d p, given that c(p) = 0.
-129, 13
Let k(i) be the second derivative of -2*i**6/15 + 17*i**4/3 + 24*i**3 + 40*i**2 + 935*i. Factor k(m).
-4*(m - 5)*(m + 1)*(m + 2)**2
Let r(y) be the second derivative of -y**9/3780 - y**8/560 + y**6/45 + 5*y**4/12 + 18*y. Let q(l) be the third derivative of r(l). Solve q(t) = 0 for t.
-2, 0, 1
Let y be 13/(-78) - 266/(-12). Suppose -2*j**3 + y*j + 0*j + 5*j**2 - 12 - 13*j**2 = 0. Calculate j.
-6, 1
Let h(g) be the second derivative of 5*g**7/42 + 361*g**6/15 + 6902*g**5/5 + 27932*g**4/3 + 69160*g**3/3 + 19600*g**2 - 294*g. Find t such that h(t) = 0.
-70, -2, -2/5
Suppose 2*b - 77 = 4*a - a, b - 3*a = 43. Let x = -31 + b. Determine m, given that -2*m**4 + 5*m**4 - 6*m - 4*m**3 + 0*m**4 - x*m**2 + 10*m**3 = 0.
-2, -1, 0, 1
Find g, given that 0 - 69/5*g**2 - 3*g**3 + 6*g = 0.
-5, 0, 2/5
Let q(c) = c**3 - 9*c**2 + 22*c - 11. Let o be q(6). Factor -s**3 + 28*s - o + 56*s - 94*s - 11*s**2 + 35*s.
-(s - 1)**2*(s + 13)
Suppose -5/4*s**2 - 15/2*s + 2835/4 = 0. What is s?
-27, 21
Let h be (-2)/(-18) + 10506/459. Suppose -916 = h*u - 985. Factor -3/4*g - 3/4*g**2 - 1/4*g**u - 1/4.
-(g + 1)**3/4
Let z(t) be the second derivative of -t**4/36 - 89*t**3/9 + 181*t**2/2 - 5788*t. Factor z(a).
-(a - 3)*(a + 181)/3
Factor -4/3*n**3 + 1624/3 + 200/3*n**2 + 1828/3*n.
-4*(n - 58)*(n + 1)*(n + 7)/3
Let p(a) be the third derivative of 21*a**2 + 0*a**3 - 1/1260*a**7 + 0*a + 0*a**4 + 1/720*a**6 + 1/180*a**5 + 0. Factor p(k).
-k**2*(k - 2)*(k + 1)/6
Let u(i) = -12*i**3 - 7*i**2 - 16*i - 25. Let n(a) = 2*a**3 + a**2 + 10*a - 1. Let q(d) = 10*n(d) + 2*u(d). Determine p, given that q(p) = 0.
-5, 1, 3
Suppose 0 = -3*l + 3*k, -l - 3*k = -5 - 3. Factor -32*v**5 - l*v**3 - 12*v**2 - 16*v**3 + 9*v + 36*v**4 + 17*v**5.
-3*v*(v - 1)**3*(5*v + 3)
Suppose 0 = 8*y + 231 - 71. Let z be (y/(-8))/((-20)/(-8)) - -1. Solve 7/3*l**z + 3 - 5*l - 1/3*l**3 = 0.
1, 3
Let w(z) be the first derivative of 5*z**3/3 + 25*z**2 + 45*z - 764. Suppose w(x) = 0. Calculate x.
-9, -1
Find y such that -58*y**2 + 48 - 86*y + 53*y**2 + 192 + 76*y = 0.
-8, 6
Let c be (10 - (2 + -1))*-93*(-26)/10881. Factor 4/5*i**c + 0 + 36/5*i.
4*i*(i + 9)/5
Let u(q) be the third derivative of -1/4*q**5 + 1/24*q**6 - 5*q**2 + 0 + 0*q**3 + 5/12*q**4 + 3*q. Find n such that u(n) = 0.
0, 1, 2
Let z(c) be the third derivative of -4/9*c**3 + 17/108*c**4 - 12*c**2 - 1 + 0*c + 1/54*c**5. Factor z(j).
2*(j + 4)*(5*j - 3)/9
Let y be (-53882)/(-203) - 6/14. Let j = y + -1051/4. Factor 0*c**2 - 3/2 - j*c + 3/4*c**3.
3*(c - 2)*(c + 1)**2/4
Suppose 0 = -4*w + 70 - 46. Let u be (-3)/w*0/(-22). Let 2/13*b**4 + u - 8/13*b**3 + 10/13*b**2 - 4/13*b = 0. What is b?
0, 1, 2
Let h(v) be the second derivative of -4*v**4 - 29 - v - 2/15*v**6 - 6*v**2 - 20/3*v**3 - 6/5*v**5. Factor h(t).
-4*(t + 1)**3*(t + 3)
Let w(q) be the first derivative of -q**4/54 + 88*q + 87. Let m(h) be the first derivative of w(h). Determine d so that m(d) = 0.
0
Let n = 28 - 34. Let o(l) = -4*l**4 - 10*l**3 + 72*l**2 - 80*l + 34. Let q(y) = -y**3 - 1. Let h(d) = n*q(d) - o(d). Factor h(w).
4*(w - 1)**3*(w + 7)
Let v be (1 + 33/(-39))/((-300)/(-975)). Factor 0 + 0*j + 3/2*j**2 - v*j**3.
-j**2*(j - 3)/2
Let d(l) = -7*l - 34. Let m be d(-6). Suppose m = -0*h + 4*h. Solve 8*z**2 + 83*z + 23*z**2 - 15*z - 11*z**h + 24 = 0 for z.
-3, -2/5
Let w be (-1 - (56/(-4))/7) + 12/(-16). Let l(v) be the second derivative of 2*v**3 - w*v**4 - 6*v**2 + 21*v + 0. Factor l(k).
-3*(k - 2)**2
Let j be 16/(-6)*3/(-12). Let f = 6461 + -19375/3. Factor -j*x**2 - 10/3*x - f.
-2*(x + 1)*(x + 4)/3
Let a(p) be the first derivative of -p**4/4 - 4*p**3 + 110*p**2 + 2992. Let a(q) = 0. What is q?
-22, 0, 10
Factor 160*a - 1/3*a**3 + 18*a**2 + 992/3.
-(a - 62)*(a + 4)**2/3
Determine k so that 6*k + 14/3*k**5 - 20/3 + 44/3*k**2 - 8*k**4 - 32/3*k**3 = 0.
-1, 5/7, 1, 2
Let c(b) = -3*b**2 - 171*b. Let q be c(0). Let s(d) be the third derivative of 0*d + q + 1/60*d**6 - 7/10*d**5 - 343/3*d**3 + 29*d**2 + 49/4*d**4. Factor s(x).
2*(x - 7)**3
Let a(o) be the second derivative of -95/2*o**2 + 185/6*o**3 + 0 + 35*o - 85/12*o**4 - 1/4*o**5. Factor a(l).
-5*(l - 1)**2*(l + 19)
Let o(h) = -168*h**2 - 1144*h - 252. Let u(v) = -56*v**2 - 380*v - 84. Let n(p) = 6*o(p) - 17*u(p). Determine f so that n(f) = 0.
-7, -3/14
Let i be 1452/308 - ((-9)/(-45) + 28/10). Factor -3/7*y**4 - 3/7 - i*y**3 - 18/7*y**2 - 12/7*y.
-3*(y + 1)**4/7
Suppose 18 = -6*p + 192. Suppose -p = -3*l - 4*r, 2*r - 4 = l - 27. Factor 3*w**2 + w**2 + w**2 - l*w**4 + w**3 + 9*w**3.
-5*w**2*(w - 1)*(3*w + 1)
Suppose 0 = -10*y - 16 - 14. Let x be (-58)/(-51) - (-2)/y. Determine c so that -2/17*c**2 - 6/17 + x*c = 0.
1, 3
Let r = -582 + 585. Factor 15*z**2 + 14*z - 72*z**2 - 2*z**5 + 17*z**2 + 36*z**3 + 3*z**5 - 8*z**4 - r*z**5.
-2*z*(z - 1)**3*(z + 7)
Let w be -3635*(26/(-40) - (-1)/4). Let z = w + -1452. Let -5/2*p**4 + 0 + 50*p**3 + 0*p - 250*p**z = 0. What is p?
0, 10
Let y(g) be the second derivative of -g**6/4 + 12*g**5/5 - 57*g**4/8 + 19*g**3/2 - 6*g**2 + 64*g - 5. Let y(t) = 0. Calculate t.
2/5, 1, 4
Let t(n) = 18*n**3 + 323*n**2 + 2779*n - 611. Let w(b) = 7*b**3 + 129*b**2 + 1112*b - 235. Let j(d) = -5*t(d) + 13*w(d). Factor j(v).
v*(v + 11)*(v + 51)
Let g(o) be the third derivative of -o**6/900 + o**5/60 + o**4/10 + 137*o**3/6 - 89*o**2. Let t(s) be the first derivative of g(s). Factor t(v).
-2*(v - 6)*(v + 1)/5
Let c(k) = 3*k**4 - 171*k**3 - 3*k**2 + 171*k. Let d(h) = -5*h**4 + 170*h**3 + 5*h**2 - 170*h. Let n(x) = 4*c(x) + 3*d(x). Factor n(z).
-3*z*(z - 1)*(z + 1)*(z + 58)
Let m = 129 + -100. Factor -911*a**4 + 18*a**4 - 504*a**2 + m*a**4 + 1296*a**3 - 2 + 76*a - 2.
-4*(a - 1)*(6*a - 1)**3
Let m = -6755 - -6757. Let c be (3/(-2))/(3/(-8)). Factor -2*t**4 + c*t + t**3 - t**m + 3*t**2 - 5*t**3.
-2*t*(t - 1)*(t + 1)*(t + 2)
Suppose -2*a - t - 28 = t, a + 5*t = -18. Let c = a + 71. Factor c - 32 - 26 - j**2 + 2*j.
-j*(j - 2)
Let i(y) be the second derivative of -3*y**5/40 + 107*y**4/4 + 215*y**3/4 + 3*y - 3924. Suppose i(m) = 0. What is m?
-1, 0, 215
Let w(t) = -2*t**3 + t**2 + t + 2. Let a(v) = -3*v**3 + 508*v**2 - 64514*v + 64011. Let y(z) = a(z) - w(z). Factor y(g).
-(g - 253)**2*(g - 1)
Find v such that 0*v - 148*v + 21*v**3 + 15*v**3 - 144*v**2 - 32*v**3 = 0.
-1, 0, 37
Suppose -40*g - 84 = -42*g. Solve 26*z**2 + 245 + 12*z**3 + g*z + 43*z**2 - 260 = 0.
-5, -1, 1/4
Let a be (30/96)/((-240)/(-576)). Let u(f) be the first derivative of 1/8*f**2 - 1/16*f**4 - 1/4*f**3 + a*f + 5. Factor u(b).
-(b - 1)*(b + 1)*(b + 3)/4
Let n(i) = -3*i**4 - i**2 - i - 1. Let r(k) = 39*k**4 - 168*k**3 - 165*k**2 + 354*k + 12. Let u(c) = -12*n(c) - r(c). Let u(v) = 0. Calculate v.
-2, 0, 1, 57
Let z = 56 - 49. Let i(w) = -w**3 + 5*w**2 + 16*w - 7. Let o be i(z). Find f such that -64*f - 3*f**4 - 2*f**5 + 66*f - 4*f**2 + o*f**4 = 0.
-1, 0, 1
Let u(k) be the second derivative of 5*k**4/12 - 135*k**3/2 + 200*k**2 - 3*k - 18. Factor u(z).
5*(z - 80)*(z - 1)
Factor 0 + 1/4*d**3 - 65/4*d**2 + 16*d.
d*(d - 64)*(d - 1)/4
Let f be (-96)/18 + ((-280)/700)/(3/(-60)). Determine r so that -16/3 + 28/3*r - f*r**2 - 4/3*r**3 = 0.
-4, 1
Factor -45*n + 7172*n**2 - 50*n - 7415*n**2 - 51*n**3 - 3*n**4 - 94*n + 6*n**4.
3*n*(n - 21)*(n + 1)*(n + 3)
Let o be 0/((-10)/4*70/(-175)). Let d(t) be the first derivative of 7 - 3/25*t**5 + 0*t - 1/20*t**4 + 2/15*t**3 + o*t**2. Factor d(j).
-j**2*(j + 1)*(3*j - 2)/5
Let w(m) be the first derivative of -3/2*m**4 + 122 - 300*m - 41*m**3 - 330*m**2. Factor w(j).
-3*(j + 10)**2*(2*j + 1)
Factor -350*j**2 - 1416 - 8875*j**3 + 1254*j + 349*j + 8874*j**3 - 191*j.
-(j - 2)**2*(j + 354)
Let d = -109 - -113. Let -12*t + 9 - 57 + 204*t - 797*t**3 - 72*t**2 + 557*t**3 - 75*t**d = 0. What is t?
-2, 2/5
Let c be 92/66*-9 + (4 - -2). Let b = -111/22 - c. Factor -b*f**2 - 15/2*f + 0.
-3*f*(f + 5)/2
Let s(d) = -5*d**2 - 80*d - 487. Let q(z) = -4*z**2 - 84*z - 479. Let n(r) = 4*q(r) - 3*s(r). Factor n(w).
-(w + 5)*(w + 91)
Let o(m) = -32*m**2 + 7972*m - 187. Let x(r) = 11*r**2 - 2656*r + 66. Let d(l) = -6*o(l) - 17*x(l). Factor d(y).
5*y*(y - 536)
Let j(a) be the second derivative of a**7/189 + a**6/135 - 19*a**5/45 + 17*a**4/27 + 37*a**3/27 - 35*a**2/9 + 463*a - 2. Find n, given that j(n) = 0.
-7, -1, 1, 5
Let w be (9/(-18))/