w.
-33, -2, 2/3
Factor 45 + 0*m**2 + 40*m**3 + 5 - 2*m**2 - 24*m**3 - 50*m - 14*m**3.
2*(m - 5)*(m - 1)*(m + 5)
Let p(m) be the second derivative of -m**6/90 - 13*m**5/120 - m**4/8 - 65*m**3/6 + 60*m. Let r(x) be the second derivative of p(x). What is c in r(c) = 0?
-3, -1/4
Factor -95348*a**2 + 102 + 74 - 16 + 90*a + 95353*a**2.
5*(a + 2)*(a + 16)
Let n be (-58)/(-4) + (30 - 43). Let b(q) be the second derivative of -n*q**3 - 15*q + 3*q**2 + 1/4*q**4 + 0. Let b(t) = 0. Calculate t.
1, 2
Determine d so that 2/5*d**3 - 34/5*d - 14/5*d**2 - 18/5 = 0.
-1, 9
Let w(u) be the second derivative of -u**6/15 + 24*u**5 - 713*u**4/6 + 158*u**3 - 4420*u. Solve w(d) = 0.
0, 1, 2, 237
Let i(a) = 1. Let d(h) = 3*h**2 + 7*h. Suppose -2*j + 13 - 5 = 0. Suppose -7*x - 3 = j. Let c(n) = x*d(n) - 2*i(n). Factor c(s).
-(s + 2)*(3*s + 1)
Let j(q) be the first derivative of -q**3/12 + 32*q**2 + 257*q/4 + 308. Factor j(h).
-(h - 257)*(h + 1)/4
Let l be (74*2/175*5 - 4)/(2078/5195). Solve 0 - 48/7*i + 36/7*i**3 + 16/7*i**2 - 24/7*i**4 + l*i**5 = 0.
-1, 0, 2, 3
Suppose -17*g + 1 = -101. Find v such that 30*v**2 + 4*v**2 + 201*v**3 + 12*v - 171*v**3 + g*v**4 - 2*v**5 = 0.
-1, 0, 6
Let s(z) be the third derivative of -168*z**3 + 120*z - 1/420*z**5 - z**4 + 0 + z**2. Solve s(r) = 0 for r.
-84
Let w be (45/(-24))/(270/(-864)) + 3/((-54)/105). Factor 5/6*h**2 + w*h - 1/6*h**3 - 5/6.
-(h - 5)*(h - 1)*(h + 1)/6
Let x = -405/109 - -2461/545. Let o be ((-4)/(-10))/(-2) - -1. Suppose 2/5*p**4 - o*p**2 - x*p**3 + 2/5*p + 2/5 + 2/5*p**5 = 0. Calculate p.
-1, 1
Let h = 282 + -208. Factor 98*a**2 + 16*a**2 + 15*a**3 + 88*a - 16 + 89*a - h.
3*(a + 3)*(a + 5)*(5*a - 2)
Let b(s) be the first derivative of -9/5*s**3 + 3/25*s**5 + 0*s**2 + 41 + 6/5*s**4 + 0*s. Find j such that b(j) = 0.
-9, 0, 1
Let c(g) = -g + 2. Let u be c(-11). Let i(x) = -x**3 + 12*x**2 + 20*x - 27. Let a be i(u). Determine p so that -10*p**3 + 69*p**2 + 5*p**4 + 3 - a*p**2 - 3 = 0.
0, 1
Suppose -f + 5*f = 184. Let x = 50 - f. Factor 84*u**2 - 84*u**2 + x*u**3 - 4*u.
4*u*(u - 1)*(u + 1)
Let q(s) be the first derivative of -2/63*s**3 - 16/7*s**2 - 73 - 384/7*s. Factor q(n).
-2*(n + 24)**2/21
What is w in -97*w + 44*w - 21*w**2 + 56 - 46*w - 26 = 0?
-5, 2/7
Let h = -11516/3 + 3929. Let c = h + -269/3. Factor -c*g**2 + 2/3*g + 4.
-2*(g - 3)*(g + 2)/3
Let q be (-1)/((-4)/3 + 1). Suppose 8*h - 90 = q*h. Suppose -8*b + h*b**2 - 14*b**2 - 4*b = 0. What is b?
0, 3
Let k(b) be the second derivative of b**4/78 + 61*b**3/39 - 126*b**2/13 - 393*b + 3. Factor k(t).
2*(t - 2)*(t + 63)/13
Let a(h) be the third derivative of -3*h**8/28 - 16*h**7/21 + 29*h**6/30 + 4*h**5/3 + 1591*h**2. Determine w, given that a(w) = 0.
-5, -4/9, 0, 1
Let v = 72 - 33. Let r be 0/1*(-13)/v. Factor -1/10*b**3 + r*b**2 - 1/10*b**4 + 0 + 0*b.
-b**3*(b + 1)/10
Let r be (532/(-817))/(42/(-903)). Suppose 1/7*k**2 + 343 + r*k = 0. What is k?
-49
Let y(n) be the second derivative of n**4/4 - 5*n**3/3 + 3*n**2/2 - 80*n. Let k be y(3). Solve -9/2*d**4 - 3*d - 3*d**3 + 21/2*d**2 + k = 0.
-2, 0, 1/3, 1
Let i = -3608999/4 - -902252. Factor 5/4*r**2 + 3/4*r + 1/4*r**3 - i.
(r - 1)*(r + 3)**2/4
Let a(g) be the first derivative of -6*g**5/55 - 61*g**4/11 + 86*g**3/33 + 82*g**2/11 - 945. Determine n so that a(n) = 0.
-41, -2/3, 0, 1
Let g(y) = -7*y + 163. Let r be g(23). Factor -208 - 18*s**2 - 4*s**3 - 64*s**2 - 34*s**r - 320*s.
-4*(s + 1)*(s + 2)*(s + 26)
Let u(a) be the third derivative of a**7/42 - 40*a**6/3 - a**5/4 + 2395*a**4/12 + 1600*a**3/3 - 53*a**2 - 28*a + 2. Solve u(h) = 0 for h.
-1, 2, 320
Suppose -5*y + 10*y - 3*j = 3, -4*y + 4 = -4*j. Solve 28/3*p**2 + 0 + 12*p**4 + y*p - 4/3*p**5 - 20*p**3 = 0 for p.
0, 1, 7
Suppose 0 = -3*o + 2*q + 136, 19 = 3*o + 3*q - 137. Let r = 90 - o. Factor 8 - 12*l**2 + 38*l**3 - r*l**3 + l**4 + 4*l**4 + 4*l - l**4.
4*(l - 2)*(l - 1)*(l + 1)**2
Suppose -27411*g + 5*n + 7 = -27410*g, 4 = g - 2*n. Suppose 0 = -3*j + 40 - 4. What is t in -9/2*t**3 - 3/2*t**g + j*t - 6 = 0?
-2, 2/3, 1
Suppose -h - 2*g = -9, 0 = -2*h + 4*g - g - 3. Factor 6 + 5*a + 17*a - 9*a**3 - 12*a**2 - 2*a - 2*a - h*a.
-3*(a - 1)*(a + 2)*(3*a + 1)
Let c(t) = -3*t**2 + t. Let d(b) = 34*b - 180. Let x(l) = -c(l) + d(l). Let x(i) = 0. What is i?
-15, 4
Factor 11*s**2 + 8583*s - 6821294 - 2*s**2 + 6827012.
3*(s + 953)*(3*s + 2)
Let q(p) be the first derivative of p**3/6 - 19*p**2/4 - 10*p + 146. Factor q(z).
(z - 20)*(z + 1)/2
Let j(f) be the third derivative of -f**6/40 - 3*f**5/10 + 115*f**4/8 - 150*f**3 - 10867*f**2. Determine d, given that j(d) = 0.
-15, 4, 5
Suppose 4*o - 54 = -l, 5*l = -0*l + 10. Suppose 12*t - o*t + 2 = 0. Factor 3/5*r**4 + 41/5*r**t + 4*r**3 - 12/5 + 4*r.
(r + 2)**2*(r + 3)*(3*r - 1)/5
Let f = 1980/89 + -9633/445. Factor f*a**2 - 21/5 - 18/5*a.
3*(a - 7)*(a + 1)/5
Factor 12659*p**3 + 264*p + 156 - 435*p**2 - 540*p - 672*p - 12620*p**3.
3*(p - 13)*(p + 2)*(13*p - 2)
Let z(h) = 2*h**3 + 164*h**2 + 640*h + 628. Let y(w) = 2*w**3 + 163*w**2 + 640*w + 626. Let v(p) = 4*y(p) - 6*z(p). Factor v(c).
-4*(c + 2)**2*(c + 79)
Suppose -17*i + 16*i - 1712 = 2*f, 3*f - 5136 = 3*i. Let y = -8552/5 - i. Factor -14/5*o - 1/5*o**3 - y - 7/5*o**2.
-(o + 1)*(o + 2)*(o + 4)/5
Let t(z) be the first derivative of -6*z + 5*z**3 + 7*z**4 + 141 - 19/2*z**2. Determine n so that t(n) = 0.
-1, -2/7, 3/4
Factor 0 + 1/4*s**2 - 33/2*s.
s*(s - 66)/4
Let d(t) be the second derivative of -2*t**6/35 - 453*t**5/140 - 195*t**4/14 - 173*t**3/14 + 15*t**2 - 6992*t. Find g, given that d(g) = 0.
-35, -2, -1, 1/4
Let t(g) be the third derivative of -9/8*g**4 + 33*g**2 + 1/20*g**5 + 0*g**3 - 2 + 0*g. Factor t(s).
3*s*(s - 9)
Let j(r) be the third derivative of 0 + 4/5*r**5 - 61*r**2 + 25/2*r**3 - 5*r**4 + 0*r. Factor j(q).
3*(4*q - 5)**2
Let y = -46 - -42. Let h be y - ((3 - 88) + 1/1). Solve 4*t**2 + 67 + 20 - h*t + 165 + 148 = 0.
10
Let y be -17 + 19 + (0/2 - 0). Solve 2*r**y - 20*r**3 + 5*r**3 + 30*r**5 + 8*r**2 - 25*r**4 = 0.
-2/3, 0, 1/2, 1
Let g(n) be the third derivative of n**5/120 - 71*n**4/8 + 425*n**3/12 - 257*n**2. Let g(k) = 0. Calculate k.
1, 425
Let z be -7*55/(-231)*3/10. Let p be ((-5)/15 - (7 + -7))*-1. Find y, given that z*y - p - 1/6*y**2 = 0.
1, 2
Suppose -16 = 77*f - 76*f - 2*k, 3*f - 42 = -3*k. Determine h so that -2/5*h + 4/5 - 22/5*h**3 - 6/5*h**f - 22/5*h**2 = 0.
-2, -1, 1/3
Determine r, given that -174*r**4 + 500*r**3 + 134*r**4 - 1008*r + 3*r**5 + 2*r**5 - r**5 - 1024 - 224*r**4 + 784*r**2 = 0.
-1, 2, 64
Suppose -170 = 389*i - 500 - 386 - 451. Factor 15/2*m + 3/4*m**i + 0 + 21/4*m**2.
3*m*(m + 2)*(m + 5)/4
Let -3*p**2 + 135 + 138*p - 734 + 335 = 0. Calculate p.
2, 44
Let q(u) be the first derivative of 2*u**5/15 + 37*u**4/12 + 181*u**3/9 + 82*u**2/3 - 44*u + 6562. Suppose q(i) = 0. What is i?
-11, -6, -2, 1/2
Let g(h) = 23*h + 647. Let j be (-1464)/52 + (-4)/(-26). Let z be g(j). Solve 0*a + 12/5*a**5 - 24/5*a**4 + 0 - 3/5*a**2 + z*a**3 = 0 for a.
0, 1/2, 1
Let 143/2*s**3 + 1995/4*s**2 + s**4 + 9725/8*s + 1000 = 0. What is s?
-64, -5/2
Let n(a) be the second derivative of a**5/25 - 49*a**4/15 - 104*a**3/5 + 4*a + 165. Factor n(s).
4*s*(s - 52)*(s + 3)/5
Let c = -3151843/4 + 787963. Factor -c*b + 0 + 1/4*b**2.
b*(b - 9)/4
Solve -2/11*x + 4/11*x**3 - 644/11 + 1288/11*x**2 - 2/11*x**5 - 644/11*x**4 = 0.
-322, -1, 1
Let o be 1/((-2)/6)*445/(-267). Determine u so that -20 - 28*u**2 + 3*u**2 + 0*u**2 + 40*u + o*u**3 = 0.
1, 2
Let d(s) = -12*s**3 - 404*s**2 + 424*s - 16. Let v(l) = l**3 + l**2 - 3*l + 2. Let b(t) = -d(t) - 8*v(t). Solve b(u) = 0 for u.
-100, 0, 1
Let m(z) be the first derivative of -z**4/7 + 80*z**3/21 + 42*z**2 + 936*z/7 - 1286. Factor m(s).
-4*(s - 26)*(s + 3)**2/7
Suppose -4*f - 28 = -2*d, 3*d = -3*f + 80 + 7. Let t be ((-918)/d)/(-17)*2/3. Let -t + 3/4*w**2 + 3/4*w = 0. Calculate w.
-2, 1
Let t(i) be the third derivative of -i**5/12 + 105*i**4/8 - 305*i**3/3 - 8*i**2 + 3. What is r in t(r) = 0?
2, 61
Let d = 57/14 - -53/42. Let g(s) be the third derivative of -10*s**2 + 0 - 2/3*s**4 - 2/15*s**5 + d*s**3 + 1/30*s**6 + 0*s. Let g(a) = 0. Calculate a.
-2, 2
Let b = -20 + 34. Suppose -5*q = -4*y - b, -4*q = -q + 5*y - 1. Factor -6*m**q - 2 - 27*m**3 - 6 + 28*m**3 + 12*m.
(m - 2)**3
Let g(t) be the second derivative of 4/3*t**3 + 33*t - 2*t**