = 2*p, 3 = l. Let j = 22 + -14. Solve p*q + j*q - 4*q**2 - 3 - 5 = 0 for q.
1/2, 4
Suppose 6066 = -4*x + 2*u, x = 2*u + 2*u - 1506. Let a = -1514 - x. Let -10/11*d**2 + 0 + 6/11*d**a + 4/11*d**3 - 8/11*d = 0. Calculate d.
-1, 0, 4/3
Let q(t) = -6*t**3 - 4*t**2 - 2*t. Let o be q(-1). Suppose -i = o*n + 2, -4*i = -n + 2 + 6. Factor n*r + 3/4*r**3 + 0 - 3/4*r**4 + 0*r**2.
-3*r**3*(r - 1)/4
Let z(q) = q**3 - 16*q**2 + 262*q. Let g be z(0). Find y, given that g*y**2 + 2*y + 0 - 1/2*y**3 = 0.
-2, 0, 2
Let i be ((-6)/198)/(6/(-36)). Let u(f) be the second derivative of 9/110*f**5 - 7*f + 0 - i*f**4 - 2/11*f**2 - 1/3*f**3. Suppose u(j) = 0. Calculate j.
-1/3, 2
Let m(j) be the first derivative of 79 + 0*j + 2/27*j**3 - 4/9*j**2. Factor m(t).
2*t*(t - 4)/9
Let b(s) be the third derivative of s**6/40 + 65*s**5/6 + 1297*s**4/72 + 12*s**3 + 2578*s**2. Determine u, given that b(u) = 0.
-216, -1/3
Let x(m) be the third derivative of -m**6/360 - m**5/180 + 17*m**4/72 - 5*m**3/6 - 576*m**2 + m. Factor x(q).
-(q - 3)*(q - 1)*(q + 5)/3
Suppose 3/2*r**2 + 810 - 207/2*r = 0. What is r?
9, 60
Let 3/5*q**5 - 132/5*q + 24*q**2 + 48/5 - 33/5*q**3 - 6/5*q**4 = 0. Calculate q.
-4, 1, 2
Let m(g) be the first derivative of 2*g**4 - 150 - 12*g**2 + 4/5*g**5 - 20/3*g**3 + 0*g. Factor m(d).
4*d*(d - 2)*(d + 1)*(d + 3)
Suppose 0*x + 6944 = -31*x. Let p = 224 + x. Determine n so that p*n + 1/2*n**2 - 1/2 = 0.
-1, 1
Let y be (-4)/(-30) - (-448)/240. Suppose y*q**2 + 5*q + 0*q**2 - 3*q**2 + 3*q + 11*q = 0. Calculate q.
0, 19
Let f(v) be the third derivative of -v**5/48 - 155*v**4/96 - 175*v**3/4 - 17*v**2 + 7*v. Solve f(z) = 0 for z.
-21, -10
Let d(w) be the second derivative of -11*w**7/84 + 59*w**6/60 + 13*w**5/40 - 155*w**4/24 - 29*w**3/6 + 10*w**2 - 2*w - 379. Let d(a) = 0. Calculate a.
-1, 4/11, 2, 5
Let k(r) be the second derivative of r**4/3 - 50*r**3/3 + 48*r**2 - 3067*r. Suppose k(v) = 0. Calculate v.
1, 24
Factor -1/10*q**2 + 223/10*q + 112/5.
-(q - 224)*(q + 1)/10
Factor 80*b + 62*b**3 - 112*b**2 + b**3 + 4*b**4 - 35*b**3.
4*b*(b - 2)*(b - 1)*(b + 10)
Let z(y) be the second derivative of 3*y**5/5 + 17*y**4/4 - 21*y**3 + 3*y - 68. Factor z(k).
3*k*(k + 6)*(4*k - 7)
Let s(g) be the first derivative of g**4/24 + 187*g**3/18 + 31*g**2/2 - 36. Factor s(j).
j*(j + 1)*(j + 186)/6
Let a(l) be the second derivative of l**5/120 + 5*l**4/24 - 73*l**3/36 + 19*l**2/4 - 459*l. Factor a(q).
(q - 3)*(q - 1)*(q + 19)/6
Suppose -104 + 106/3*j - 2/9*j**2 = 0. Calculate j.
3, 156
Let v = 18/7 + -51/28. Suppose 0 = 1241*m - 3006 + 524. What is o in 0 - 1/2*o**4 + m*o**2 + v*o**3 + o - 1/4*o**5 = 0?
-2, -1, 0, 2
Factor 1213682/5 + 3116/5*t + 2/5*t**2.
2*(t + 779)**2/5
Let o(w) = -5*w**2 - 35*w - 14. Let f = 67 + -73. Let k(h) = 5*h**2 + 35*h + 12. Let j(a) = f*o(a) - 7*k(a). Factor j(z).
-5*z*(z + 7)
Find h, given that 0*h + 0 + 69*h**2 + 135/4*h**3 - 3/8*h**4 = 0.
-2, 0, 92
Let z(d) = -2*d**2 + 3*d**2 + 9*d - 3*d. Let p(j) be the third derivative of -j**4/24 - 12*j**2. Let u(b) = 2*p(b) + z(b). Factor u(k).
k*(k + 4)
Suppose 5*o - 73 = -4*x, 4*o = -12*x + 14*x - 4. Suppose -39*f + 90 = x. Factor 0 + 0*p**f + 0*p + 1/4*p**3 + 1/4*p**4.
p**3*(p + 1)/4
Let t(k) be the first derivative of k**5 - 3335*k**4/4 + 3320*k**3 - 2199. Factor t(w).
5*w**2*(w - 664)*(w - 3)
Find n such that -1/9*n**5 + 14/9*n**3 - 46/3*n**2 + 75 + 7/9*n**4 - 5*n = 0.
-3, 3, 5
Let u(b) be the first derivative of -b**4/4 + 146*b**3/3 + b**2/2 - 146*b - 1908. Factor u(o).
-(o - 146)*(o - 1)*(o + 1)
Let a(z) be the first derivative of -18*z**2 - z**3 - 14*z**2 - 2*z**2 + 11*z**2 + 165 - 16*z**2. Factor a(v).
-3*v*(v + 26)
Let x(c) be the first derivative of -2/9*c**4 - 128/9*c + 4/45*c**5 - 13 - 16/9*c**3 + 80/9*c**2. Suppose x(j) = 0. Calculate j.
-4, 2
Let z(g) be the third derivative of g**8/504 - g**7/45 - 2*g**6/45 - 2613*g**2. Suppose z(p) = 0. Calculate p.
-1, 0, 8
Let c(i) be the second derivative of -5*i**4/12 + 5*i**3/2 + 10*i**2 + 280*i - 2. Suppose c(o) = 0. What is o?
-1, 4
Let b(q) = 2*q**2 + 6*q - 8. Let f(j) = 11*j**2 - 4 + 25*j - 24 - 4 - 4*j**2. Let t be (-1 - -5) + (8 - 10). Let s(m) = t*f(m) - 9*b(m). Factor s(x).
-4*(x - 1)*(x + 2)
Let a(i) be the second derivative of -i**5/20 + 527*i**4/12 - 11528*i**3 - 34848*i**2 + 791*i. Find w, given that a(w) = 0.
-1, 264
Let k(d) be the third derivative of -d**7/350 - 7*d**6/200 + 113*d**5/100 - 21*d**4/8 + 1682*d**2 - 2. Find q, given that k(q) = 0.
-15, 0, 1, 7
Let q be (-31822)/(-45) + 129/(-15) + 9. Let a = -707 + q. Suppose -a*y**2 - 4/9*y**4 - 2/9*y + 0 + 11/9*y**3 = 0. Calculate y.
-1/4, 0, 1, 2
Let r be (1104/(-230))/(3/(-5)). Suppose r*n - 5*k = 4*n, 2*k = 3*n. Solve -1/7*s**3 + n + 1/7*s**2 + 0*s = 0 for s.
