1)/4
Let q = 361/996 + 193/498. Find j such that 15/2 - q*j**3 - 63/4*j + 9*j**2 = 0.
1, 10
Let f(z) = 23*z**4 - 1215*z**3 + 1230*z**2 + 2432*z + 8. Let x(v) = -7*v**4 + 2*v - 2. Let k(j) = f(j) + 4*x(j). Factor k(c).
-5*c*(c - 2)*(c + 1)*(c + 244)
Let y(x) be the second derivative of -3/2*x**3 + 36*x + 0 - x**2 + 57/80*x**5 + 11/60*x**6 - 1/8*x**7 - 7/24*x**4. Determine j so that y(j) = 0.
-1, -2/3, -2/7, 1, 2
Factor -10*j + 5741*j**3 - 32*j**2 - 10*j - 5745*j**3 + 56.
-4*(j - 1)*(j + 2)*(j + 7)
Suppose 4*b - 36 = -4*i, -4*i + i = b - 33. Suppose 2*a = 4*g, -3*a + 20 - 12 = -2*g. Factor -3*n**g + i*n - 1 + 0*n**2 - 8*n + 0*n**2.
-(n - 1)*(3*n - 1)
Let k(s) be the first derivative of 9*s**5/140 - 25*s**4/28 - 53*s**3/42 - 9*s**2/14 + 75*s + 143. Let u(c) be the first derivative of k(c). Factor u(q).
(q - 9)*(3*q + 1)**2/7
Let j = 426 - 423. Let u(g) be the first derivative of 0*g - 7/12*g**4 + 0*g**2 - 4/15*g**5 + 12 - 1/3*g**j. Solve u(o) = 0.
-1, -3/4, 0
Let q be ((8/6)/(768/1152))/(0 - 6/(-9)). Factor 80/13*u**2 - 2/13*u**q - 874/13*u + 1444/13.
-2*(u - 19)**2*(u - 2)/13
Let t(b) be the second derivative of b**6/45 + 71*b**5/5 + 45793*b**4/18 + 30104*b**3/3 + 44944*b**2/3 + 743*b. Factor t(l).
2*(l + 1)**2*(l + 212)**2/3
Solve 4*v**3 + 0 - 352/3*v**2 + 28/3*v**4 + 448/3*v - 1/3*v**5 = 0.
-4, 0, 2, 28
Suppose -94*u + 592 = -78*u. Let -33*o - 2*o - 38 + 2*o**2 - 40*o - 2 - u*o**2 = 0. What is o?
-8/7, -1
Let q be (1/45 - 6*(-6)/(-162))/((-4)/430). Factor -29/4 + q*v + 1/4*v**4 + 13/2*v**3 - 21*v**2.
(v - 1)**3*(v + 29)/4
Let w be (-38 - (-3115)/70)/13. What is q in -w*q**2 + 2 + 3/2*q = 0?
-1, 4
Let o be -6*(-8 + 5 - -1). Find u, given that 0*u**4 - 4 + 30*u + o - 9*u**4 - 30*u**3 + 1 = 0.
-3, -1, -1/3, 1
Let g(f) be the first derivative of 0*f - 8*f**2 + 312 + 4/3*f**3. Determine l, given that g(l) = 0.
0, 4
Let a(t) be the second derivative of -130/3*t**4 - 215/2*t**3 - 4*t**5 - 225/2*t**2 + 72*t + 0. Factor a(w).
-5*(w + 5)*(4*w + 3)**2
Let t(k) be the third derivative of 5*k**9/2016 - 3*k**8/448 + 3*k**7/560 + 8*k**4/3 + 76*k**2. Let y(m) be the second derivative of t(m). Factor y(i).
3*i**2*(5*i - 3)**2/2
Suppose 376 = 42557*v - 42463*v. Find t, given that -2/3*t**3 + 74/3*t - 20 - v*t**2 = 0.
-10, 1, 3
Let w = 26726 - 26723. Let q(r) be the second derivative of 45*r + 0 + 1/4*r**w + 0*r**2 + 1/24*r**4. Let q(j) = 0. What is j?
-3, 0
Let u = -41 + 45. Suppose -u*i - 3 + 19 = 0. Solve -21*w**5 - 5*w**3 + 0*w**5 - 63*w**i - 25*w**3 - 6*w**5 + 18*w**2 + 9*w - 3 = 0.
-1, 1/3
Let a(l) = -3*l**3 + 63*l**2 + 363*l + 360. Let j(v) = 3*v**3 - 60*v**2 - 366*v - 360. Let k(p) = -6*a(p) - 5*j(p). Suppose k(h) = 0. Calculate h.
-2, 30
Let k(a) be the second derivative of a**4/30 + 109*a**3/15 - 222*a**2/5 - 14*a + 84. Factor k(w).
2*(w - 2)*(w + 111)/5
Let o(t) be the second derivative of -t**7/14 + 4*t**6/5 + 3*t**5/2 - 2*t**4 - 9*t**3/2 + 278*t. Solve o(l) = 0 for l.
-1, 0, 1, 9
Let z = 376 + 324. Suppose -9*b = -14*b + z. Factor -71 - 9*q**4 + 3*q**5 - 3*q**2 - 69 + b + 9*q**3.
3*q**2*(q - 1)**3
Suppose -1/6*k**4 - 13/3*k**3 + 12*k + 360 - 59/2*k**2 = 0. Calculate k.
-12, -5, 3
Suppose 15 = c + 11. What is q in 4026*q**3 + q**2 - c - 3996*q**3 + 3*q**4 - 34*q**2 + 4 = 0?
-11, 0, 1
Let h be (-33 + 2871/58)/3. Let 2/3 - 31/6*o**2 + 0*o - 7/6*o**5 - 53/6*o**3 - h*o**4 = 0. What is o?
-2, -1, 2/7
Let v be (-1455)/(-4074)*24/5. Let l be 5/55 + (-2)/22. Let 8/7 + l*r**2 - v*r + 4/7*r**3 = 0. What is r?
-2, 1
Let b = 1851 + -1844. Let t(z) be the second derivative of -1/9*z**6 + 0 - 1/5*z**5 + 7/9*z**3 + 1/9*z**4 + z**2 - 17*z - 1/63*z**b. What is g in t(g) = 0?
-3, -1, 1
Let h(s) be the second derivative of -s**7/2520 + s**6/720 + s**5/60 - 5*s**4/4 - 8*s - 4. Let k(f) be the third derivative of h(f). Let k(v) = 0. What is v?
-1, 2
Factor -290/3 + 1/3*r**2 - 143/3*r.
(r - 145)*(r + 2)/3
Determine r so that -2/11*r**4 + 0 + 20164/11*r + 288/11*r**3 - 10650/11*r**2 = 0.
0, 2, 71
Let v(z) be the second derivative of -17*z**5/100 - 11*z**4/12 + 8*z**3/5 + 18*z**2 - 805*z + 1. Determine y so that v(y) = 0.
-3, -2, 30/17
Let o(w) be the first derivative of 11*w**6/3 - 148*w**5/35 - 225*w**4/14 + 100*w**3/21 + 148*w**2/7 + 48*w/7 - 4977. Suppose o(y) = 0. What is y?
-1, -6/7, -2/11, 1, 2
Let l = 7194 - 3629. Let a = l + -6983/2. Suppose -84*b**2 - 24*b + 84*b**4 - 99/2*b**3 + 0 + a*b**5 = 0. What is b?
-1, -4/7, 0, 1
Suppose 4*i = -2*i + 180. Suppose 0 = -i*m + 33*m - 24. Solve 20*u**2 - m*u**3 + 10*u**3 + 3*u**3 - 20 - 5*u = 0.
-4, -1, 1
Determine w, given that 3446/3*w**2 + 1176 - 41/3*w**3 - 24164*w = 0.
2/41, 42
Let t(b) be the second derivative of -3*b**2 + 25/12*b**3 + 166 - 1/12*b**4 - b. Let t(r) = 0. What is r?
1/2, 12
Let a = 15 + -10. Suppose 0 = 2*m - 582 + 576. Find z such that -z**m + 5*z**2 - 5*z**3 + 30*z - 4*z**3 - 20*z - a*z**4 = 0.
-2, -1, 0, 1
Factor -6*m**2 + 6*m - m - 177486*m**3 - m + 177488*m**3.
2*m*(m - 2)*(m - 1)
Let p(y) = y**4 - y**3 - 3*y**2 + y - 2. Let i(x) = x**4 - 3*x**3 - 5*x**2 + 3*x - 1. Let h(a) = 4*i(a) - 5*p(a). Factor h(d).
-(d - 1)*(d + 1)**2*(d + 6)
Let r be (-12)/(-21)*(-287)/(-328)*4*1. Find q, given that 0*q**4 - 2*q + 9/2*q**r - 11/4*q**3 + 0 + 1/4*q**5 = 0.
-4, 0, 1, 2
Let i = -159 - -114. Let g = i + 49. Find n, given that 14580*n - 32805 - 35*n**4 + 14*n**4 - 2430*n**2 + 180*n**3 + 8*n**4 + 8*n**g = 0.
9
Let m be 12/15*(188/8 - 16). Let o(q) be the second derivative of 5*q - 7/10*q**m - 51/16*q**4 + 17/8*q**3 + 0 - 3/4*q**2 + 12/5*q**5. Solve o(n) = 0 for n.
2/7, 1/2, 1
Find f, given that 1/7*f**2 - 296/7*f + 21904/7 = 0.
148
Let r(t) = 8*t**3 + 17*t**2 - 99*t - 3. Let m(n) = 7*n**3 + 18*n**2 - 101*n - 2. Let k(j) = -3*m(j) + 2*r(j). Solve k(c) = 0 for c.
-7, 0, 3
Let t(d) = -3. Let v(x) = -14. Let b(a) = 5*t(a) - v(a). Let y(c) = -5*c**2 - 3 - 3*c**4 + 0*c**4 + 8*c**2. Let r(l) = -3*b(l) + y(l). Factor r(n).
-3*n**2*(n - 1)*(n + 1)
Let r(o) = -o - 6. Let g(q) = 5*q**2 - 425*q + 11850. Let d(s) = g(s) + 55*r(s). Determine z, given that d(z) = 0.
48
Let -27*r + 3/2*r**2 - 189/2 = 0. What is r?
-3, 21
What is v in -3146 + 768*v - 40893*v**2 + 40897*v**2 + 10 = 0?
-196, 4
Let q(h) = -53*h**2 + 466*h + 144. Let s be q(9). Solve 18*o**2 + 3*o**3 + s*o + 81/2 + 1/6*o**4 = 0.
-9, -3
Let d(n) = 19*n - 13*n**2 - 34*n + 1 + 5*n**3 + 25*n**2. Let b(p) = 7*p**3 + 13*p**2 - 15*p - 1. Let m(v) = -3*b(v) + 4*d(v). Solve m(i) = 0.
1, 7
Let p = 224/93 + 8/31. Let b = -62269 - -62271. Find v, given that 0*v + p*v**b + 0 + 14*v**4 + 40/3*v**3 = 0.
-2/3, -2/7, 0
Let q(f) = 31 - 34*f - 34*f + 64*f. Let b be q(7). Find i such that -11*i**2 - i**b + i**2 + 4*i + 2*i + 9*i**2 = 0.
-3, 0, 2
Let n = 61177/2603 + -3191/137. Solve 0*t**3 + 0*t - 2/19 - 2/19*t**4 + n*t**2 = 0 for t.
-1, 1
Let m(v) = 4*v**2 + 48 + v**2 - 2*v**2 - 9*v**2 + 3*v. Let j(q) = 11*q**2 - 7*q - 95. Let l(a) = 3*j(a) + 5*m(a). Factor l(d).
3*(d - 5)*(d + 3)
Let w(f) be the first derivative of 35*f**4/4 + 190*f**3 - 1320*f**2 - 800*f - 296. Solve w(m) = 0.
-20, -2/7, 4
Let 1/4*p**2 - 99/4 + 49/2*p = 0. What is p?
-99, 1
Let q = -2 - -1. Let u be (q + 0)/((-7)/5761*1). Determine t so that -3 + 3042*t**2 + 26364*t**3 + u*t + 85683*t**4 - 667*t + 6 = 0.
-1/13
Let u be 35/350*(1949/(-3) + 1). Let o = -321/5 - u. Factor -8/9 - o*y + 2/9*y**2.
2*(y - 4)*(y + 1)/9
Let l be (-52)/(-572)*(-462)/(-56). Let -9/4*y**2 - 3/4*y**3 + 3/2 + 3/4*y**4 + l*y = 0. Calculate y.
-1, 1, 2
Let o(s) be the third derivative of -s**5/360 - 13*s**4/36 + 97*s**2 - 3*s. Factor o(z).
-z*(z + 52)/6
Let p be 2 - 0 - (9 - 9). Let z be (-2)/3*-3*327/436. Factor z*q**p + 11/4*q**4 - 1/4*q + 7/2*q**3 + 3/4*q**5 - 1/4.
(q + 1)**4*(3*q - 1)/4
Let u = 300 + 9. Let q = u - 305. Factor 16*k**2 + 8/3 + 40/3*k + 7/6*k**q + 22/3*k**3.
(k + 2)**3*(7*k + 2)/6
Let g be -3*2/3 - (-1 - 4). Factor -4*k**5 + k**3 + 20*k**2 + 9*k**5 - 20*k**4 - 4*k**g - 2*k**3.
5*k**2*(k - 4)*(k - 1)*(k + 1)
Let v(t) be the first derivative of -t**5/96 + t**4/12 - t**3/16 - 58*t**2 - 115. Let h(b) be the second derivative of v(b). Factor h(z).
-(z - 3)*(5*z - 1)/8
Let l(f) be the first derivative of f**3 - 1893*f**2/2 - 1896*f - 4017. Solve l(u) = 0 for u.
-1, 632
Let h(o) be the third derivative of -1/330*o**5 + 15*o**2 - 1/44*o*