b + 2)/7
Let n(m) be the second derivative of -3/10*m**5 + 1/2*m**3 + 78*m + 1/10*m**6 - 1/2*m**4 + 0 + 1/14*m**7 + 3/2*m**2. Factor n(z).
3*(z - 1)**2*(z + 1)**3
Suppose r = 4*j, -3*r = 2*j - 22 + 22. Let k(q) be the second derivative of -33*q + r + 216*q**2 + 1/4*q**4 - 12*q**3. Let k(f) = 0. Calculate f.
12
Let u(o) = -o**3 - 12*o**2 - 13*o - 24. Let a be u(-11). Let i be 0/(a - -4 - 1). Factor 13*x + 20*x**2 - 39*x**2 + i*x**3 + 14*x**2 - x**3 - 7.
-(x - 1)**2*(x + 7)
Let s(b) = b**3 + 2*b + 131. Let f be s(0). Determine h, given that -369 + 4*h**5 - f - 1160*h**2 - 68*h**4 + 424*h**3 + 102043*h - 100743*h = 0.
1, 5
Suppose 2*v - 1 = 3*v, 2*v - 158 = 5*w. Let g = -32 - w. Factor g + a**2 + 15*a - 12*a + 2.
(a + 1)*(a + 2)
Let v(z) be the first derivative of -4/3*z**3 - 24*z**2 - 80*z - 167. Factor v(h).
-4*(h + 2)*(h + 10)
Factor -975 + 405/2*d - 3/2*d**2.
-3*(d - 130)*(d - 5)/2
Let q(f) be the first derivative of f**6/1440 - 7*f**5/40 + 147*f**4/8 + 86*f**3/3 - 168. Let a(d) be the third derivative of q(d). Factor a(c).
(c - 42)**2/4
Suppose 0 = 5*h, -4*o + 3*h + 23 = 7. Solve i**2 - i**2 - 12*i**3 - 8*i**2 - 4*i**o = 0 for i.
-2, -1, 0
Let n(k) = 2*k**3 + 14*k**2 - 2*k - 22. Let i be n(-7). Let b(y) = y**2 + y + 1. Let a(u) = 4*u**2 - 20*u - 16. Let q(x) = i*b(x) + a(x). Factor q(t).
-4*(t + 1)*(t + 6)
Factor 5/4*z**4 - 17/2*z - 15/4*z**2 - 4 + 2*z**3.
(z - 2)*(z + 1)**2*(5*z + 8)/4
What is s in 0 - 1/2*s**5 + 43/2*s**2 - 7*s + 17/2*s**4 - 45/2*s**3 = 0?
0, 1, 14
Suppose -5960 = -7*h - 5876. Let k(c) be the third derivative of h*c**2 - 1/240*c**6 - 1/60*c**5 + 0*c**3 - 1/48*c**4 + 0 + 0*c. Solve k(d) = 0.
-1, 0
Let q be (2165/120)/((-50)/(-15)). Let l = -29/16 + q. Factor 2*x**3 + 14/5*x + l*x**2 + 2/5*x**4 + 4/5.
2*(x + 1)**3*(x + 2)/5
Let l(f) be the first derivative of 4*f**5/5 + 2*f**4 - 20*f**3 + 8*f**2 + 80*f + 1328. Factor l(a).
4*(a - 2)**2*(a + 1)*(a + 5)
Suppose -4*q**2 + 72/13*q**3 - 30/13*q**4 + 4/13*q**5 + 18/13 - 12/13*q = 0. What is q?
-1/2, 1, 3
Let m(l) be the second derivative of 5/273*l**7 + 6/13*l**2 - 7/39*l**3 - 4/13*l**4 + 1/65*l**5 + 41 + l + 6/65*l**6. Determine b, given that m(b) = 0.
-3, -1, 2/5, 1
Let y(x) be the second derivative of 36*x + 1/3*x**5 - x**4 - 2/45*x**6 + 0 + 14/9*x**3 - 4/3*x**2. Let y(c) = 0. Calculate c.
1, 2
Factor 1051 - 132*y + 10*y**3 - 4*y**4 + 32*y**3 + y**4 + 9*y**2 - 967.
-3*(y - 14)*(y - 1)**2*(y + 2)
Let h(a) be the third derivative of 1/35*a**7 + 0*a + 0 - 7/30*a**6 + 1/3*a**4 + 41*a**2 + 7/30*a**5 + 0*a**3. Solve h(g) = 0.
-1/3, 0, 1, 4
Let o = -9 + 17. Let h be ((-18)/o)/(24/(-256)). Factor h*j**2 - 26*j**2 + 0*j**3 - 5*j**3.
-j**2*(5*j + 2)
Factor -275*o**2 + 285*o**2 - 19*o**4 + 22*o**4 - 1162*o**2 - 9504*o + 6*o**3.
3*o*(o - 22)*(o + 12)**2
Let h be (-9)/2*19712/(-9504). Determine j, given that -8/3*j - 20/3*j**3 + h*j**2 + 0 = 0.
0, 2/5, 1
Let w(t) be the third derivative of t**5/15 + 755*t**4/2 + 4528*t**3/3 + 5*t**2 + 2*t + 208. Factor w(n).
4*(n + 1)*(n + 2264)
Suppose 7*m - 38 = 4*w, 3*m + 80*w - 83*w - 24 = 0. What is t in 8/17 + 18/17*t**m - 2/17*t**3 - 2/17*t**4 - 22/17*t = 0?
-4, 1
Let k(i) be the third derivative of -i**7/105 + i**6/15 + 7*i**5/30 - 5*i**4/6 - 45*i**2 + 8*i. Let k(o) = 0. What is o?
-2, 0, 1, 5
Let t(g) = -242*g**2 - 6750*g - 28. Let q(s) = 26*s**2 + 750*s + 3. Let d(x) = -28*q(x) - 3*t(x). Let d(r) = 0. Calculate r.
-375, 0
Let m be 9 + (11/28)/((-773)/9276). Factor -m*o + 0 + 2/7*o**2.
2*o*(o - 15)/7
Let x = -65212 - -65215. Solve 46/9*r**2 + 22/9*r + 26/9*r**x + 2/9*r**4 + 0 = 0 for r.
-11, -1, 0
Let x(w) be the first derivative of 25/6*w**2 - 5/12*w**4 + 5/9*w**3 + 150 + 5*w. Factor x(y).
-5*(y - 3)*(y + 1)**2/3
Let i be (3 - (-55)/(-11)) + (-8462)/(-6). Let z = i - 1408. Factor 2/3 + z*m - 1/3*m**2.
-(m - 2)*(m + 1)/3
Let j(z) = 75079*z**2 + 1093*z + 1. Let u(n) = -n**2 + n + 1. Let r(g) = -j(g) - 3*u(g). Factor r(c).
-4*(137*c + 1)**2
Let f = -180 - -189. Find v, given that -3*v**3 + 10 - f*v**2 - 4*v + 3*v**4 - 18*v + 25*v - 4 = 0.
-1, 1, 2
Let q(t) be the third derivative of t**11/332640 - t**5/15 + 2*t**3/3 - 14*t**2. Let a(c) be the third derivative of q(c). Let a(f) = 0. Calculate f.
0
Let -r**3 + 8*r**2 + 50*r**4 + 40 - 61*r + 95*r - 54*r - 98*r**2 + 15*r**5 + 6*r**3 = 0. What is r?
-2, -1, 2/3, 1
Let v be (5805/12)/(9*(-12)/(-288)). Let i be (-215)/v*(-81)/2. Determine s so that 6*s**2 + i*s**5 + 0*s + 9/2*s**4 - 15*s**3 + 0 = 0.
-2, 0, 2/3
Let d(g) = 2*g**2 - 6*g - 16. Let z(m) = -m**3 - 15*m**2 + 16*m + 5. Let l be z(-16). Let x be d(l). Factor 1 - 1 + 348*j - 340*j + x*j**2.
4*j*(j + 2)
Let x(r) be the third derivative of -r**5/90 + 205*r**4/9 - 168100*r**3/9 - 2051*r**2. Find n such that x(n) = 0.
410
Find u such that -164 - 192*u**2 - 191*u**2 - 175*u**2 + 551*u**2 - 96*u = 0.
-82/7, -2
Let m be (-1)/4*-2*(105 - -39). Let g(c) = -c**2 - 11*c - 18. Let s be g(-5). Factor -m*t + s*t**2 + 37*t + 43*t.
4*t*(3*t + 2)
Let k(h) be the third derivative of -122*h**7/245 - 53*h**6/280 + 123*h**5/70 + 53*h**4/56 - h**3/7 - 3070*h**2. Let k(t) = 0. Calculate t.
-1, -1/4, 2/61, 1
Let g(q) be the second derivative of -13*q**5/30 - q**4/3 + 89*q. Factor g(l).
-2*l**2*(13*l + 6)/3
Let c(b) = -5*b**2 - b + 2*b + 3*b**2. Let g(a) = -a + 20*a**2 + 41*a**2 - 1 - 60*a**2. Let y(i) = 2*c(i) + 6*g(i). Factor y(q).
2*(q - 3)*(q + 1)
Factor 17*r**2 - 72*r**4 + 75*r**3 - 52*r**3 + 3*r**2 - 36*r**3.
-r**2*(8*r + 5)*(9*r - 4)
Let v = 2/29025 - -290236/203175. Factor -v*r**2 + 12/7*r + 2/7*r**3 + 0.
2*r*(r - 3)*(r - 2)/7
Let 727 + 288*y - 112*y**2 + 82*y**2 + 3*y**5 - 354*y**2 - 84*y**3 + 63*y**4 - 199 = 0. What is y?
-22, -2, -1, 2
Suppose 0 = 7*x - 9*x - 4. Let b be (-15)/x*4/6. Find k, given that 23*k - 59*k + 2*k**3 - 84*k**4 + 16*k**5 + 66*k**3 + 132*k**2 + 0*k**b = 0.
-1, 0, 1/4, 3
Let d(h) be the first derivative of -5*h**4/4 - 455*h**3 + 685*h**2 - 316. Factor d(q).
-5*q*(q - 1)*(q + 274)
Suppose -171*f + 3 + 51 + 459 = 0. Factor -56*o**2 + 4/3*o**4 - 176/3*o - 16*o**f - 20.
4*(o - 15)*(o + 1)**3/3
Suppose 200*n - 112 - 252 = 18*n. Determine p so that -1/3*p**n + 8/3 - 7/3*p = 0.
-8, 1
Let p be 0/(-3*1/(-4) - (-1715)/1372). Suppose p + 12/7*r - 36/7*r**2 + 15/7*r**3 = 0. What is r?
0, 2/5, 2
Factor 43/2*d - 30 + 9*d**2 - 1/2*d**3.
-(d - 20)*(d - 1)*(d + 3)/2
Suppose 3*t + 20 = s, -5*s - t - 26 = -30. Let u(d) be the third derivative of -4*d**s + 49/8*d**4 + 0 + 1/120*d**6 - 7/20*d**5 + 0*d - 343/6*d**3. Factor u(n).
(n - 7)**3
Determine v so that 8 + 14/3*v + 2/3*v**2 = 0.
-4, -3
Let m(b) = b**3 + 5*b**2 + 3*b - 6. Let p be m(-3). Suppose -3*f + 18 - p = 0. Solve 2/9*s**3 + 0*s + 0 + 10/9*s**4 - 2/9*s**2 + 2/3*s**f = 0 for s.
-1, 0, 1/3
Let s be ((-1)/(116/(-24)))/(1296/18792). Factor -2/3*b**s + 0 + 0*b - 8/3*b**2.
-2*b**2*(b + 4)/3
Let t be -2 - -5 - (7 - 7). Suppose 0 = -5*x - t*x + 64. Suppose 17*c**3 + 5 - 2*c + 3 - 13*c**3 - 2*c - x*c**2 = 0. Calculate c.
-1, 1, 2
Let v(r) be the third derivative of -7*r**2 - 1/1512*r**8 - 4/27*r**3 + 7/270*r**5 + 0*r**4 + 1/540*r**6 - 1/315*r**7 + 2 + 0*r. Suppose v(d) = 0. Calculate d.
-2, -1, 1
Suppose -847 = 22*q - 11*q. Let f be (-9)/(q/35 - -1). Factor -3/2*k**2 + f + 6*k.
-3*(k - 5)*(k + 1)/2
Let z(f) = 12*f**2 + 304*f - 1912. Let b(o) = -7*o**2 - 203*o + 1275. Let u(l) = -8*b(l) - 5*z(l). Find j, given that u(j) = 0.
10, 16
Factor -2/7*w**2 + 130/7*w - 36.
-2*(w - 63)*(w - 2)/7
Let h(z) = -78*z**2 - 1481*z - 1468. Let i(u) = 109*u**2 + 2222*u + 2204. Let b(j) = 7*h(j) + 5*i(j). Let b(x) = 0. Calculate x.
-1, 744
Let d = 14 + -10. Suppose 2*c - 5 = -h, -d*c - 6*h = -3*h - 5. Find r, given that -20*r - 12*r**3 + c*r**3 + 9*r**3 + 4*r - 4*r**2 = 0.
-2, 0, 4
Let i(b) be the second derivative of 0 + 1/60*b**5 - 5/9*b**3 - 4/3*b**2 + 244*b - 1/36*b**4. Factor i(h).
(h - 4)*(h + 1)*(h + 2)/3
Let k(r) be the second derivative of -2 + 12/13*r**3 + 8/13*r**2 + 40*r + 5/13*r**4 - 5/26*r**5. Suppose k(v) = 0. Calculate v.
-2/5, 2
Suppose -15*n = -19*n - 4*t + 48, -46 = -4*n - 2*t. Let r be (5 - n/2)*(-2 + 2). Suppose r - 5/4*a**2 - 15/4*a = 0. Calculate a.
-3, 0
Let v(n) be the second derivative of -3 - 23/48*n**4 + 3/80*n**5 - 9/8*n**2 - 32*n - 35/24*n**3. Suppose v(f) = 0. What is f?
-1, -1/3, 9
Suppose 0 = -3*