 0, 2
Let g = 230 + -228. Factor -9*c**2 + 12*c**4 + 62*c - 26*c - 12*c**3 - 8*c**3 - 3*c**g - 16.
4*(c - 1)**3*(3*c + 4)
Let p be ((-3 - -3)/(-4))/1. Suppose -5*t = 3*l - 13, -3*l + p*l + 7 = 2*t. Factor 0 + 2*u - 4*u**2 + 0 - u**3 + 3*u**t.
-u*(u - 1)*(u + 2)
Let k(y) be the third derivative of 9*y**2 + 0*y + 7/2*y**3 - 1/40*y**5 + 0 - 13/16*y**4. What is a in k(a) = 0?
-14, 1
Suppose -33990*h + 33893*h = 0. Factor h*w**2 - 54/5*w**5 + 32/5*w**3 + 0 + 0*w - 12/5*w**4.
-2*w**3*(3*w - 2)*(9*w + 8)/5
Factor 0 + 3/7*p**4 + 27/7*p + 9/7*p**2 - 15/7*p**3.
3*p*(p - 3)**2*(p + 1)/7
Let z = -4153/6 - -693. Let s(w) be the second derivative of -11*w + 5/2*w**2 - z*w**3 + 1/4*w**5 - 5/12*w**4 + 0. Factor s(f).
5*(f - 1)**2*(f + 1)
Let m(u) be the first derivative of u**6/27 + 58*u**5/45 + 181*u**4/18 + 62*u**3/3 + 14*u**2 + 1219. Determine p, given that m(p) = 0.
-21, -6, -1, 0
Let k(a) = 6*a**2 - a - 2. Let x be k(-2). Suppose 18 = 4*b - 2*b + 2*t, -b + x = 4*t. Factor 4*l - 2*l - l**2 - l**b + 2*l + 5*l**3 - 7*l**2.
-l*(l - 2)**2*(l - 1)
Let t = -2945 + 2949. Let x(m) be the first derivative of 0*m**2 + 1/14*m**6 + 9/28*m**t + 29 - 1/7*m**3 - 9/35*m**5 + 0*m. Factor x(u).
3*u**2*(u - 1)**3/7
Let d(a) be the second derivative of 8*a**5/55 - 76*a**4/33 - 79*a**3/33 - 10*a**2/11 - 4*a + 1126. Let d(q) = 0. What is q?
-1/4, 10
Suppose -19*n + 284 = 43*n + 9*n. Let d = -27 + 109/4. Factor 0 + d*h**5 - 1/2*h**n + 1/4*h**3 + 0*h + 0*h**2.
h**3*(h - 1)**2/4
Let d(h) be the third derivative of -h**8/448 - 19*h**7/56 + 99*h**6/40 - h**5/5 - 49*h**4 + 198*h**3 + 624*h**2 - 2*h - 2. Suppose d(n) = 0. What is n?
-99, -2, 2
Let p(t) be the second derivative of -t**4/54 - 427*t**3/27 + 286*t**2/3 - 3849*t. Factor p(h).
-2*(h - 2)*(h + 429)/9
Let w be (-21120)/(-1188) - (-5 - -13). Factor -2/9*u**2 - 968/9 - w*u.
-2*(u + 22)**2/9
Let s be 15/25 - 0 - (-9)/(-15). Factor s + 2/9*t - 2/9*t**2.
-2*t*(t - 1)/9
Let l(c) be the first derivative of -c**4/12 + 169*c**3/9 + 85*c**2/3 + 1683. Factor l(h).
-h*(h - 170)*(h + 1)/3
Let x(f) = -3*f**2 + 269*f + 8667. Let v(o) = 5*o**2 - 404*o - 12996. Let l(a) = 5*v(a) + 8*x(a). Suppose l(t) = 0. Calculate t.
-66
Let f(p) = 248*p**4 + 44*p**3 + 311*p**2 - 11*p - 11. Let r(h) = 45*h**4 + 9*h**3 + 62*h**2 - 2*h - 2. Let o(w) = 2*f(w) - 11*r(w). Factor o(b).
b**2*(b - 15)*(b + 4)
Suppose 2*o + c - 30 = 0, -4*c = -5*c + 2. Suppose -2*z = 5*n + 6, -z - 3*n - o = -5*z. Factor 1/11*m**z - 1/11*m + 0.
m*(m - 1)/11
Factor 5*s**3 - 9503 - 2299 - 1677 + 2832*s - 921 - 1152*s + 215*s**2.
5*(s - 5)*(s + 24)**2
Let d(s) be the second derivative of s**6/60 - 3*s**5/2 - 87*s**4/8 + 80*s**3/3 + 1262*s. Factor d(w).
w*(w - 64)*(w - 1)*(w + 5)/2
What is g in 19235 + 68*g**3 - 65*g**4 + 8*g**4 + 468*g**2 - 75*g**4 - 472*g - 19139 - 28*g**5 = 0?
-4, -3, 2/7, 1
Suppose -85/4*i + 75/2 - 9/4*i**2 - 1/4*i**4 + 9/4*i**3 = 0. What is i?
-3, 2, 5
Determine c, given that -32/3*c + 50/3*c**2 - 19/3*c**3 + 0 + 1/3*c**4 = 0.
0, 1, 2, 16
Let i(a) = -8*a**2 - 668*a + 12. Let c(v) = v**2 + 7*v - 1. Let s(u) = 12*c(u) + i(u). Factor s(h).
4*h*(h - 146)
Let a be (-114)/27 - (-4185)/972. Determine s so that -a*s**2 - 961/12 + 31/6*s = 0.
31
Suppose 3*b - 2*l = 66554, 2*b - 22166 - 22206 = 2*l. Factor -b*f**2 + 22200*f**2 + 39*f + f + 24 + 2*f**3.
2*(f + 1)*(f + 2)*(f + 6)
Let r(o) be the second derivative of o**5/48 + 19*o**4/96 + o**3/2 + 176*o**2 - 2*o - 32. Let z(l) be the first derivative of r(l). Factor z(n).
(n + 3)*(5*n + 4)/4
Let i(a) be the first derivative of 5/4*a**4 + 160 + 25/3*a**3 - 20*a**2 - 60*a. Factor i(f).
5*(f - 2)*(f + 1)*(f + 6)
Let v = 1547 + -747. Let h = v - 3197/4. Find w such that -3/4*w + 0*w**2 + 0 + h*w**3 = 0.
-1, 0, 1
Suppose 0 = 2*l - 5*q - 8, 2*q - 11 = -3*l + 1. Let j(v) = -v + 11. Let k be j(6). What is w in -4*w**3 - 2*w**l - 3*w**2 - k*w**3 + w**3 - 5*w**2 = 0?
-2, 0
Let m(b) = -2*b**3 + 35*b**2 + 17*b + 22. Let t be m(18). Factor -3*s**2 + t*s - 4*s + 5*s**2.
2*s**2
Let d(h) = 9*h + 33. Let g(i) = -5*i - 17. Let l(u) = 4*d(u) + 7*g(u). Let v be l(-9). Factor -v*t**2 + 16*t + 71*t + 65 - 27*t - t**2.
-5*(t - 13)*(t + 1)
Let d(f) be the third derivative of 0*f**4 + 2*f**2 + 1/75*f**5 - 1/100*f**6 + 1/525*f**7 + 0*f**3 - 58*f + 0. Factor d(r).
2*r**2*(r - 2)*(r - 1)/5
Let c(v) = -v + 6. Let j be c(-4). Suppose -j*h + 3 = -9*h. Solve -4*s**3 - h*s - 11*s**2 + s - 2*s + 7*s = 0.
-3, 0, 1/4
Let h(r) be the first derivative of 2*r**3/3 - 96*r**2 - 1010*r - 7529. Factor h(g).
2*(g - 101)*(g + 5)
Let h(o) = -o**3 + 4*o**2 - 2*o. Let m be h(3). Let y be (36/32)/(3078/3420). Suppose -y*f**2 - 1 - 1/4*f**m - 2*f = 0. Calculate f.
-2, -1
Let k be 20*(-497)/(-12780)*12/14. Factor -22/3*x - k + 85/6*x**2 + 125/6*x**3.
(x + 1)*(5*x - 2)*(25*x + 2)/6
Factor 13*a**2 + 123 + 42 - 178*a + 2*a**3 - 46*a + 347 + 3*a**2.
2*(a - 4)**2*(a + 16)
Let z be ((-528)/495)/(408/(-1275)). Let v = 26/9 + 49/9. Suppose 1/3*x**2 + v + z*x = 0. Calculate x.
-5
Suppose -x - 6*m = -25 + 7, 0 = 5*x - 5*m - 20. Factor 13/2 + x*k - 1/2*k**2.
-(k - 13)*(k + 1)/2
Let i be ((-3)/13)/((-993)/8606). Let z(t) be the second derivative of -t**i - 18*t + 1/6*t**4 - 1/10*t**5 + 0 + 1/3*t**3. Suppose z(y) = 0. Calculate y.
-1, 1
Let a(y) be the third derivative of y**8/336 + y**7/35 + y**6/120 - 2*y**5/5 + 2*y**4/3 + 518*y**2 + 2. Suppose a(g) = 0. Calculate g.
-4, 0, 1
Suppose -30 - 318 = -3*t. Let -42*d**2 + 252 + t*d**2 - 348 + 112*d + 10*d**3 = 0. What is d?
-4, 3/5
Let f = 1326898/5 + -265372. Solve 0 - f*x + 7/5*x**3 + 131/5*x**2 = 0 for x.
-19, 0, 2/7
Let d = -351 - -141. Let p = 638/3 + d. Factor 16/3*v**3 + p*v - 4/3*v**4 - 20/3*v**2 + 0.
-4*v*(v - 2)*(v - 1)**2/3
Suppose 4*a + 56 = 32*a. Suppose 0 = -2*o + 5*m - 30 + 10, 0 = -a*o - m + 4. Factor 1/7*j**3 + 0*j**2 - 1/7*j**4 + 0 + o*j.
-j**3*(j - 1)/7
Let m(c) = -c**3 + c + 3. Let x(q) = 2*q**3 - q**2 - q - 5. Let w be ((-4)/6)/((-6)/(-54)). Let h = w + 3. Let y(v) = h*x(v) - 5*m(v). Factor y(a).
-a*(a - 2)*(a - 1)
Factor -1049/4*x - x**2 - 131/2.
-(x + 262)*(4*x + 1)/4
Let y be ((-780)/(-32)*(-4)/(-18))/((-5)/(-4)). Factor 4*p**2 + 1/3*p**4 + 0*p + 0 + y*p**3.
p**2*(p + 1)*(p + 12)/3
Factor 1671858 + 3980*s + 271614 + s**2 - 177731 + 214309 + s**2.
2*(s + 995)**2
Let x be ((-20)/8 + 0)*((-1592)/(-320) - 5). Let w(s) be the first derivative of -1/6*s**3 + 0*s - 3 - x*s**4 - 1/8*s**2. Factor w(t).
-t*(t + 1)**2/4
Let f(n) be the first derivative of -5/16*n**3 + 8*n + 1/8*n**2 - 7 + 7/96*n**4. Let a(j) be the first derivative of f(j). Factor a(u).
(u - 2)*(7*u - 1)/8
Let c(q) be the third derivative of q**5/60 + 3*q**4 - 74*q**3/3 + 130*q**2 + 1. Determine g so that c(g) = 0.
-74, 2
Let g be -6 + 7 + 2 - (-57 + 1). Suppose -62*o = -g*o. Solve o + 2/13*f**4 - 6/13*f**3 + 0*f**2 + 8/13*f = 0.
-1, 0, 2
Let i = -224146 - -2465630/11. Let q = 2714/11 - 246. Suppose -18/11 + 4/11*f**2 - i*f + q*f**3 - 2/11*f**4 = 0. What is f?
-1, 3
Factor 4*f**3 - 340*f + 37*f - 92*f**2 + 207*f.
4*f*(f - 24)*(f + 1)
Let o(b) be the first derivative of -3 - 18*b**2 + 2*b**3 - 27*b + 3*b**4 - 3/5*b**5. Factor o(g).
-3*(g - 3)**2*(g + 1)**2
Factor -4063 + 64*f - 4063 + 8078 - 28*f**2 + 4*f**3.
4*(f - 3)*(f - 2)**2
Let f = 3876920/1254297 - 2/1254297. Determine n, given that f - 100/11*n - 8/11*n**3 - 142/11*n**2 = 0.
-17, -1, 1/4
Let a(t) = -39*t**3 + 567*t**2 + 780*t - 1308. Let w(m) = 8*m**3 - 113*m**2 - 157*m + 262. Let u(q) = 5*a(q) + 24*w(q). Factor u(c).
-3*(c - 42)*(c - 1)*(c + 2)
Let i(t) be the third derivative of -t**5/12 - 60*t**4 + 1445*t**3/6 + 7220*t**2 + 2*t. Factor i(s).
-5*(s - 1)*(s + 289)
Factor 0*g + 2/9*g**5 + 16/3*g**3 + 0 + 20/9*g**4 + 0*g**2.
2*g**3*(g + 4)*(g + 6)/9
Suppose 2*b - 4*t = -48, 71 = -3*b + 4*t - 1. Let y(n) = n**3 + 27*n**2 + 72*n + 3. Let j be y(b). Factor -6/5*l + 9/5*l**3 + 0 + j*l**2.
3*l*(l + 2)*(3*l - 1)/5
Let p(g) = -3*g**2 - g. Let s(w) = -3*w**3 + 57*w**2 + 88*w - 450. Let z(c) = -5*p(c) + s(c). Suppose z(q) = 0. What is q?
-3, 2, 25
Let f(k) be the first derivative of -k**5/40 + 23*k**4/32 - 31*k**3/12 - 203*k**2/4 - 147*k + 3157. Solve f(w) = 0.
-3, -2, 14
Let k be (-4)/(-16)*40/(-112)*-14. Find u such that -1/12*u**2 - 7/6*u + k = 0.
-15, 1
Factor 4547*w**2 - 2232*w - 2288*w**2 + 4480 - 2263*w**